Model Rationale

Microsimulation is well established as a computational platform for tobacco control policy appraisal, with the Sheffield Tobacco and Alcohol Policy Model (STAPM) being used to inform policy making in a UK context [gillespie23], including the previous UK Government's plan to reduce smoking prevalence to 5% by 2030 [dhsc2023]. In microsimulations, agents transition between smoking states according to probabilities derived from historical data; the impact of a policy is then modelled as an adjustment to these probabilities. For price-based policies, empirical evidence on tobacco price elasticities inform the adjustments. However, for other major policies (such as mass media campaigns to encourage smoking cessation, and investment in the provision of services to support cessation attempts), the evidence to inform the adjustments is very limited and often not specific to the policy jurisdiction.

In the absence of evidence of direct policy effects on transition probabilities, we can instead seek to estimate these effects indirectly using theories or frameworks that synthesise empirical evidence on the psychological and social factors that influence smoking behaviours. Policies are then modelled in terms of transparent explainable effects on psychosocial factors rather than unsupported assumptions about transition probability adjustments. Agent-based modelling (ABM) is useful in this context since it enables: (a) psychosocial theory to be formalised explicitly in terms of agents' action and interaction processes; (b) population heterogeneity in psychosocial factors to be represented in terms of agents' attributes; (c) transition probabilities to become emergent outcomes of a generative policy process.

The SimCOM ABM described in this ODD protocol is based on the COM-B conceptual model of behaviour change [michie11]. COM-B describes how an individual's capabilities (C), opportunities (O) and motivations (M) influence behaviour (B). COM-B is a coherent framework for organising the factors that influence an individual to make and maintain an attempt to quit smoking [west13], and has been widely used in this context [gilbert23,fulton16,steed17,shoesmith22]. A further benefit of using COM-B is that rich evidence is available from the Smoking Toolkit Study for SimCOM's policy jurisduction---England---to inform both population heterogeneity in capabilities, opportunities and motivations, and how these factors combine to shape behaviour [fidler11].

Overview (O)

Purpose and Patterns

Purpose

SimCOM is a policy model. Its purpose is to appraise the impact of prospective tobacco control policies on smoking cessation rates in England. SimCOM aims to be both explanatory and predictive in the sense that policy impacts are: (i) represented in terms of a mechanism-based logic model of behaviour change that is familiar to policymakers and practitioners; and (ii) quantified using projections informed by evidence that is specific to the policy jurisdiction.

SimCOM is designed for integration with the existing STAPM microsimulation. SimCOM's estimates of the quit rates arising from a policy are used as inputs to STAPM, which then estimates the health and health economic outcomes of the policy.

Patterns

[List the key qualitative or quantitative patterns (observations, phenomena, or expected relationships) from the real-world system or from theory that the model is designed to reproduce, explain, or explore. These patterns are essential for model evaluation (see Section [ref]

Pattern 1 (Individual-level): [e.g., Agents exhibit memory-based movement bias.]
Pattern 2 (System-level): [e.g., Population size shows non-linear collapse above a critical resource threshold.]

Entities, State Variables, and Scales

SimCOM has been constructed using the mechanism-based social systems modelling (MBSSM) architecture [vu2020software]. MBSSM abstracts entities at either the macro-level or micro-level, where only the micro-level entities possess agency (where, in the form of action mechanisms, the future behaviour of a micro-level entity is generated from its present state. Following [hedstrom96], the dynamic relationship between macro-level and micro-level entities is represented using situational mechanisms (where the future state of a micro-level entity is a generated from its present state and the present states of macro-level entities) and transformational mechanisms (where the future state of a macro-level entity is generated from its present state and the present behaviour of micro-level entities).

The model has been designed using object-oriented principles [tian2024incorporating] and is implemented in Repast4Py [collier2022distributed].

Entities and State Variables

The entities in the model are: (1) individual humans (i.e. the agents); (2) the environment within which the individuals reside; (3) the emotional support network in which the individuals are embedded; (4) a population-level e-cigarette diffusion process; and (5) healthcare services as an institution.

Individual: The model includes a synthetic population of agents. All state variables relating to COM-B are drawn from the Behaviour Change Intervention Ontology (BCIO), which provides formal definitions for entities and their relationships in the behavioural sciences. The full set of state variables for an individual is shown in Table [ref]. These variables are explained in more detail below:
- Activation state: All agent entities exist for the entire duration of the simulation but they are only active once they reach the age of 16 and are deactivated upon death. This state variable, isActive, is needed for management of the synthetic network.
- Smoking state: The smoking status of the individual is represented at the current model tick, k, is represented by the state variable:
  bState[k] ∈ {0 never smoker,1 smoker,2 new quitter,3 ongoing quitter,4 ex-smoker}.
  These states are defined in Table [ref].
- Behaviours: The model includes two behaviours that are enacted every tick, conditional on an individual's current smoking state. These behaviours are governed by COM-B mechanisms. Agents with smoking state smoker have an opportunity to make a new quit attempt, bQuitAttempt[k]={0 no,1 yes}. Agents with smoking state new quitter or ongoing quitter have an opportunity to maintain an ongoing quit attempt, bQuitMaintain[k]={0 no,1 yes}. After 12 consecutive successes at maintaining a quit attempt, an individual transitions to smoking state ex-smoker. Individuals in smoking states never smoker and ex-smoker may also transition to new states, but these transitions are not related to COM-B mechanisms. The full state-transition diagram is shown in Figure [ref]. Behaviours are enacted probabilistically, based on dispositions lbQuitAttempt[k] and lbQuitMaintain[k].
- Capabilities, opportunities and motivations: Each behaviour is influenced by a respective capability, opportunity and motivation, which are conceptualised as latent composite variables, lcQuitBehave[k], loQuitBehave[k], and lmQuitBehave[k], where Behave is either Attempt or Maintain depending on the behaviour. Each latent composite variable is itself an aggregation of multiple lower level capability, opportunity and motivation components, where the state variables are prefixed by c, o and m respectively. Columns 3 and 4 in Table [ref] indicate which of these components are used for each behaviour.
- Personal attributes: Individuals also have a number of personal attributes that influence the dynamics of the model or are used for reporting purposes. The most important of these are gender pGender ∈ {0 male,1 female}, age pAge[k] ∈ {16,…,89} and deprivation level pIMDQuintile ∈ {1,…,5}. Deprivation levels relate to quintiles of the Index of Multiple Deprivation, where 1 is the most deprived and 5 is the least deprived. Some personal attributes are also translated to components of COM-B, e.g. age is also a capability, cAge[k]---but where the coding is categorical rather than integer.
Environment: Individuals reside in an environment that aims to represent the jurisdiction of England from 1 January 2011 to 1 January 2031. The environment is a very basic entity that acts as a container for the agents, manages the active and inactive population, and acts as a conduit for exogenous inputs. The state variables are:
- Tick counter: The current month since initialisation is denoted by k ∈ ℕ₀
- Population container: The set of all agents in the model (both active and inactive), 𝒫
- Population counts: The population size is maintained at sub-group level, N[k]_γ,α,δ ∈ ℕ, where γ, α and δ partition the population by sex, age group, and deprivation level.
- Annual quit attempts: The number of agents who have made at least one quit attempt in the past 12 months, Q_A[k]_γ,α,δ ∈ ℕ₀
- Annual quit successes: The number of agents who have successfully quit smoking (i.e. maintained a quit attempt for 12 months), Q_S[k]_γ,α,δ ∈ ℕ₀
- Regional smoking prevalence: Since the model is only representative of the population of England as a whole, regional smoking prevalence is not directly an aggregation across agents, but is rather represented separately as S[k]_ρ ∈ [0,1], where ρ ∈ {1 North East,2 North West, 3 Yorkshire and the Humber,4 East Midlands,5 West Midlands,6 East of England, 7 London,8 South East,9 South West} are government office regions of England.
Network: Individuals interact with their close social connections. The network is static over the course of the simulation and is defined by an adjacency matrix state variable, A, containing directed edges a_j,i ∈ {0 no,1 yes } that define whether agent i perceives a close social connection with agent j. For further details on the network, see Section [ref].
E-cigarette Diffusion Process: Since the focus of the model is smoking, we have not developed individual-level mechanisms for e-cigarette use. However, e-cigarette use is an important predictor of smoking cessation. For this reason, the model includes an e-cigarette diffusion process as a specific entity with three vector state variables:
- E-cigarette prevalence: The current e-cigarette prevalence in the population is defined as E[k]_γ,α,σ ∈ [0,1], where γ, α and σ partition the diffusion process by sex, age group, and smoking status.
- Population size of partitions: The current potential number of e-cigarette users in each diffusion sub-group, N[k]_γ,α,σ ∈ ℕ
- Change in e-cigarette prevalence: The change in the number of individuals using e-cigarettes to be applied within a population sub-group at the current tick is defined as Δ E[k]_γ,α,σ ∈ ℕ.
For further details of the e-cigarette diffusion process, refer to Section [ref].
Healthcare services: Healthcare services are represented using a single entity that captures the prevalence of healthcare service use in the population. The state variables relate to different aspects of service provision:
- Mass media campaign expenditure
- Stop smoking services expenditure
- Provision of family doctor advice

All state variables in the model are drawn from the Behaviour Change Intervention Ontology (BCIO), which provides formal definitions for entities and their relationships in the behavioural sciences. The full set of state variables for an individual are shown in Table [ref].

The smoking states of an agent.

States	Description
never-smoker	a person who has never progressed to established smoking
smoker	a person with an established smoking behaviour
new quitter	a person who began a quit attempt at the start of the previous month
ongoing quitter	a person who has successfully maintained smoking abstinence for at least
	one month and for less than a year
ex-smoker	a person who last smoked more than a year ago

[Figure: Possible state transitions for an individual at a tick k. In the ongoing quitter tunnel state, the number of fully completed months of maintained abstinence is indicated by i. Note that the new quitter state, indicated by the broken lines, is a temporary state at tick k, with the transition to either smoker or ongoing quitter occurring within the same tick.]

State variables of an agent

Variable Name	Ontology IRI	Dynamic	Attempt	Maintain	STS Variable	Measure	Type and values
Variable Name	Ontology IRI	Dynamic	Attempt	Maintain	STS Variable	Measure	Type and values
`agentID`		`×`				Individual unique identifier	1-10,000; 25,842
`arrivalYear`		`×`				Integer calendar year	2011 to 2100
`bCigConsumption`	r: HSO:0000067 e: ADDICTO:0000690	`×`			basecpd3	Avg cigarettes per day	0.003 - 78.413
`bMonthsSinceQuit`					q632b8	Months since quitting	0 - 11
`bNumberOfRecentQuitAttempts`					q632b7\_1	Count of recent attempts	0 - 7
`bState`					smokstat	Smoking status	0 - 4
`bState23`		`×`				2023 status pattern	0, 1
`bYearsSinceQuit`					yearsquit	Years since quitting	1 - 77
`bQuitAttempt`			●			Quit attempt behaviour	Binary, `0=no,1=yes`
`bQuitMaintain`				●		Quit maintenance behaviour	Binary, `0=no,1=yes`
`lbQuitAttempt`			●			Log-odds of making a quit attempt	`(- ∈ f,+ ∈ f)`
`lbQuitMaintain`				●		Log-odds of maintaining a quit attempt	`(- ∈ f,+ ∈ f)`
`lcQuitAttempt`			●			Latent composite capability for making a quit attempt	Log-odds utility, `(- ∈ f,+ ∈ f)`
`loQuitAttempt`			●			Latent composite opportunity for making a quit attempt	Log-odds utility, `(- ∈ f,+ ∈ f)`
`lmQuitAttempt`			●			Latent composite motivation for making a quit attempt	Log-odds utility, `(- ∈ f,+ ∈ f)`
`lcQuitMaintain`				●		Latent composite capability for maintaining a quit attempt	Log-odds utility, `(- ∈ f,+ ∈ f)`
`loQuitMaintain`				●		Latent composite opportunity for maintaining a quit attempt	Log-odds utility, `(- ∈ f,+ ∈ f)`
`lmQuitMaintain`				●		Latent composite motivation for maintaining a quit attempt	Log-odds utility, `(- ∈ f,+ ∈ f)`
`cAge`	r: HSO:0000067 e: ADDICTO:0001370			●	actage	Categorical age with indicator variable coding	`cAgeGroup30To44 ∈ {0,1}` `cAgeGroup45To64 ∈ {0,1}` `cAgeGroup65plus ∈ {0,1}`
`cAlcoholConsumption`	r: HSO:0000067 e: ADDICTO:0001395	`×`		●	auditc	Categorical alcohol consumption with indicator variable coding	`cAlcoholConsumptionGroupLowerRisk` `∈ {0,1}` `cAlcoholConsumptionGroupIncreasingRisk` `∈ {0,1}` `cAlcoholConsumptionGroupHigherRisk` `∈ {0,1}`
`cCigAddictStrength`	r: RO:0000091 e: ADDICTO:0001339			●	sturge	Strength of tobacco urges	0 - 5
`cCigConsumption`	r: HSO:0000067 e: ADDICTO:0000690	`×`		●	basecpd3	Avg cigarettes per day	0.003 - 78.413
`cCytisineUse`				●	@q632b1q	1 = Used cytisine	0, 1
`cECigUse`	r: RO:0000056 e: ADDICTO:0001125			●	allecig	1 = uses EC	0, 1
`cEducationalLevel`	r: RO:0000053 e: BCIO:015043	`×`		●	qual	Education level (1-3)	1 - 3
`cMentalHealthCondition`	r: RO:0000053 e: ADDICTO:0001394	`×`		●	sy012	Mental health indicator	0, 1
`cPrescriptionNRT`	r: RO:0000056 e: ADDICTO:0001338			●	allnrt	1 = prescription NRT	0, 1
`cUseOfBehaviouralSupport`	r: RO:0000056 e: ADDICTO:0001341			●	behc	1 = Behavioural support	0, 1
`cVareniclineUse`	r: RO:0000056 e: ADDICTO:0001340			●	chac	1 = Used Champix	0, 1
`mAge`	r: HSO:0000067 e: ADDICTO:0001370			●	actage	Categorical age with indicator variable coding	`mAgeGroup30To44 ∈ {0,1}` `mAgeGroup45To64 ∈ {0,1}` `mAgeGroup65plus ∈ {0,1}`
`mEnjoymentOfSmoking`	r: RO:0000091 e: ADDICTO:0001327	`×`	●		qfac1	0 = No; 1 = Yes	0, 1
`mExpenditure`	r: HSO:0000067 e: ADDICTO:0001343	`×`	●		qspend\_1	Weekly tobacco spend	1 - 500
`mIntentionToQuit`	r: RO:0000091 e: ADDICTO:0001414	`×`	●		qmotiv	Intention (0-6)	0 - 6
`mNonSmokerSelfIdentity`	r: RO:0000091 e: ADDICTO:0000714			●	q632e9	1 = Non-smoker identity	0, 1
`mNumberOfRecentQuitAttempts`	r: HSO:0000067 e: ADDICTO:0001333		●		q632b7\_1	Count of recent attempts	0 - 7
`mPositiveSmokerIdentity`	r: RO:0000091 e: ADDICTO:0000392	`×`	●		qfac9	1 = Like being a smoker	0, 1
`mSelfEfficacy`	r: RO:0000091 e: BCIO:006043	`×`	●		@qfeel20	1 = Confident to stop	0, 1
`mUseOfNRT`	r: RO:0000056 e: ADDICTO:0001338		●		allnrt	1 = uses NRT	0, 1
`oNumberOfSmokersInSocialNetwork`	r: RO:0000053 e: ADDICTO:0001369		●	●	@qimw891	Smoker count in network	0 - 7
`oReceiptGPAdvice`	r: RO:0000056 e: ADDICTO:0000464	`×`	●		@q632x4a1	1 = Received GP advice	0, 1
`oSEP`	r: RO:0000053 e: ADDICTO:0001324	`×`		●	sgz	Social grade category	0, 1
`oSocialHousing`	r: RO:0000053 e: ADDICTO:0001402	`×`	●	●	tenure	1 = Social housing rent	0, 1
`pAge`	r: HSO:0000067 e: ADDICTO:0001370				actage	Integer age (years)	16 - 89
`pAlcoholConsumption`	r: HSO:0000067 e: ADDICTO:0001395	`×`			auditc	Alcohol indicator (0-3)	0 - 3
`pIMDquintile`	r: RO:0000053 e: ADDICTO:0001324	`×`				Deprivation quintile	1 - 5
`pRegion`	r: RO:0001025 e: ADDICTO:0001325	`×`			gore	Region indicator (1-9)	1 - 9

Scales

Spatial Scale: The agent population aims to be representative of adults aged 16-80 in England in terms of sex, age and deprivation socio-demographics. There are initially 10,000 individuals in the model, with additional individuals added on a yearly basis to account for trends in fertility. Mortality is included in the model, but migration flows are not represented.
Temporal Scale: Each model tick is representative of one month. The model is initialised in January 2011 and runs until January 2031 inclusive (2030 is the year corresponding to the UK Government's `smokefree' target, which is considered to be achieved when adult smoking prevalence falls to 5% or less). Each model tick represents the first day of each month, with the between-tick dynamics representing processes occurring during the calendar month.

Process Overview and Scheduling

Initialization

Model tick k=0 corresponds to 1 January 2011. The model is initialised with a population, 𝒫, of XX,XXX agents. 10,000 of these agents are active at k=0, representing the scaled population of England on 1 January 2011. A portion of the remaining agents are activated every tick, representing the next cohort of 16 year olds. The initial values for all agent state variables are read from a synthetic population data file (see Section [ref] for further details). The edges in the network are read from a synthetic network edge list data file (see Section [ref]). E-cigarette smoking prevalences for the diffusion model are initialised with observed data for 2011 (see Section [ref]).

Scheduling (what Robin hopes happens)

The following sequence of processes is executed at each model tick k:

Activate new agents: Incoming agents with an arrival time corresponding to k are activated. For k>0 these new agents are all incoming 16 year olds to the 16-89 population.
Apply transformational mechanisms to the e-cigarette diffusion entity:
1. Update the e-cigarette prevalence, E[k], for the diffusion models to match e-cigarette use across the population of agents
2. Calculate the change in the number of e-cigarette users to be applied this tick, Δ E[k]
Apply the e-cigarette diffusion situational mechanism: if the change in the number of e-cigarette users is positive/negative then randomly assign/deassign e-cigarette use, pECigUse[k+1], to/from agents to match Δ E[k].
Apply STPM action mechanisms to active agents. These are exogenous probabilities of transitioning between different smoking states, based on sex, age and deprivation level:
1. Agents who were previously never smokers aged under 25, i.e. bState_i[k]=0, become smokers, bState_i[k+1]=1, or stay as never smokers, bState_i[k+1]=0.
2. Agents who were previously smokers aged under 25, i.e. bState_i[k]=1, become ex-smokers, bState_i[k+1]=4, or stay as smokers, bState_i[k+1]=1.
3. Agents who were previously ex-smokers of any age, bState_i[k]=4, relapse to smoking, bState_i[k+1]=1, or remain as ex-smokers, bState_i[k+1]=4.
Apply COM-B situational mechanisms to update personal attributes, capabilities, opportunities and motivations for active agents aged 25 and over, i.e. ∀ i ∈ 𝒫 :(pAge_i[k]≥25) ∧ (active_i=1):
1. For every agent, i, update the number of smokers in the agent's ego network:
  oNumberOfSmokersInSocialNetwork_i[k+1]=Σ_{j≠ i}a_j,i×(bState_j[k] ∧ 1)
2. For agents who are ongoing quitters, i.e. bState_i[k]=3, reduce their cigarette addiction strength to cCigAddictStrength_i[k+1]. For quitters who also identify as smokers,
  mNonSmokerSelfIdentity_i[k]=0, test whether they transition to a non-smoker self identity.
3. Using exogenous trend data, update the regional smoking prevalence for every agent,
  oPrevalenceOfSmokingInGeographicLocality_i[k+1]
4. Using exogenous trend data, update whether smoking agents, i.e. bState_i[k-1]=1, have received advice from their family doctor to quit smoking, oReceiptGPAdvice_i[k+1], and/or have started using nicotine replacement therapy, mUseOfNRT_i[k+1].
Apply the COM-B quit attempt action mechanism to active agents aged 25 and over who were previously smokers to check whether they make a new quit attempt at the start of the month, bQuitAttempt_i[k]=1, or whether they remain as smokers, bQuitAttempt_i[k]=0. Update agent states to bState_i[k]=2 or bState_i[k+1]=1 respectively.
For new quitters aged 25 and over, bState_i[k]=2, apply the COM-B cessation aid use situational mechanism. Using exogenous trend data, this mechanism defines the cessation aids to be used by the agent for the duration of the quit attempt: cCytisineUse_i[k], cPrescriptionNRT_i[k], cUseOfBehaviouralSupport_i[k], and cVareniclineUse_i[k].
Apply the COM-B quit maintenance action mechanism to new quitters and ongoing quitters aged 25 and over, i.e. bState_i[k]={2,3}, to check whether they can sustain the quit attempt for the duration of the current month, bQuitMaintenance_i[k]=1, or whether they fail the attempt bQuitMaintenance_i[k]=0. For agents who sustain the attempt, increment the duration of the quit bMonthsSinceQuit_i[k+1]. If the quit duration is 12 months, i.e. bMonthsSinceQuit_i[k+1]=12, the agent becomes an ex-smoker, bState_i[k+1]=4; otherwise they continue as an ongoing quitter, bState_i[k+1]=3. Agents who fail the attempt return to being smokers, bState_i[k+1]=1, with bMonthsSinceQuit_i[k+1]=0.
Apply life course events: Active agents age by one year at the end of every year, i.e. if (k mod 12)=11 then pAge[k+1]=pAge[k]+1.
Deactivate dead agents: Sample mortality rates for every active agent to determine if they die and are deactivated. Agents are also deactivated if they survive to age pAge=90.

Scheduling (what Shang says happens)

The following sequence of processes is executed at each model tick k:

Activate new agents: Incoming agents with an arrival time corresponding to k are activated. For k>0 these new agents are all incoming 16 year olds to the 16-89 population.
Apply transformational mechanisms to the e-cigarette diffusion entity:
1. Update the e-cigarette prevalence, E[k], for the diffusion models to match e-cigarette use across the population of agents
2. Calculate the change in the number of e-cigarette users to be applied this tick, Δ E[k]
Apply the e-cigarette diffusion situational mechanism: if the change in the number of e-cigarette users is positive/negative then randomly assign/deassign e-cigarette use, pECigUse[k+1], to/from agents to match Δ E[k].
Apply STPM action mechanisms to active agents. These are exogenous probabilities of transitioning between different smoking states, based on sex, age and deprivation level:
1. Agents who were previously never smokers aged under 25, i.e. bState_i[k]=0, become smokers, bState_i[k+1]=1, or stay as never smokers, bState_i[k+1]=0.
2. Agents who were previously smokers aged under 25, i.e. bState_i[k]=1, become ex-smokers, bState_i[k+1]=4, or stay as smokers, bState_i[k+1]=1.
3. Agents who were previously ex-smokers of any age, bState_i[k]=4, relapse to smoking, bState_i[k+1]=1, or remain as ex-smokers, bState_i[k+1]=4.
Apply COM-B situational mechanisms to update personal attributes, capabilities, opportunities and motivations for active agents aged 25 and over, i.e. ∀ i ∈ 𝒫 :(pAge_i[k]≥25) ∧ (active_i=1):
1. For every agent, i, update the number of smokers in the agent's ego network:
  oNumberOfSmokersInSocialNetwork_i[k+1]=Σ_{j≠ i}a_j,i×(bState_j[k] ∧ 1)
2. For agents who are ongoing quitters, i.e. bState_i[k]=3, reduce their cigarette addiction strength to cCigAddictStrength_i[k+1]. For quitters who also identify as smokers,
  mNonSmokerSelfIdentity_i[k]=0, test whether they transition to a non-smoker self identity.
3. Using exogenous trend data, update the regional smoking prevalence for every agent,
  oPrevalenceOfSmokingInGeographicLocality_i[k+1]
4. Using exogenous trend data, update whether smoking agents, i.e. bState_i[k-1]=1, have received advice from their family doctor to quit smoking, oReceiptGPAdvice_i[k+1], and/or have started using nicotine replacement therapy, mUseOfNRT_i[k+1].
Apply the COM-B quit attempt action mechanism to active agents aged 25 and over who were previously smokers to check whether they make a new quit attempt at the start of the month, bQuitAttempt_i[k]=1, or whether they remain as smokers, bQuitAttempt_i[k]=0. Update agent states to bState_i[k]=2 or bState_i[k+1]=1 respectively.
For new quitters aged 25 and over, bState_i[k]=2, apply the COM-B cessation aid use situational mechanism. Using exogenous trend data, this mechanism defines the cessation aids to be used by the agent for the duration of the quit attempt: cCytisineUse_i[k], cPrescriptionNRT_i[k], cUseOfBehaviouralSupport_i[k], and cVareniclineUse_i[k].
Apply the COM-B quit maintenance action mechanism to new quitters and ongoing quitters aged 25 and over, i.e. bState_i[k]={2,3}, to check whether they can sustain the quit attempt for the duration of the current month, bQuitMaintenance_i[k]=1, or whether they fail the attempt bQuitMaintenance_i[k]=0. For agents who sustain the attempt, increment the duration of the quit bMonthsSinceQuit_i[k+1]. If the quit duration is 12 months, i.e. bMonthsSinceQuit_i[k+1]=12, the agent becomes an ex-smoker, bState_i[k+1]=4; otherwise they continue as an ongoing quitter, bState_i[k+1]=3. Agents who fail the attempt return to being smokers, bState_i[k+1]=1, with bMonthsSinceQuit_i[k+1]=0.
Apply life course events: Active agents age by one year at the end of every year, i.e. if (k mod 12)=11 then pAge[k+1]=pAge[k]+1.
Deactivate dead agents: Sample mortality rates for every active agent to determine if they die and are deactivated. Agents are also deactivated if they survive to age pAge=90.

Design Concepts (D)

Design Concepts

The conceptual design of the model is based on systems maps derived from the COM-B theory of behaviour change and maintenance. Most of the aspects of complexity covered in this section relate to capabilities, opportunities and motivations that influence quit attempts and quit maintenance.

Emergence: The model generates the incidence of smoking cessation in the population of England over time, including the patterning of cessation by sex, age and level of deprivation.
Objectives: None.
Learning: Agents can remember the number of quit attempts they have made in the past 12 months, which influences their motivation to make another attempt. Agents engaged in a quit attempt may change their identity from a smoker to a non-smoker during the course of the attempt, affecting their motivation to maintain the attempt. Their strength of addiction to cigarettes also reduces over the course of the attempt, improving their capability to sustain the attempt over future months.
Prediction: None.
Sensing and interaction: Agents can perceive the pervasiveness of tobacco in their physical environment, where pervasiveness affects opportunities to begin and sustain quit attempts. Agents can also perceive the smoking status of their close social connections: the smoking status of alter agents influences the opportunity that an ego agent has for both initiating a quit attempt and maintaining that attempt.
Stochasticity: Initiation of quit attempts, maintenance of quit attempts, the portfolio of cessation aids used in a quit attempt, the transition from smoker to non-smoker identity, e-cigarette use, and mortality are generated probabilistically.
Collectives: None.
Adaptation: None.
Observation: Monthly smoking state for every active agent in the model, together with population summary statistics that are used to construct the emergent patterns.

Details (D)

Initialization

Agents are initialised using a synthetic population with a population distribution of state variables that aims to be representative of England on 1 January 2011. All state variables in the synthetic population are estimated using empirical data. The synthetic population is described in more detail below.

The network entity is initialised using a synthetic network that is matched to the synthetic population, with outgoing ties that are representative of a non-implausible network of close social connections for England. The synthetic network is described in more detail below.

The e-cigarette diffusion entity is initialised with empirical e-cigarette prevalence data to be representative of England on 1 January 2011.

Input Data

[List any data (e.g., maps, time series, empirical distributions) used to initialize, parameterize, or force the model that are external] to the core model logic. Specify the source, format, and how the data are integrated.

Data Set 1: [Source, purpose, and integration method.]

Smoking Toolkit Study survey questions

A set of survey questions were designed and added to one wave of the Smoking Toolkit Study in November 2023. Questions included 'How many people, if any, do you discuss matters that are important to you with nowadays?', 'How many of these currently smoke tobacco?' and 'How many of these currently vape?'. For each person, up to 5 people, that the individual discusses important matters with, questions were asked about the ego's perception of their age, gender, highest educational qualification, cigarette use, vape use, their relationship, and whether or not the person encourages or discourages them from smoking or not. Finally, a question was added about whether all, most, some or none of the individuals that the person discusses important matters with would discuss important matters with each other. A total of 1659 adults aged 16 years or older were surveyed [Jackson2024associations]. The results of the survey were used to inform the static network.

Network Generator Model

Purpose

The purpose of the social network generator submodel is to generate a realistic synthetic social network structure within an agent-based population informed by empirical network data. This will provide the basis for behavioural contagion in the ABM. The network created is a static network that exhibits structural properties observed in empirical data collected by a networks module in the STS survey.

The submodel uses an adaptation of stochastic actor-based modelling (SABM) method as a basis for the agent level decision making. Each agent chooses to form or dissolve network ties based on a logistic regression that maximises the its utility through connection choices. The agent gains utility through connecting with agents who are similar itself. It also gains utility by connecting to agents who are already connected to it or connecting to agents who are friends of its existing connections, thus driving reciprocal and transitive ties. The agent loses utility by forming too many connections, as a social penalty for holding connections. The weights of these effects are calibrated to match target network statistics. An emergent network structure arises from individual decisions that matches target network statistics. This approach explicitly models the micro-level decision processes to generate a network structure.

Patterns

The generated network model is calibrated to empirical network statistics from the observed social network in the STS survey data. The calibration process is described in section [ref]. The targets capture network structural statistics and homophily metrics of demographic and behavioural information. Target values vary by age group and are shown in Table [ref] in [ref]. The ABM timeline begins in 2011, yet the observed social network data are from 2023. This temporal mismatch means that network behaviour distributions in the 2023 targets are not representative of a 2011 network, as smoking and vaping distributions have changed substantially over this period. To align with 2023 target conditions while maintaining a 2011 starting point, we infer the 2011 network structure assuming 2023 behavioural patterns. This approach allows us to analyse the 2023 behaviour distribution against targets measured in 2023, acknowledging that behaviours and structure are dynamic and coevolutionary. However, our network data are static, collected in a single wave with no information about network evolution. The calibration process is described in Section [ref].

Entities, State Variables, and Scales

Entities

The network generator submodel inherits the entities in the main ABM. The entities relevant to the network generator are the Agent and the SocialNetworkEntity.

Agent State Variables

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Agent state variables relevant to the social network generator

Variable	Type	Range	Description
`mPotentialBuddies`	vector`<`Agent*`>`	Fixed size (1000)	Pool of agents under consideration
			for connection changes
`mAge`	int	16--89	Agent's age in years
`mAgeCat`	int	1--7	Age category^*
`microsim.init.sex`	int	0 or 1	Sex (0=female, 1=male)
`microsim.init.education`	int	1--3	Education level category
`smokingstatus`	int	0--1	Smoking behaviour category
`vapingstatus`	int	0--1	Vaping behaviour category
`arrivalYear`	int	year	Year agent entered simulation

Scales

The network generator operates only during model initialisation, producing a single static network structure. Agent connections do not evolve over time. Agents entering the simulation in subsequent time steps are pre-assigned connections at initialisation but remain inactive until their arrival year. Agents exiting through mortality become inactive nodes and their edges connecting to active nodes are no longer included in model calculations. Consequently, network composition is semi-dynamic (through entry/exit) but tie formation and dissolution do not occur post-initialisation.

To create a semi-dynamic network from static cross-sectional data, the model generates a single network at initialisation that includes all future agents (those entering between 2011 and the model end). Agents who have not yet arrived remain inactive in the network until their designated entry year, at which point they become active network participants. This approach mimics a dynamic network using a static structure, addressing the limitation that network data were collected in a single wave with no information about network evolution. Validation is required to confirm that network statistics remain relatively constant over model time despite the entry and exit of agents. Dynamic network updating based on population demographic and behaviour change is not implemented in the current model version due to the cross-language architecture (Python ABM, C++ network generator), though this remains a potential extension for future versions.

The network is built at tick 0 through a warmup process consisting of 10 discrete decision rounds (micro-ticks) where agents sequentially make connection decisions. Agents start with 0 connections and make decisions in each round. The population comprises 10,000 initial agents plus 5,568 agents entering over time, from the synthetic population generated for the ABM.

Process Overview and Scheduling

The network generator submodel runs as a distinct model in the initialisation phase before the main ABM simulation begins. Each agent in the population is first initialised with a potential buddy list of 1000 randomly selected agents. The network then undergoes 10 warmup micro-ticks, during which agents are processed in random order. In each micro-tick, each agent adds non-reciprocated incoming links to their potential buddies list, computes effect vectors for each agent in this list, applies the SABM logistic regression to convert effects into selection probabilities, and stochastically selects one agent from the choice set. Based on this selection, the agent either adds an edge, removes an edge, or does nothing (by selecting themselves). After each decision, agents refresh their potential buddies lists with two new random agents to maintain list size and introduce variability. The entire network generation process occurs at tick 0 of the ABM. Each warmup micro-tick iteration processing all agents exactly once.

Design Concepts

Basic Principles

The submodel adapts Stochastic Actor-Oriented Models (SAOMs) from the SIENA framework (Snijders et al. 2010), which model network evolution as a series of micro-decisions by individual actors. The principle is that network structure emerges from individual-level decisions that balance attribute-based selection (agents prefer connections with similar others), structural effects (agents respond to the existing network configuration they are embedded within, being more likely to reciprocate existing ties, close transitive triangles, and less likely to form connections as their outgoing degree increases), and behaviour-based selection (agents prefer connections based on similar behavioural tendencies).

The decision-making process defining the probability of an ego connecting to an alter is formalised as a multinomial logistic regression model (eq.logitmodel) where each effect contributes to the overall utility of forming or dissolving a tie. The weights (beta parameters) govern the importance of each network statistic effect size on determining an agents desire to connect to an alter. An agent generates a cumulative probability distribution over possible connection changes defined by the potential buddy list and stochastically selects one action per decision round.

P i (x ij) = (exp(U i (x ij) = 1))/(Σ h exp(U i (x ih) = 1))

The utility of forming a tie from the perspective of the ego agent i to any alter agent j, U_i(x_ij), is specified by a linear utility function based on SABM components:

U i (x ij) = Σ ℓ=1 L β_ℓ \cdot s iℓ (x ij)

where the functions s_iℓ(x_ij) represent network structural and attribute similarity effects:

s iℓ (x ij) = Σ j x ij (outdegree) [0.5em] Σ j x ij x ji (reciprocated ties) [0.5em] Σ j,k x ij x jk x ik (transitive triplets) [0.5em] (1 - (|v i age - v j age |)/(K age - 1)) (age similarity) [0.5em] (1 - |v i sex - v j sex |) (sex similarity) [0.5em] (1 - (|v i edu - v j edu |)/(K edu - 1)) (education similarity) [0.5em] (1 - |v i smoke - v j smoke |) (smoking similarity) [0.5em] (1 - |v i vape - v j vape |) (vaping similarity)

Where x_ij = 1 if agent i nominates agent j (outgoing tie), 0 otherwise; v_i^attr denotes agent i's value for a given attribute; K_age and K_edu are the number of categories for age and education respectively; k indexes the third agent in transitive triplets; ℓ indexes the effects in the utility function; h indexes all possible alters in the choice set; and β_ℓ are calibrated parameters controlling effect strength. The homophily effects of sex, smoking and vaping are simplifications of the general similarity formula, as these are binary attributes so the denominator cancels to 1.

The probabilities are converted into a cumulative distribution to be used for stochastic sampling, shown in equation (eq.cumulativeprob). An agent draws a uniform random number u U(0,1) and selects the first index where the cumulative probability exceeds u. The cumulative probability for choice j is the sum of all probabilities up to and including j.

CumulativeProb i (j) = Σ n=0 j P i (x in)

Emergence, Adaptation, and Objectives

The emergent property is the network structure, arising from micro-level decisions endogenous to the model. Agents adapt their connection decisions based on the current network state, local network position, and attribute similarity. Existing ties influence new tie formation through reciprocity and transitivity effects, while an agent's current degree affects their propensity to form additional ties through the outdegree effect. Agents continuously evaluate similarity with others in their consideration set based on demographic and behavioural attributes. Each agent's implicit objective is to maximize a utility function that represents the desirability of their current network configuration. This utility is defined by the equations shown in section [ref]. Agents make decisions that increase this utility by forming or dissolving connections that maximise the weighted combination of similarity and structural effects. Decisions are made based only on current network state and immediate utility, without anticipating future or past network configurations.

Sensing and Interaction

Agents sense attributes of all agents in their consideration set (current outgoing ties, incoming ties, and randomly selected others). They also observe structural features: friends-of-friends relationships (transitivity), reciprocation status of potential ties, and their own outdegree. Agents have perfect information about attributes and structural positions within their consideration set. The primary interaction is network tie formation or dissolution. The interaction protocol is asynchronous: agents make decisions sequentially rather than simultaneously, with order randomised each iteration. Agents do not communicate. Connections are formed unilaterally (directed ties), though reciprocation is influenced by the reciprocity effect.

Stochasticity, Collectives and Observation

Multiple sources of stochasticity ensure realistic network variation. Initial buddies are randomly selected during network seeding. Consideration set members (potential buddies) are randomly selected and periodically refreshed. Agents make stochastic selections from probability distributions using a softmax choice function. The ordering of agents to act is randomised at each iteration. A global random seed controls overall reproducibility. These stochastic elements allow multiple plausible network candidates, representing uncertainty inherent in human decision-making processes.

The submodel does not explicitly represent group-level entities, but the SocialNetworkEntity serves as a collective structure that maintains and controls the global graph information, calculates network-level statistics, and provides graph query functions (successors, predecessors). Community structures emerge but are not represented as explicit entities; these can be identified in analysis and visualisation using Leiden clustering. During execution, the model outputs an edge list of the final network structure.

Initialisation

Agents are created with demographic attributes read from the population input file that is preprocessed in R (smoking\_agents.csv). All agents start with empty networks. An empty directed graph structure (SocialNetworkEntity) is created, and agents are linked to the network entity. For each agent, initPotentialBuddies() populates the consideration set with random agents. Beta coefficients for network effects are sampled from the posterior distributions to define the weights for the decision function. The random seed is set for reproducibility.

Input Data

Required Input Files

The network generator requires two primary input files. First, the population csv file contains agent attributes with individual-level demographic data sourced from a synthetic population preprocessed in R. It requires at minimum ID, age, age category, sex, education, smoking status, vaping status, and arrival year. Second, the model properties file specifies model parameters and settings. It requires network formation beta coefficients for the SABM utility function, effect enable/disable flags for the utility function, random seed for reproducibility, scheduling parameters (stop.at, start.year, social.network.warmup.init), social network settings (social.network, social.network.update.buddy.count, social.network.init.output, social.network.potential.buddy.count), and population size and entry parameters (count.of.agents, file.rank0).

Parameter Ranges

As the calibration process employs approximate Bayesian computation (ABC) to identify optimal parameter sets, the final weights used in the SABM utility function are derived from posterior distributions. The calibrated ranges are shown in Table [ref].

Social Network Model Calibration

The synthetic network generator model is calibrated using an approximate Bayesian computation approach known as history matching. The goal is to adjust the parameters of the model, the SABM betas, to ensure that the output of the model closely matches target statistics derived from real-world networks observed in the STS survey.

Parameters to be Calibrated

The parameters to be calibrated in the synthetic network generator model are the SABM betas. These parameters influence the weight that agents give to the importance of each SABM attributes when assessing potential connections. The calibration process aims to identify the optimal values for these betas that result in synthetic networks that closely resemble the observed networks. Since it is a Bayesian approach, these will be expressed as posterior distributions. The prior distributions for each of the SABM betas based on common values in previous SABM literature, shown in table [ref].

Prior distributions for calibrated parameters.

Parameter	Prior Distribution
`β_age`	`U(0, 5)`
`β_sex`	`U(0, 5)`
`β_education`	`U(0, 5)`
`β_smoking`	`U(0, 5)`
`β_vaping`	`U(0, 5)`
`β_outdegree`	`U(-15, 0)`
`β_reciprocity`	`U(0, 15)`
`β_{transitive triples}`	`U(0, 15)`

Target Statistics

The target statistics used for calibration are derived from a set of real-world network observed in the STS survey. These networks are ego centric, so it is not a complete sociocentric network, and information pertaining to alter-alter connections; reciprocity, transitivity, indegree are unavailable to calculated. Therefore we estimate these target statistics from literature with wide standard deviations to account for the uncertainty. The target statistics that are calculated are; average outdegree, average homophily by age, gender and education status, average homophily on health behaviour attribute smoking status adn vaping status both in all observations and the average homophily given the ego is a smoker or vaper, and the proportion of agents with no outgoing connections. The targets calculated from the observed networks are split into three age groups; Under 35, 35-54, and 55+. The target statistics, table [ref] serve as benchmarks against which the candidate networks produced by each synthetic network generator model is compared during the calibration process.

tables/networkTargets

Calibration Methodology

The calibration of the synthetic network generator model is conducted through a series of history matching steps [Craig1997pressure]. This process involves selecting a number of sets of candidate parameter values, referred to as calibration waves, and running the model to generate synthetic networks. The statistics of the candidate networks are compared to the target statistics of the observed networks. An implausibility measure is calculated for each candidate parameter set to quantify the discrepancy between the model output and the target statistics. For a given network candidate, each network statistic is evaluated against its target to give an implausibility, and the overall network implausibility score is the maximum of all the individual implausibilities. In general, parameter sets that result in implausibility measures below a threshold of 3 are deemed plausible.

The implausibility function is defined as:

I(θ s) = max j (|{z j}(θ s) - x j |)/(\sqrt{Var({z j}(θ s)) + Var(j)})

where {z_j}(θ^s) is the mean model prediction for target statistic j given parameter set θ^s , x_j is the observed value of target statistic j , Var({z_j}(θ^s)) is the variance of the model prediction or the uncertainty in the model output, and Var(_j) is the variance associated with the observation error for target statistic j .

The reciprocity standard error is widened in the implausibility calculation due to uncertainty from the limitations of the ego-centric network data. Since the STS survey provides ego-centric networks, true reciprocity cannot be directly observed, and the target value of 0.79 is estimated from literature with substantial uncertainty (needs ref). To accommodate this uncertainty while preventing unrealistic network structures, reciprocity implausibility is deemed acceptable (given implausibility = 0) if it falls within the plausible region. This is implemented by modifying the implausibility calculation for reciprocity as follows:

I reciprocity = 0 if |{z} reciprocity - 0.61| < 0.18 (|{z} reciprocity - 0.79|)/(0.213) otherwise

This formulation assigns zero implausibility to any reciprocity value within the range [0.43, 0.79], effectively treating all values in this plausible range as equally acceptable. Outside this range, standard implausibility calculation applies. This approach acknowledges the high uncertainty in reciprocity estimates while ensuring the calibrated networks maintain reasonable reciprocal tie structures.

The first wave of calibration involves uniformly sampling parameter values from the prior beliefs based on possible range of parameter values found in SABM literature. Sample sets are created using Latin hypercube sampling (LHS) , which divides the range of each parameter into a grid of N strata and samples once from each stratum. The components from different parameters are then matched at random to form N parameter sets. This ensures that each sample set better explores the parameter space, guaranteeing representation of all portions of each parameter's distribution[McKay1979comparison]. The model is run with these parameter sets to generate synthetic networks. The top 10% of parameter sets with the lowest implausibility measures are retained as plausible parameter sets for the next wave of calibration.

To prepare for subsequent waves, a beta distribution is fitted to each retained parameter through a normalization and rescaling procedure. First, the parameter values from the top 10% of plausible sets are normalized to the range [0,1] using the minimum and maximum values observed within this subset. Beta distributions are then fitted to these normalized values using maximum likelihood estimation. For the next wave, new parameter values are sampled from these fitted beta distributions and rescaled back to the original parameter space using the bounds determined by the top 10% subset. This approach ensures that subsequent waves concentrate sampling effort in the most promising regions of parameter space while maintaining appropriate distributional properties. The sample distributions of these plausible parameter sets are then used to inform the sampling for the next wave of calibration.

Subsequent waves of calibration focus on refining the parameter space by sampling more densely around the plausible regions identified in previous waves. 10 waves of history matching were performed, with each wave involving the generation of 1,000 synthetic networks. The implausibility measures had converged across the whole wave by the final wave, indicating that further waves would not yield significant improvements in calibration.

Calibration Results

The calibration distribution conditioning can be seen in figure [ref]. All waves are are shown, with the first wave in red and the final wave in blue. It can be seen that the distributions have converged by the final wave.

[Figure: Calibration distributions across waves of history matching.]

The posterior distributions of the calibrated parameters from the final wave of calibration are shown in table [ref]. The posterior distributions are expressed as beta distributions fitted to the normalised set of plausible parameter sets, along with the scaled bounds of the parameters.

Posterior beta distributions shape and scaled bounds of calibrated parameters from the final wave of calibration.

Parameter	Distribution	Bounds
`β_age`	Beta(1.672, 1.497)	[1.223, 1.963]
`β_sex`	Beta(1.368, 1.519)	[-0.400, 0.239]
`β_education`	Beta(1.993, 1.550)	[0.606, 1.748]
`β_smoking`	Beta(1.890, 1.693)	[0.739, 1.316]
`β_vaping`	Beta(1.766, 1.860)	[0.938, 1.166]
`β_outdegree`	Beta(1.707, 1.508)	[-11.414, -10.325]
`β_reciprocity`	Beta(1.971, 0.869)	[11.619, 14.840]
`β_{transitive triples}`	Beta(1.982, 1.470)	[8.935, 14.748]

The parameter set that produced the best fitting synthetic network by minimum implausibility from the final wave of calibration is shown in table [ref].

Parameter values used to generate the best fitting synthetic network.

Parameter	Value
`β_age`	1.707
`β_sex`	-0.043
`β_education`	0.922
`β_smoking`	1.035
`β_vaping`	1.001
`β_outdegree`	-10.792
`β_reciprocity`	14.261
`β_{transitive triples}`	12.822

The comparison between target statistics and simulated outputs from the best fitting parameter set is shown in Table [ref].

Comparison of target statistics from the observed STS sampled ego network data against statistics of the best fitting generated network structure produced in the simulation by lowest implausibility.

Type	Age Group	Target (SE)	Simulation	Implausibility
Age	Under 35	0.783 (0.009)	0.721	2.326
Age	35-54	0.832 (0.005)	0.776	2.205
Age	55+	0.790 (0.006)	0.728	2.413
Clustering	Overall	0.100 (0.100)	0.194	0.911
Contacts	Under 35	4.222 (0.197)	3.461	2.391
Contacts	35-54	3.942 (0.178)	4.114	0.561
Contacts	55+	3.603 (0.146)	4.060	1.578
Education	Under 35	0.716 (0.014)	0.726	0.355
Education	35-54	0.693 (0.013)	0.729	1.258
Education	55+	0.674 (0.014)	0.689	0.523
Gender	Under 35	0.532 (0.016)	0.501	1.046
Gender	35-54	0.523 (0.015)	0.485	1.317
Gender	55+	0.456 (0.014)	0.495	1.371
Reciprocity	Overall	0.790 (0.213)	0.946	0.727
Smoking	Under 35	0.772 (0.016)	0.844	2.420
Smoking	35-54	0.810 (0.014)	0.844	1.185
Smoking	55+	0.860 (0.011)	0.873	0.490
Smoking (given smoker)	Under 35	0.511 (0.041)	0.425	1.776
Smoking (given smoker)	35-54	0.419 (0.047)	0.388	0.578
Smoking (given smoker)	55+	0.318 (0.049)	0.361	0.794
Vaping	Under 35	0.767 (0.016)	0.856	2.963
Vaping	35-54	0.824 (0.014)	0.890	2.302
Vaping	55+	0.919 (0.009)	0.932	0.499
Vaping (given vaper)	Under 35	0.479 (0.035)	0.358	2.798
Vaping (given vaper)	35-54	0.303 (0.042)	0.273	0.621
Vaping (given vaper)	55+	0.201 (0.055)	0.235	0.572
Zero contacts	Under 35	0.098 (0.105)	0.052	0.423
Zero contacts	35-54	0.084 (0.091)	0.035	0.521
Zero contacts	55+	0.084 (0.061)	0.032	0.798

Dynamic Exogenous Variables

Smoking Transition Probabilities

Mortality Rates

Submodels

For each distinct process, provide the full mathematical or logical formulation.

Latent Composite Model for Quit Attempts

Latent Composite Model for Quit Maintenance

Feedback Processes

This submodel describes five feedback processes, where the behaviour (quit attempt or quit maintenance) affects the values of the individual variables which affect the behaviour.

Relationship between quit attempt and mNumberOfRecentQuitAttempts

The number of recent quit attempts in the past 12 months is updated according to whether or not the individual attempted to quit in that tick:

mNumberOfRecentQuitAttempts = Count(QuitAttempts in past 12 month)

The number of recent quit attempts will then affect the individual's composite motivation to quit which will affect the probability of a quit attempt.

Relationship between quit attempt and oNumberOfSmokersInSocialNetwork

The number of smokers in the social network is recalculated each tick according to whether or not individuals have quit smoking. The number of smokers in an individual's network will then affect their composite opportunity to quit which will affect the probability of a quit attempt in the next tick.

Relationship between quit maintenance and oNumberOfSmokersInSocialNetwork

The number of smokers in the social network is recalculated each tick according to whether to not individuals have maintained their smoking quit. The number of smokers in an individual's network will then affect their composite opportunity to quit which will affect their probability of maintaining the quit in the next tick.

Relationship between quit maintenance and cCigAddictStrength

Cigarette addition strength decreases the longer a smoking quit is maintained. Beard et al. (2012) undertook an analysis of the urge to smoke over 52 weeks of abstinence [ussher2013urge]. They report an analysis of the mean ratings of strength of urges to smoke for people who had been abstinent for 1 week (n=197), 2 weeks (n=156), 3 weeks (n=139), 4 weeks (n=131), 26 weeks (n=57) and 52 weeks (n=38). The authors found that an exponential distribution provided a good fit to this data. The graph and exponential fitting was replicated using non-linear least squares regression. The output is rounded since cigarette addiction strength needs to be an integer on a scale from 0 to 5 where 0 is low addiction strength and 5 is high addiction strength. The resulting equation is:

cCigAddictStrengtht+1 = round(cCigAddictStrengtht · \ e-wλ)

where w = tick length (weeks) and λ = 0.0368 based on the data fitting.

Cigarette addiction strength will then affect the composite capability to maintain the quit which will affect the probability of maintaining the quit in the next tick. Cigarette addiction strength will return to the pre-quit state if the individual relapses or fails in the quit attempt.

Relationship between quit maintainance and mNonSmokerSelfIdentity

The probability of having a non-smoker self identity will increase the longer a smoking quit is maintained. We could not identify any longitudinal evidence. Tombor et al. (2015) reported an analysis of the cross sectional Smoking Toolkit Study data using the question for ex-smokers who had quit in the past 12 months, “Which one of the following best describes you?” - “I still think of myself as a smoker” or “ I think of myself as a non-smoker” [Tombor2015does]. The authors reported the number of post-quitters with a non-smoker identity and with a smoking identity by length of smoking abstinence. The following time points for the bands provided in the paper were used for fitting a distribution: 1-4 weeks = 4 weeks; 4 - 8 weeks = 8 weeks; 8-12 weeks = 12 weeks; 12-26 weeks = 19.5 weeks, 26 - 52 weeks = 39.5 weeks. We fitted an Exponential, Weibull, Gompertz and Log-logistic distribution to this data and found the Log-logistic to be the best fitting. The resulting equation is:

p(having a smoker identity) = (1)/(1+α(s \cdot w)^β)

where alpha = 1.1312, beta = 0.500, s = no. of consecutive quit successes and w = tick length (weeks)

Within the model, the probability of whether or not the individual has a smoker identity is sampled. All smokers are assumed to have a NonSmokerSelfIdentity equal to 0, so if a quitter or ex-smoker relapses, their NonSmokerSelfIdentity will return to 0. Non smoker self identity will then affect composite motivation to maintain a quit which will affect the probability of maintaining the quit in the next tick.

Purpose and overview

This submodel uses repeated cross-sectional data from the Smoking Toolkit Study (STS) to estimate and project the diffusion of e-cigarettes in the population, stratified by smoking status and birth cohort. Non-disposable (reusable) and disposable e-cigarettes appear to have followed different diffusion processes: non-disposable use rises and then declines in several subgroups, whereas disposable use shows a later and sharper rise. We therefore treat these as two distinct diffusion processes, estimate separate models for each, and then combine them to obtain a single time series of ``any e-cigarette use'' by subgroup. The resulting trajectories provide a historical reconstruction of e-cigarette prevalence (from 2010 onwards) and projections to 2034. These time-varying subgroup-specific prevalences are used as exogenous inputs to the agent-based model.

Data processing and subgroups

We use monthly STS data from 2010 onwards. For each respondent, we derive smoking status by collapsing original categories into never smoker, ex-smoker, and current smoker. Birth year is computed from age and survey year, and respondents are assigned to broad birth cohorts (<1940, 1941--1960, 1961--1980, 1981--1990, 1991+). Smoking status and birth cohort are then combined to form a subgroup label (e.g.\ ``Smoker, 1961--1980'').

Survey dates are harmonised to a monthly time index t, with t = 0 corresponding to the first observed month in the relevant series (January 2010 for the non-disposable series; January 2021 for the disposable series). For each month and subgroup we compute the survey-weighted prevalence of any e-cigarette use and, separately, the prevalence of non-disposable and disposable use. To reduce sampling noise, we apply a three-month rolling mean within each subgroup, yielding smoothed monthly prevalence series. For some subgroup–product combinations where there is little or no evidence of diffusion (e.g.\ selected older cohorts for disposables, or never-smoker cohorts for non-disposables), we do not fit a diffusion model. The smoothed, subgroup-specific monthly prevalence series for non-disposable and disposable e-cigarettes form the targets for model fitting.

Bass diffusion model

We describe diffusion using the Bass model [bass1969new], which assumes that new adoption of a product is driven by two mechanisms: ``innovation'' (external influence) and ``imitation'' (social influence from existing adopters). p denotes the innovation parameter and q is the imitation parameter. For a given subgroup with saturation level m, the Bass model for the cumulative number (or prevalence) of adopters at time t is

y(t) = m (1 - exp( - (p + q)t ))/(1 + (q)/(p) exp( - (p + q)t )).

This standard Bass form is used for disposable e-cigarette diffusion.

For non-disposable e-cigarettes, the empirical prevalence clearly rises and then declines in several subgroups. To capture this, we extend the Bass model by allowing the saturation level to decay exponentially over time. Specifically, we model the time-varying saturation level as

m(t) = m exp(-d t),

where d ≥ 0 is a decline (dis-adoption or replacement) rate. Substituting m(t) into the Bass solution in Equation (eq.eq:bass-standard) gives

y(t) = m exp(-d t) (1 - exp( - (p + q)t ))/(1 + (q)/(p) exp( - (p + q)t )).

When d = 0, Equation (eq.eq:bass-decline) reduces to the standard Bass model. For each subgroup, we fix m at the maximum observed smoothed prevalence for that subgroup (non-disposable or disposable, respectively). For the youngest never-smoker cohort, where visual inspection suggests further growth, we allow m to exceed the observed maximum by a small increment (a 6 percentage-point increase) based on expert judgement.

For each subgroup defined by smoking status and birth cohort, we estimate the relevant parameters (p, q, m) for disposables and (p, q, m, d) for non-disposables by non-linear least squares, using the smoothed monthly prevalence series and constraining all parameters to be non-negative. The monthly index is used as t, with t = 0 corresponding to the start of the relevant series (2010 for non-disposables, 2021 for disposables).

Construction of diffusion trajectories for the agent-based model

Once parameters have been estimated, we use Equations (eq.eq:bass-standard) and (eq.eq:bass-decline) to generate predicted prevalence trajectories for each subgroup from 2010 projected to 2034. We then construct a single trajectory for ``any e-cigarette use'' in each subgroup by adding together the modelled non-disposable and disposable prevalence on the same monthly timeline.

Before 2021, the combined curve is therefore driven solely by non-disposable diffusion; from 2021 onwards, the disposable contribution is added. For each subgroup defined by smoking status and birth cohort, this procedure yields a smooth monthly trajectory of any e-cigarette use from 2010 to 2034. These trajectories are passed to the agent-based model as time-varying, subgroup-specific targets or external conditions for the prevalence of e-cigarette use in the simulated population, as shown in Figure [ref].

[Figure: Monthly combined prevalence of any e-cigarette use by smoking status and birth cohort]

Submodel A: [e.g., 'Agent Movement']

Process: [Provide the step-by-step logic, pseudocode, or equations. Use mathematical notation for clarity.] ${x} i, t+1 = {x} i, t + {v} i, t \cdot Δ t$ where {v}_{i, t} is the velocity vector, calculated as: ${v} i, t = (1 - p rand) \cdot {v} objective + p rand \cdot {w}$
Parameters: List all parameters specific to this submodel and their values/ranges.
- [Random walk probability (p_{rand]):} [Value: 0.1 or range [0, 0.2]]

Submodel B: [e.g., 'Resource Consumption and Decay']

Process: [Describe how agents consume resources and how resources decay or regenerate in the environment.]
Parameters:
- [Consumption Rate (c):] [Value: 5 units per time step]

Model Evaluation

[Describe the methods used for model checking, verification (debugging code and logic), and validation (comparing model output to real-world data). State the criteria used to determine if the model successfully reproduces the **Patterns** specified in Section [ref]

Verification (Code Checking): [e.g., Used unit testing for submodels; used analytical checking of boundary cases.]
Validation (Pattern Comparison): [e.g., Used the Approximate Bayesian Computation (ABC) method to fit the model to Pattern 1; performed qualitative comparison against Pattern 2.]

Verification

Phase 1 verification demonstrates that the SimCOM-Quit agent-based machinery reproduces the behaviour of the Sheffield Tobacco Policy Model (STPM) when it is driven by the same transition probabilities. This stage confirms that the ABM can act as a faithful STPM emulator before any COM-B extensions are activated. We judge the phase successful when the ABM smoking prevalence matches the STPM prevalence at the end of each calendar year from 2011 through 2019.

STPM-Emulator View

To enable a like-for-like comparison with the STPM, the ABM's detailed smoking states are collapsed into the categories reported by the policy model (Table [ref]). Every quit-related state is recorded as ex-smoker in this ``STPM-emulator view'', mirroring how the STPM treats abstinent individuals and allowing the prevalence trajectories to be compared without additional post-processing.

Mapping of SimCOM-Quit smoking states to STPM smoking-status categories used for verification and for aligning calibration outputs.

SimCOM-Quit state	STPM category	Description
`NEVERSMOKE`	`STPM\_NEVER`	Never established regular smoking.
`SMOKER`	`STPM\_CURRENT`	Ongoing regular smoking.
`NEWQUITTER`	`STPM\_EX`	Abstinent within the first month of a quit attempt.
`ONGOINGQUITTER1--11`	`STPM\_EX`	Months 1--11 of maintained abstinence (tunnel states).
`EXSMOKER`	`STPM\_EX`	Twelve or more consecutive months of abstinence.

Verification Plan

Verification proceeds by disabling COM-B mechanisms and driving the population entirely with transformed STPM probabilities:

Disable COM-B effects: Set quitting\_behaviour: "STPM" in the configuration so that agents react only to STPM transition inputs.
Align baseline states: Transform all baseline NEWQUITTER and ONGOINGQUITTER agents into EXSMOKER with quit\_duration=0 so the tunnel starts empty.
Quit-attempt probability: For every SMOKER agent, apply the STPM net quit probability transformed to a monthly rate: $p attempt,1month = 1 - (1 - P annual) 1/12$ where P_annual is the STPM annual quit probability.
Quit-maintenance probability: Maintain p_maint,1month = 1.0 so the tunnel acts as a deterministic 12-month delay.
Tunnel completion: After 12 ticks each tunnel state transitions to EXSMOKER with quit\_duration=0, matching the STPM treatment of successful quits.
Relapse application: Apply the STPM relapse probabilities, including the newly integrated year-0 rows, to all EXSMOKER agents.

Fence Post Alignment

Quit attempts are aligned to the first day of the month (the ``fence post'') rather than occurring between ticks. At tick t-1 an agent in SMOKER is tested for a quit attempt, and at tick t a successful attempt moves the agent to NEWQUITTER. The tunnel therefore delivers exactly 12 maintenance tests between the quit attempt and the eventual transition to EXSMOKER.

Short-Term Relapse (Year 0)

The Relapse\_sample.csv file now includes time\_since\_quit = 0 rows for every stratum, enabling Phase 1 verification runs to capture immediate relapse. Short-term relapse (<12 months) uses the Jackson et al.\ (2019) placebo curve, while long-term relapse (≥ 12 months) uses the Hawkins et al.\ (2010) data with the established covariate adjustments. Results for the verification phase will be reported once the emulator run is complete.

Calibration

Phase 2 calibrates the COM-B parameters, θ, using Bayesian history matching. Two behavioural mechanisms are treated distinctly throughout: the quit-attempt rate (the fraction of smokers who make at least one attempt in a year) is anchored to empirical estimates from the Smoking Toolkit Study (STS), while the quit-success rate (the probability that a quit attempt results in sustained cessation as defined in the STPM) is taken from the Sheffield Tobacco Policy Model (STPM) and used as the primary set of calibration targets.

A second key design choice is temporal: targets and constraints for 2011--2013 and 2014--2016 are used during calibration, whereas all 2017--2019 quantities are held out and used only for validation (Section [ref]).

What We're Calibrating

Let θ denote the vector of COM-B parameters governing quit attempts and quit maintenance (34 parameters in total across the two modules). Parameters governing smoking initiation, mortality and relapse are held fixed (taken from STPM inputs) and are not included in θ.

Calibration Targets and Constraints

For each candidate θ we evaluate two conceptually distinct sets of outputs:

STPM quit-success targets (fit): J=22 calibration targets for 2011--2013 and 2014--2016, stratified by Age group × Sex × period and by IMD quintile × period (Tables [ref] and [ref]).
STS quit-attempt constraints (satisfice): K=22 empirical constraints for 2011--2013 and 2014--2016, stratified by Age group × Sex × period and by IMD quintile × period (Tables [ref] and [ref]).
Hold-out (validation only): all 2017--2019 STPM quit-success targets (J_val=11) and STS quit-attempt rates (K_val=11) are not used during calibration and are evaluated only in validation (Tables [ref], [ref], [ref], and [ref]).

Conceptually, this corresponds to seeking parameterisations that minimise the worst target implausibility while remaining non-implausible with respect to the constraints:

minθ\ maxj=1,…,J I(T)j(θ)  subject to  maxk=1,…,K I(C)k(θ) ≤ cC.

STPM Quit-Success Targets

The STPM provides the quit-success probability targets used to calibrate the ABM's quit-success dynamics. We report and calibrate these targets using two complementary stratifications: (i) Age group × Sex × period; and (ii) IMD quintile × period. To avoid conflating fitting with hold-out evaluation, the calibration-period targets (2011--2016) and the validation-period targets (2017--2019) are presented in separate tables.

STPM quit-success probability targets used for calibration (Age group × Sex × period; 2011--2016).

Calendar year category	Age group	Sex	Quit probability	Beta variance
2011--2013	25--44	Male	[--]	[--]
2011--2013	25--44	Female	[--]	[--]
2011--2013	45--64	Male	[--]	[--]
2011--2013	45--64	Female	[--]	[--]
2011--2013	65--74	Male	[--]	[--]
2011--2013	65--74	Female	[--]	[--]
2014--2016	25--44	Male	[--]	[--]
2014--2016	25--44	Female	[--]	[--]
2014--2016	45--64	Male	[--]	[--]
2014--2016	45--64	Female	[--]	[--]
2014--2016	65--74	Male	[--]	[--]
2014--2016	65--74	Female	[--]	[--]

STPM quit-success probability targets used for calibration (IMD quintile × period; 2011--2016).

Calendar year category	IMD quintile	Quit probability	Beta variance
2011--2013	IMD 1 (most deprived)	[--]	[--]
2011--2013	IMD 2	[--]	[--]
2011--2013	IMD 3	[--]	[--]
2011--2013	IMD 4	[--]	[--]
2011--2013	IMD 5 (least deprived)	[--]	[--]
2014--2016	IMD 1 (most deprived)	[--]	[--]
2014--2016	IMD 2	[--]	[--]
2014--2016	IMD 3	[--]	[--]
2014--2016	IMD 4	[--]	[--]
2014--2016	IMD 5 (least deprived)	[--]	[--]

STPM quit-success probability targets reserved for validation (Age group × Sex; 2017--2019).

Age group	Sex	Quit probability	Beta variance
25--44	Male	[--]	[--]
25--44	Female	[--]	[--]
45--64	Male	[--]	[--]
45--64	Female	[--]	[--]
65--74	Male	[--]	[--]
65--74	Female	[--]	[--]

STPM quit-success probability targets reserved for validation (IMD quintile; 2017--2019).

IMD quintile	Quit probability	Beta variance
IMD 1 (most deprived)	[--]	[--]
IMD 2	[--]	[--]
IMD 3	[--]	[--]
IMD 4	[--]	[--]
IMD 5 (least deprived)	[--]	[--]

STS Quit-Attempt Constraints

The STS provides independent empirical estimates of the annual quit-attempt rate, which we use as plausibility constraints to anchor the quit-attempt mechanism. The outcome is trylyc (tried to quit in last year): trylyc=1 if an individual made ≥ 1 quit attempt in the past 12 months, trylyc=0 if they made none, and trylyc=NA if they were not a past-year smoker. The denominator is past-year smokers only (smokstat ∈ {2, 3}).

We apply the constraints using the same two stratifications as the STPM quit-success targets (Age group × Sex and IMD quintile), and we separate the calibration-period constraints (2011--2016) from the validation-period constraints (2017--2019).

STS quit-attempt rate constraints used for calibration (Age group × Sex × period; 2011--2016).

Calendar year category	Age group	Sex	Quit attempt rate	Uncertainty
2011--2013	25--44	Male	[--]	[e.g. [L, U] or SE]
2011--2013	25--44	Female	[--]	[e.g. [L, U] or SE]
2011--2013	45--64	Male	[--]	[e.g. [L, U] or SE]
2011--2013	45--64	Female	[--]	[e.g. [L, U] or SE]
2011--2013	65--74	Male	[--]	[e.g. [L, U] or SE]
2011--2013	65--74	Female	[--]	[e.g. [L, U] or SE]
2014--2016	25--44	Male	[--]	[e.g. [L, U] or SE]
2014--2016	25--44	Female	[--]	[e.g. [L, U] or SE]
2014--2016	45--64	Male	[--]	[e.g. [L, U] or SE]
2014--2016	45--64	Female	[--]	[e.g. [L, U] or SE]
2014--2016	65--74	Male	[--]	[e.g. [L, U] or SE]
2014--2016	65--74	Female	[--]	[e.g. [L, U] or SE]

STS quit-attempt rate constraints used for calibration (IMD quintile × period; 2011--2016).

Calendar year category	IMD quintile	Quit attempt rate	Uncertainty
2011--2013	IMD 1 (most deprived)	[--]	[e.g. [L, U] or SE]
2011--2013	IMD 2	[--]	[e.g. [L, U] or SE]
2011--2013	IMD 3	[--]	[e.g. [L, U] or SE]
2011--2013	IMD 4	[--]	[e.g. [L, U] or SE]
2011--2013	IMD 5 (least deprived)	[--]	[e.g. [L, U] or SE]
2014--2016	IMD 1 (most deprived)	[--]	[e.g. [L, U] or SE]
2014--2016	IMD 2	[--]	[e.g. [L, U] or SE]
2014--2016	IMD 3	[--]	[e.g. [L, U] or SE]
2014--2016	IMD 4	[--]	[e.g. [L, U] or SE]
2014--2016	IMD 5 (least deprived)	[--]	[e.g. [L, U] or SE]

STS quit-attempt rate constraints reserved for validation (Age group × Sex; 2017--2019).

Age group	Sex	Quit attempt rate	Uncertainty
25--44	Male	[--]	[e.g. [L, U] or SE]
25--44	Female	[--]	[e.g. [L, U] or SE]
45--64	Male	[--]	[e.g. [L, U] or SE]
45--64	Female	[--]	[e.g. [L, U] or SE]
65--74	Male	[--]	[e.g. [L, U] or SE]
65--74	Female	[--]	[e.g. [L, U] or SE]

STS quit-attempt rate constraints reserved for validation (IMD quintile; 2017--2019).

IMD quintile	Quit attempt rate	Uncertainty
IMD 1 (most deprived)	[--]	[e.g. [L, U] or SE]
IMD 2	[--]	[e.g. [L, U] or SE]
IMD 3	[--]	[e.g. [L, U] or SE]
IMD 4	[--]	[e.g. [L, U] or SE]
IMD 5 (least deprived)	[--]	[e.g. [L, U] or SE]

Implausibility Metrics

History matching rules out regions of parameter space that are unlikely to yield an acceptable match once observation uncertainty, simulator stochasticity and model discrepancy are accounted for. We compute separate implausibility measures for the STPM quit-success targets and the STS quit-attempt constraints.

Target implausibility (STPM quit success).

For each calibration target j ∈ {1,…,J}, define

I (T) j (θ) = (| x j - 𝔼[Z (T) j (θ n)] |)/(\sqrt{Var(x j) + 𝔼[Var(Z (T) j (θ n))] + σ m 2}).

We set the model-discrepancy standard deviation to one tenth of the observed range across the J calibration targets,

d m = (max j x j - min j x j)/(10), σ m 2 = d m 2 .

Constraint implausibility (STS quit attempts).

For each constraint k with admissible interval [L_k, U_k], define a distance-to-interval term

δ k (θ) = 0, if 𝔼[Z (C) k (θ n)] \in [L k, U k], min(|L k -𝔼[Z (C) k (θ n)]|, |𝔼[Z (C) k (θ n)]-U k |), otherwise.

We then compute

I (C) k (θ) = (δ k (θ))/(\sqrt{Var(a k) + 𝔼[Var(Z (C) k (θ n))] + σ m,C 2}),

where a_k denotes the STS estimate with sampling variance Var(a_k) (SE²). The key property is satisficing: if the simulated attempt rate lies within [L_k,U_k], then I^(C)_k(θ)=0.

Overall criteria.

We summarise the two sets of implausibilities as

I (T) (θ) = max j=1,\dots,J I (T) j (θ), I (C) (θ) = max k=1,\dots,K I (C) k (θ).

At history-matching wave w, a candidate parameter set is retained (``not ruled out yet'', NROY) if

I (T) (θ) \leq c T (w) and I (C) (θ) \leq c C (w),

with potentially distinct thresholds for targets and constraints.

Calibration Workflow

The calibration follows a history matching approach (Figure [ref]):

[Figure: Calibration workflow via history matching.]

Global Sensitivity Analysis: Using Morris elementary effects to identify which of the COM-B parameters materially influence I^(T)(θ) and I^(C)(θ).
History Matching Waves: Iteratively sample candidate θ from the ``not ruled out yet'' region, run the ABM with multiple seeds, compute I^(T)(θ) and I^(C)(θ), and rule out parameterisations that exceed either threshold.
Convergence: Continue until the NROY region is sufficiently small and acceptance rates stabilise.

Note: Results for the calibration phase are currently pending.

Validation

Phase 3 involves validating the calibrated model against a hold-out period (2017--2019) which is not used during the calibration phase (2011--2016).

Plan

The calibrated parameter sets will be run on the 2017--2019 period. The model outputs will be compared against observed data for this period to assess goodness of fit and the model's ability to generalize. Specific metrics for validation are defined in the calibration protocol. Note: Results for the validation phase are currently pending.

CRUK Smoking ABM