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ABM-SIRTEM: A Hybrid Agent-Based and Epidemiological Model for Pandemic Response
Sheryl Paul, Samuel Williams, Preetom K. Biswas, Giulia Pedrielli, Jyotirmoy V. Deshmukh
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Summary
The paper introduces ABM-SIRTEM, a hybrid modeling framework that integrates an agent-based model (ABM) with the SIRTEM epidemiological model to study pandemic response. The ABM simulates individual behaviors, including occupation-based economic incentives, mental well-being, and health risks, to dynamically model compliance with government restrictions. This compliance feedback loop influences disease transmission rates in the SIRTEM model. The framework is calibrated using historical test data from four U.S. states to analyze the interplay between public health policies, socioeconomic factors, and disease dynamics.
Entities (8)
Relation Signals (7)
ABM-SIRTEM → integrates → SIRTEM
confidence 95% · The integrated ABM-SIRTEM model (Fig. 1) combines SIRTEM (Azad et al., 2022), a population-level epidemiological model, with an ABM that simulates agent interactions.
Welfare → composedof → Health Risk
confidence 90% · We define welfare as a combination of economic productivity, mental well-being, and health risk
Welfare → composedof → Economic Productivity
confidence 90% · We define welfare as a combination of economic productivity, mental well-being, and health risk
Welfare → composedof → Mental Well-being
confidence 90% · We define welfare as a combination of economic productivity, mental well-being, and health risk
Compliance → influences → Disease Spread
confidence 90% · The ABM supplies mean compliance to SIRTEM. This changes the infection rate and the simulated daily positive and negative test counts.
ABM-SIRTEM → models → Compliance
confidence 90% · We introduce a quantitative notion of compliance to represent differences in how individuals respond to regulatory restrictions.
ABM-SIRTEM → calibratedwith → Historical Test Data
confidence 85% · We calibrate the model against historical positive and negative test counts from four U.S. states
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Abstract
Abstract:The COVID-19 pandemic has had profound impacts on global health, social structures, and economies. It disproportionately affected lower socioeconomic groups and those reliant on interaction-based jobs. Regulatory bodies faced the challenge of designing policies that preserve public health while limiting disruption to economic stability and productivity. Epidemiological models such as SIR and agent-based models (ABMs) have been used to study disease dynamics and the socioeconomic impacts of disease and interventions. Population-level models often simplify individual heterogeneity, while detailed ABMs can become computationally expensive as the numbers of agents and interactions increase. We propose ABM-SIRTEM, a hybrid model that incorporates occupation categories, economic productivity, and welfare at the individual level while dynamically modeling compliance with government interventions. We calibrate the model against historical positive and negative test counts from four U.S. states and examine the resulting compliance dynamics. This framework provides a basis for studying the interaction between disease spread and socioeconomic behavior in pandemic-response planning.
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- Source: https://arxiv.org/abs/2609.18223v1
- Canonical: https://arxiv.org/abs/2609.18223v1
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ABM-SIRTEM: A Hybrid Agent-Based and Epidemiological Model for Pandemic Response Sheryl Paul Note: Equal contribution Affiliation: University of Southern California, Los Angeles, USA , Sam Williams Affiliation: University of Southern California, Los Angeles, USA , Preetom Kumar Biswas Affiliation: Arizona State University, Phoenix, USA , Giulia Pedrielli Affiliation: Arizona State University, Phoenix, USA and Jyotirmoy V. Deshmukh Affiliation: University of Southern California, Los Angeles, USA © none Abstract. The COVID-19 pandemic has had profound impacts on global health, social structures, and economies. It disproportionately affected lower socioeconomic groups and those reliant on interaction-based jobs. Regulatory bodies faced the challenge of designing policies that preserve public health while limiting disruption to economic stability and productivity. Epidemiological models such as SIR and agent-based models (ABMs) have been used to study disease dynamics and the socioeconomic impacts of disease and interventions. Population-level models often simplify individual heterogeneity, while detailed ABMs can become computationally expensive as the numbers of agents and interactions increase. We propose ABM-SIRTEM, a hybrid model that incorporates occupation categories, economic productivity, and welfare at the individual level while dynamically modeling compliance with government interventions. We calibrate the model against historical positive and negative test counts from four U.S. states and examine the resulting compliance dynamics. This framework provides a basis for studying the interaction between disease spread and socioeconomic behavior in pandemic-response planning. Keywords: Epidemiological models, agent-based models, evolutionary game theory 1. Introduction The COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), resulted in widespread mortality, long-term health impairments, and pressure on healthcare systems (Mathieu et al., 2020; Shi et al., 2020). It also disrupted economies and social interactions. These effects were particularly severe for people with lower incomes and those whose livelihoods depended on in-person interactions (International Monetary Fund, 2020; Gopinath, 2020). Governments introduced a wide range of restrictions and support measures in response to these challenges (Hale et al., 2020; Cheng et al., 2020). Understanding the interaction between disease spread, individual behavior, and economic activity is therefore important for evaluating pandemic responses. Models of COVID-19 have been used to study disease spread and the effects of interventions (IHME COVID-19 Forecasting Team, 2021; Kucharski et al., 2020). A common approach uses population-level compartmental models, such as the SIR (susceptible, infected, recovered) model, to describe transitions between health categories (Cooper et al., 2020; Chen et al., 2020; Kudryashov et al., 2021). Extensions of these models can represent additional disease stages and support the assessment of intervention strategies (Annas et al., 2020; Ghamizi et al., 2020). These models depend on parameter estimation; simple formulations also assume homogeneous mixing within compartments, which can limit their ability to represent individual differences. Agent-based models (ABMs) capture such differences by simulating individual behaviors and interactions (Bosse et al., 2012; Hackl and Dubernet, 2019; Hunter and Kelleher, 2022; Cuevas, 2020; Kerr et al., 2021; Shamil et al., 2024; Silva et al., 2020; Krivorotko et al., 2022). They can represent heterogeneity in susceptibility, social behavior, and contact patterns, and can be used to assess social distancing and economic effects. Detailed ABMs can require substantial data and computation, while sensitivity to parameter choices complicates validation against observations. Methods based on stochastic gradient descent and automatic differentiation can integrate ABMs with deep learning frameworks to learn parameters from heterogeneous data (Chopra et al., 2023). Hybrid agent-based and population-level models also provide a way to combine individual detail with aggregate disease dynamics (Hunter et al., 2020). Our work focuses on coupling these dynamics with occupation-dependent economic incentives and the evolution of compliance with government restrictions. Contributions. We propose ABM-SIRTEM, a method that combines population-level simulation of disease spread with agent-based analysis of behavior and welfare. Its main features are as follows: (1) We model occupation types and economic payoffs that depend on agents’ occupations. (2) We model the effects of government public health restrictions on agents’ mobility and contact patterns. (3) We introduce a quantitative notion of compliance to represent differences in how individuals respond to regulatory restrictions. (4) We model the evolution of compliance as agents respond to economic incentives, social interactions, and perceived health risks. These dynamics provide a mechanism for studying the relationship between restrictions, public health, and economic productivity. (5) We calibrate time-varying transmission rates and compare the resulting simulated daily positive and negative test counts with historical COVID-19 data from four U.S. states. Model Overview. (1) The integrated ABM-SIRTEM model (Fig. 1) combines SIRTEM (Azad et al., 2022), a population-level epidemiological model, with an ABM that simulates agent interactions. SIRTEM provides the distribution of health categories from which agent health states are sampled. These categories are susceptible, exposed, infected, tested, hospitalized, and recovered (Table 3). (2) The ABM represents agents by their occupation, health status, and compliance with government restrictions. Interactions depend on mixing rates derived from daily contact frequencies. We define welfare as a combination of economic productivity, mental well-being, and health risk; we collectively refer to these components as welfare parameters. (3) A regulatory body imposes a restriction index that affects the number of agent interactions. (4) Agent compliance evolves over time according to a rule motivated by evolutionary game theory. Compliance updates depend on the welfare associated with agents’ behavior within groups defined by occupation and health state. (5) The ABM supplies mean compliance to SIRTEM. This changes the infection rate and the simulated daily positive and negative test counts. Figure 1. Overview of ABM-SIRTEM. R denotes the government restriction index; agent_health is sampled from the health distribution d produced by SIRTEM. SEIRTH denotes the health categories in Table 3.SIRTEM provides a distribution of health states to the ABM. The ABM simulates interactions under government restrictions and updates compliance, which feeds back into SIRTEM through its infection rate. 2. Agent-Based Model In this section, we describe the agent-based model (ABM), including agent attributes, the restriction index, and the interaction mechanism. Each agent is initialized with parameters that influence its behavior and interactions. Variable Description Domain EsE_s Economic productivity unit (0,∞)(0,∞) MwM_w Mental well-being unit (0,∞)(0,∞) γ Essential-worker risk discount factor [0,1][0,1] α Compliance learning rate [0,1][0,1] wEPw_EP, wMWw_MW, wHRw_HR Weights for economic productivity, mental well-being, and health risk [0,1][0,1] σNI2σ^2_NI, σVI2σ^2_VI Variances of necessary and voluntary interaction counts (0,∞)(0,∞) σC2 _C^2 Variance used to sample compliance (0,∞)(0,∞) m Population fraction used to scale voluntary interactions [0,1][0,1] Table 1. Hyperparameters of the agent-based model Variable Domain or possible values Agent set (N)(N) 1,…,|N|\1,…,|N|\ Occupation (O)(O) Essential, Remote, Non-essential non-remote Health state (HS)(HS) S,E,T,I,R,H\S,E,T,I,R,H\ Compliance (C)(C) [0,1][0,1] Economic productivity (EP)(EP) [0,∞)[0,∞) Mental well-being (MW)(MW) [0,∞)[0,∞) Health risk (HR)(HR) (−∞,0](-∞,0] Welfare (W)(W) ℝR Necessary interactions (NI)(NI) NIti⊆N∖iNI^i_t N \i\ Voluntary interactions (VI)(VI) VIti⊆N∖iVI^i_t N \i\ Government restriction policy (RtRP)(R^RP_t) [0,1][0,1] Table 2. Agent attributes and parameters of the agent-based model 2.1. Agent Description Let N denote the set of agents, indexed by i∈1,…,|N|i∈\1,…,|N|\. Agent attributes are summarized in Table 2. Each agent belongs to one of three occupation groups: Essential, Remote, or Non-essential non-remote. We denote the set of occupation groups by O and the occupation of agent i by Oi∈O^i∈ O. These categories encode the following assumptions about work and compliance: • Essential workers work regardless of government restrictions. Their non-compliance models additional social interactions beyond work-related interactions. • Remote workers also work regardless of government restrictions, and their employment does not incur additional interaction-related health risk. Their non-compliance concerns voluntary social interactions. • Non-essential non-remote workers benefit economically from non-compliance because additional interactions can represent opportunities to work as well as socialize. The ABM simulation runs for T daily time periods. In addition to occupation, each agent has the following time-varying attributes: (1) Health State: The health state of agent i at time t is denoted by HSti∈HSHS^i_t∈ HS, where HS=S,E,T,I,R,HHS=\S,E,T,I,R,H\. These categories correspond to susceptible, exposed, tested, infected, recovered, and hospitalized, respectively. (2) Economic Productivity: The economic productivity EPti∈[0,∞)EP^i_t∈[0,∞) represents the monetary benefit that agent i receives from employment and interactions at time t, such as wages, commissions, and tips. (3) Mental Well-being: The mental well-being MWti∈[0,∞)MW^i_t∈[0,∞) represents the non-monetary benefit that agent i receives from interactions with other agents at time t. Previous studies have examined and attempted to quantify the mental health and social impacts of isolation during lockdowns (Eddy, 2021; Alradhawi et al., 2020; Biester et al., 2020). We similarly represent the benefits of social interactions using a mental well-being score proportional to the number of voluntary interactions. (4) Health Risk: The health risk HRti∈(−∞,0]HR^i_t∈(-∞,0] represents the daily health risk penalty incurred by agent i through interactions at time t. In an interaction between agents i and j, each agent incurs a penalty based on the other agent’s health state. The penalty incurred by agent i when interacting with agent j is (1) Risktij=−pSif HStj=S,−pEif HStj=E,−pTif HStj=T,−pIif HStj=I,−pRif HStj=R,−pHif HStj=H,Risk^ij_t= cases-p_S&if HS^j_t=S,\\ -p_E&if HS^j_t=E,\\ -p_T&if HS^j_t=T,\\ -p_I&if HS^j_t=I,\\ -p_R&if HS^j_t=R,\\ -p_H&if HS^j_t=H, cases where pR<pS<pE≤pT≤pI<pHp_R<p_S<p_E≤ p_T≤ p_I<p_H are positive constants representing the relative infection risk of interacting with agents in these categories. (5) Compliance: The compliance Cti∈[0,1]C^i_t∈[0,1] represents the degree to which agent i conforms to government restrictions by reducing voluntary interactions, defined in Section 2.2. For a fixed restriction index, a compliance score of 11 sets the mean voluntary interaction count to zero, whereas a score of 00 maximizes that mean. (6) Welfare Index: The welfare Wti∈ℝW^i_t of agent i at time t is a weighted sum of economic productivity, mental well-being, and health risk. We use this index as a modeling proxy motivated by research and debate on measuring welfare and subjective well-being (Dolan and Metcalfe, 2012; Johns and Ormerod, 2007; Fabian, 2019). We calculate welfare as (2) Wti= W^i_t= wEP⋅EPti+wMW⋅MWti w_EP· EP^i_t+w_MW· MW^i_t +wHR⋅HRit, +w_HR· HR^i_t, where wEPw_EP, wMWw_MW, and wHRw_HR are the respective component weights.11 1 We use equal weights for the three components. Restriction Policy. We represent government restrictions in each time period by a restriction index RtRP∈[0,1]R^RP_t∈[0,1], which influences agent interactions. A value of 00 represents no restrictions, and a value of 11 represents a full lockdown. Compliance and Health Dynamics. We use the population-level SIRTEM model, described in Section 3, to simulate disease dynamics, while the ABM simulates population compliance. Let HStHS_t denote the categorical distribution of health states in the population at time t, and let C¯t=1|N|∑i∈NCti C_t= 1|N| _i∈ NC^i_t denote mean population compliance. The coupled updates are summarized by (3) HSt+1 HS_t+1 =SIRTEM(HSt,C¯t), = SIRTEM(HS_t, C_t), (4) C¯t+1 C_t+1 =ABM(HSt+1,C¯t,RtRP), = ABM(HS_t+1, C_t,R^RP_t), where SIRTEM runs for one day and ABM performs the iteration detailed in Algorithm 1 and Section 2.3. We first describe how simulated interactions affect welfare and, in turn, individual compliance. Let G=O×HSG=O× HS denote the set of occupation–health groups. For each group g∈Gg∈ G, let Ng=i∈N:(Oi,HSti)=g.N_g=\i∈ N:(O^i,HS^i_t)=g\. For the nonempty groups G+=g∈G:|Ng|>0G_+=\g∈ G:|N_g|>0\, mean compliance is C¯gt=1|Ng|∑i∈NgCti,g∈G+. C^g_t= 1|N_g| _i∈ N_gC_t^i, g∈ G_+. We model the evolution of compliance using a version of the replicator equation (Maynard Smith, 1982; Alexander, 2021), in which agents mimic the compliance of agents with high welfare. Agents imitate only members of their own occupation–health group because behavior that benefits an agent in another group may lower their own welfare. For example, a non-essential non-remote worker may fare worse by imitating a remote worker whose economic productivity is unaffected by compliance. For agent i∈Ngi∈ N_g, the compliance update is (5) δCti=α∑j∈Ng(Wti−Wtj)(Cti−Ctj),δ C_t^i=α _j∈ N_g(W_t^i-W_t^j)(C_t^i-C_t^j), where α is a learning rate controlling adaptation. Averaging over agents in a nonempty group gives (6) δC¯gt δ C^g_t =1|Ng|∑i∈NgδCti, = 1|N_g| _i∈ N_gδ C_t^i, (7) C¯gt+1 C^g_t+1 =C¯gt+δC¯gt. = C^g_t+δ C^g_t. ABM State. Mean population compliance provides the following summary of the ABM state: (8) st=C¯t=1|N|∑g∈G+|Ng|C¯gt.s_t= C_t= 1|N| _g∈ G_+|N_g|\, C^g_t. For a fixed sampled population and its group memberships, the corresponding update is (9) δst=1|N|∑g∈G+|Ng|δC¯gt,δ s_t= 1|N| _g∈ G_+|N_g|\,δ C^g_t, with st+1=st+δsts_t+1=s_t+δ s_t. 2.2. Agent Interactions Simulated interactions determine economic productivity, mental well-being, and health risk for each agent i∈Ni∈ N. We distinguish necessary interactions NItiNI^i_t from voluntary interactions VItiVI^i_t. Their numbers depend on the agent’s occupation, health state, and compliance, as well as the restriction index at time t. 2.2.1. Classification of Interactions (1) Necessary Interactions: Necessary interactions are unavoidable in daily life, regardless of compliance or government restrictions. They arise from an agent’s occupation or home environment. Essential workers must interact at work as well as at home, so their necessary interaction count depends on both the at-home mixing rate rhomer_home and the at-work mixing rate rworkr_work. For remote and non-essential non-remote workers, only rhomer_home is relevant. Let NItiNI^i_t denote the set of agents with whom agent i has necessary interactions at time t. Its size is sampled according to |NIti|∼(μNIi,σNI2),|NI^i_t| ( _NI^i, _NI^2), where μNIi=(rhome+rwork)|N|if Oi=Essential,rhome|N|otherwise. _NI^i= cases(r_home+r_work)|N|&if O^i=Essential,\\ r_home|N|&otherwise. cases Thus, the occupation determines the mean interaction count, and σNI2 _NI^2 is the variance. (2) Voluntary Interactions: Voluntary interactions are optional and depend on an agent’s compliance and the government restriction index. Let VItiVI^i_t denote the set of agents with whom agent i voluntarily interacts. The parameter m∈[0,1]m∈[0,1] scales the interaction count relative to the population size. The number of voluntary interactions is sampled according to |VIti|∼(μVIi,σVI2),|VI^i_t| ( _VI^i, _VI^2), where μVIi=m|N|(1−Cti)(1−RtRP), _VI^i=m|N|(1-C^i_t)(1-R^RP_t), and σVI2 _VI^2 is the variance. 2.2.2. Interaction Simulation Interactions affect welfare according to their type and number and the occupations and health states of the interacting agents. (1) Economic Productivity: Economic productivity depends on an agent’s occupation and interactions. • Essential and remote workers can work regardless of government restrictions and receive a fixed payoff determined by the mixing rates, the interaction-scale parameter m, and the population size |N||N|. • Non-essential non-remote workers receive a payoff proportional to their number of voluntary interactions with non-hospitalized agents. The indicator HStj≠H1_HS^j_t≠ H equals 11 when agent j is not hospitalized and 00 otherwise. We define economic productivity as (10) EPti=Es(rhome+rwork)m|N|if Oi∈Essential, Remote,Es∑j∈VItiHStj≠Hotherwise,EP^i_t= casesE_s(r_home+r_work)m|N|& gatheredif O^i∈\\[-2.0pt] \Essential, Remote\, gathered\\ E_s _j∈ VI^i_t1_HS^j_t≠ H&otherwise, cases where Es>0E_s>0 is the unit of economic gain. Essential and remote workers receive a fixed payoff, while non-essential non-remote workers can increase their payoff through additional voluntary interactions with non-hospitalized agents. (2) Mental Well-being: Each voluntary interaction gives each agent a mental well-being payoff of Mw>0M_w>0. The total is MWti=Mw|VIti|.MW^i_t=M_w|VI^i_t|. (3) Health Risk Penalty: A discount factor γ∈[0,1]γ∈[0,1] reduces the health risk penalty for essential workers’ necessary interactions, reflecting the assumption that these interactions take place with appropriate precautions and protective measures.22 2 Examples include masking and sanitization requirements in supermarkets and personal protective equipment for healthcare workers. Using the risk function in Equation 1, we define (11) HRti= HR^i_t= ∑j∈VItiRisktij _j∈ VI^i_tRisk^ij_t +γ∑j∈NItiRisktijif Oi=Essential,∑j∈NItiRisktijotherwise. + casesγ _j∈ NI^i_tRisk^ij_t&if O^i=Essential,\\ _j∈ NI^i_tRisk^ij_t&otherwise. cases 2.3. ABM Iteration Algorithm 1 summarizes an ABM iteration. At time t, the ABM receives the health state distribution HSt+1HS_t+1 from SIRTEM. In each of RbR_b rounds, it samples agents stratified into occupation–health groups using HSt+1HS_t+1 and the occupation distribution. Compliance scores are sampled from the corresponding group distribution, Cti∼(C¯gt,σC2)C^i_t ( C^g_t, _C^2), and bounded to [0,1][0,1]. The ABM uses the mixing rates rhomer_home and rworkr_work and the restriction index RtRPR^RP_t to sample necessary and voluntary interactions. It then computes each agent’s economic productivity, mental well-being, health risk, and welfare, followed by the compliance update in Equation 5. These updates yield the group mean updates in Equation 7 and the population mean update in Equation 9. The updates are averaged over the RbR_b rounds to obtain updated group means and the updated population mean C¯t+1 C_t+1, which is fed back into SIRTEM. Averaging over rounds reduces the variance arising from agent sampling and interaction simulation. The round budget RbR_b therefore controls the tradeoff between variance and computational cost. Algorithm 1 ABM Iteration Overview Input: ABM state summary st=C¯ts_t= C_t Health state distribution HSt+1HS_t+1 At-home mixing rate rhomer_home At-work mixing rate rworkr_work Government restriction index RtRPR^RP_t Round budget RbR_b 1 for n=1,…,Rbn=1,…,R_b do 2 N←SampleAgents(st,HSt+1)N← SampleAgents(s_t,HS_t+1); 3 SimMandatoryInteractions(N,RtRP,rwork) SimMandatoryInteractions(N,R^RP_t,r_work); 4 SimVoluntaryInteractions(N,RtRP,rwork,rhome) SimVoluntaryInteractions(N,R^RP_t,r_work,r_home); 5 δstn←ComputeComplianceUpdate(N)δ s_t^n← ComputeComplianceUpdate(N); 6 δst←1Rb∑n=1Rbδstnδ s_t← 1R_b _n=1^R_bδ s_t^n; 7 st+1←st+δsts_t+1← s_t+δ s_t; 8 C¯t+1←PopulationMeanCompliance(st+1) C_t+1← PopulationMeanCompliance(s_t+1); Output: ABM state summary st+1s_t+1 Government restriction index RtRPR^RP_t Mean compliance C¯t+1 C_t+1 3. Integration with SIRTEM SusceptibleExposedInfectedasymptomaticInfectedsymptomaticTestingQuarantineDeathHospitalizationRecoveredFlu infected /non-infectednegativenegativepositiveloss of immunity Figure 2. High-level overview of the SIRTEM model. Dashed boxes are the infected compartments; arrows show the transitions between compartments.SIRTEM health states and transitions through infection, testing, quarantine, hospitalization, and recovery. Health state SIRTEM subcompartments Susceptible (S) S, FPS, FPI, FS, GS Exposed (E) E Infected (I) PA, PS, IA, IS Tested (T) AT, ST, QAP, QSP Hospitalized (H) HBQ, HBT, HDQ, HDT Recovered (R) KR, UR, IM S: susceptible; FPS: falsely presumed susceptible; FPI: falsely presumed immune; FS: flu symptomatic; GS: general symptoms; E: exposed; PA: pre-asymptomatic; PS: presymptomatic; IA: infected asymptomatic; IS: infected symptomatic; AT: asymptomatic tested; ST: symptomatic tested; QAP: quarantined after an asymptomatic test; QSP: quarantined after a symptomatic test; HBQ: hospitalized before quarantine; HBT: hospitalized before testing; HDQ: hospitalized during quarantine; HDT: hospitalized during testing; KR: known recovered; UR: unknown recovered; IM: immune. Table 3. Aggregation of SIRTEM subcompartments into ABM health states. SIRTEM (Spatially Informed Rapid Testing for Epidemic Modeling) (Azad et al., 2022) extends compartmental epidemic models to represent testing, quarantine, hospitalization, and immunity. It distinguishes asymptomatic and symptomatic infections, non-COVID illness, and incorrectly presumed susceptibility or immunity. It also accounts for false-positive and false-negative test results and for spatial differences in population concentrations and mixing rates. Its subcompartments provide a detailed representation of the population, with transitions governed by delay differential equations (DDEs) and their associated rates (Figure 2). The exposure process is modeled by (12) dEdt=(βS(t)+β′FPI(t))Inf(t)Npop−(pera+pers)E(t), dEdt= (β S(t)+β FPI(t) ) Inf(t)N_pop- (per_a+per_s )E(t), where E(t)E(t) is the number of exposed individuals at time t, NpopN_pop is the epidemiological population size, and Inf(t)Inf(t) is the infectious-population term defined by SIRTEM (Azad et al., 2022). In SIRTEM, this term accounts for differences in infectiousness between symptomatic and asymptomatic individuals. The populations S(t)S(t) and FPI(t)FPI(t) are susceptible and falsely presumed immune individuals, respectively, with corresponding infection rates β and β′β . Falsely presumed immunity can arise from a false-positive antibody test. The parameters peraper_a and persper_s denote the fractions of infected individuals who are asymptomatic and symptomatic, respectively. Variable Description Domain rhomer_home At-home mixing rate [0,1][0,1] rworkr_work At-work mixing rate [0,1][0,1] β Infection rate [0,1][0,1] peraper_a Asymptomatic fraction [0,1][0,1] persper_s Symptomatic fraction [0,1][0,1] ϕs _s Testing rate [0,1][0,1] λq _q Quarantine length (days) ℤ>0Z_>0 Table 4. Selected SIRTEM model parameters and their stated domains. The remaining dynamic processes and equations are described in the SIRTEM paper (Azad et al., 2022). We aggregate its subcompartments into the ABM health states listed in Table 3. SIRTEM also produces daily positive and negative test counts, which we compare with observations when calibrating the integrated model. The key SIRTEM parameters for our work are the infection rate β, testing rate ϕs _s, and quarantine duration λq _q (Table 4). The default quarantine duration is 14 days. The original SIRTEM calibration models weekly infection and testing rates using second-order autoregressive, or AR(2), models (Azad et al., 2022). To couple SIRTEM with the mean population compliance C¯t C_t produced by the ABM, we introduce a weekly transmission parameter τwtrτ^tr_w and compute the daily infection rate as (13) βt=τwtr⋅C¯t. _t=τ^tr_w· C_t. Here, τwtr∈ℝ>0τ^tr_w _>0 is the transmission parameter for week w. Let W=⌈T/7⌉W= T/7 denote the number of weeks in a T-day simulation, and let τtr=(τwtr)w=0W−1τ^tr=(τ^tr_w)_w=0^W-1 denote the sequence of weekly transmission parameters. These learned parameters capture virus transmission together with effects of mixing and government restrictions. Because C¯t C_t changes daily, we evaluate βt _t daily using the transmission parameter for the corresponding week. SIRTEMpopulationmodelAgent-based modelC¯t=1|N|∑g∈G+|Ng|C¯tg C_t= 1|N| _g∈ G_+|N_g|\, C^g_tHStHS_tC¯t+1 C_t+1rhomer_homerworkr_workmixing ratesRtRPR^RP_t|VIti||VI^i_t||NIti||NI^i_t|Agent-interactionsimulationsEvolutionary complianceupdate δC¯tgδ C^g_tC¯t+1g=C¯tg+δC¯tg C^g_t+1= C^g_t+δ C^g_tsampleagentsupdate agentparameterswelfare WtiW^i_t Figure 3. Coupling between SIRTEM and the ABM. SIRTEM supplies the health-state distribution HStHS_t and the mixing rates; the ABM samples agents, simulates their interactions, and returns the mean compliance C¯t+1 C_t+1.Interaction between the SIRTEM and ABM models. Equations (3) and (4) describe the integrated model. It operates daily, alternating between SIRTEM and the ABM and updating their inputs as shown in Figure 3. (1) SIRTEM initialization: Initialize the health-state distribution HS0HS_0 with 20 infected individuals and the remainder susceptible. Set all other health-state counts to zero. (2) ABM initialization: Initialize the occupation–health group compliance means as C¯0g=0.5 C^g_0=0.5 for all g∈Gg∈ G. (3) ABM-SIRTEM iteration: At time t, run SIRTEM for one day to compute HSt+1HS_t+1. Then run the ABM iteration in Algorithm 1, using this updated health-state distribution to obtain C¯t+1 C_t+1. (4) State and compliance updates: Use the updated occupation–health group compliance means C¯gt+1 C^g_t+1 in the ABM iteration at time t+1t+1. Use C¯t+1 C_t+1 to compute βt+1 _t+1 according to Equation (13), and pass this infection rate to SIRTEM. This sequence couples disease dynamics and agent behavior: health states affect the payoffs from interactions, payoffs affect compliance, and compliance feeds back into SIRTEM’s infection rate. 3.1. Bayesian Optimization of Transmission Rates We estimate τtrτ^tr using Bayesian optimization (Frazier, 2018) to minimize the normalized mean squared error (MSE) between simulated and observed daily positive and negative test counts over a T-day horizon: (14) J(τtr)=12T∑t=1T[(y^t(+)(τtr)−yt(+)y¯(+))2+(y^t(−)(τtr)−yt(−)y¯(−))2]. splitJ(τ^tr)= 12T _t=1^T [& ( y_t^(+)(τ^tr)-y_t^(+) y^(+) )^2\\ +& ( y_t^(-)(τ^tr)-y_t^(-) y^(-) )^2 ]. split Here, y^t(+)(τtr) y_t^(+)(τ^tr) and y^t(−)(τtr) y_t^(-)(τ^tr) are the model’s simulated positive and negative test counts on day t. The corresponding observations, yt(+)y_t^(+) and yt(−)y_t^(-), are obtained from the COVID Tracking Project.33 3 https://covidtracking.com/data The normalizing constants are the average observed counts over the evaluation horizon: y¯(±)=1T∑t=1Tyt(±). y^(±)= 1T _t=1^Ty_t^(±). We optimize over a receding horizon of K weeks. At week w, the candidate horizon contains (τw+ktr)k=0K−1(τ^tr_w+k)_k=0^K-1. Given candidate initial rates τwtrτ^tr_w and τw+1trτ^tr_w+1, subsequent rates follow an AR(2) recurrence with coefficients a,b∈ℝa,b : (15) τtrw+k=aτtrw+k−1+bτtrw+k−2,k=2,…,K−1.τ^tr_w+k=aτ^tr_w+k-1+bτ^tr_w+k-2, k=2,…,K-1. We simulate each candidate horizon and evaluate Equation (14) over the corresponding days. These evaluations are used to fit a surrogate model of the objective. New candidates maximize the surrogate model’s expected improvement. The candidate with the lowest evaluated objective provides the transmission parameter for week w, after which the procedure advances by one week. Algorithm 2 summarizes the process. Algorithm 2 Bayesian Optimization to Estimate τtrτ^tr Input: Number of weeks W; initial samples ninitn_init; lookahead horizon K≥2K≥ 2; additional evaluation budget B 1 for w=0,…,W−1w=0,…,W-1 do 2 Randomly sample ninitn_init candidate tuples x=(τwtr,τw+1tr,a,b)x=(τ^tr_w,τ^tr_w+1,a,b); 3 For each x, construct the K-week horizon H(x)H(x) using Equation (15); 4 Evaluate J(H(x))J(H(x)) by simulating ABM-SIRTEM over the evaluation horizon; 5 Fit a surrogate model M to the candidate–objective pairs (x,J(H(x)))(x,J(H(x))); 6 for n=1,…,Bn=1,…,B do 7 Select x∈argmaxxEI(x,M)x∈ _xEI(x;M); /* EI denotes expected improvement. */ 8 Construct H(x)H(x) and evaluate J(H(x))J(H(x)); 9 Update M with (x,J(H(x)))(x,J(H(x))); 10 Retain τwtrτ^tr_w from the candidate with the lowest evaluated objective; Output: Estimated transmission parameters (τwtr)w=0W−1(τ^tr_w)_w=0^W-1 4. Experiments Wave Start End Home Work 0 22 Mar 2020 9 Apr 2020 1.5 1.38 1 10 Apr 2020 16 Jun 2020 3.58 1.73 2 17 Jun 2020 10 Sep 2020 3 1.81 3 11 Sep 2020 1 Mar 2021 3.81 1.86 Table 5. Average daily contacts per person used for Arizona, derived from (Feehan and Mahmud, 2021). Dates indicate the periods over which each wave’s estimates are applied in the model. We calibrate the transmission parameters τtrτ^tr for four U.S. states: Arizona, Florida, Minnesota, and Wisconsin. For each state, we estimate the occupation distribution, set the restriction index RtRPR^RP_t, and calculate the at-home and at-work mixing rates, rhomer_home and rworkr_work, using publicly available data. We estimate τtrτ^tr by Bayesian optimization as described in Section 3.1. Figure 4 shows the fitted test counts, simulated daily compliance, and observed restriction index. The implementation details are as follows.44 4 The code repository is planned for release upon publication. Figure 4. Calibration results for Arizona, Florida, Minnesota, and Wisconsin (columns). Top and middle rows: simulated (y^t(±) y^(±)_t) and observed (yt(±)y^(±)_t) daily positive and negative test counts. Bottom row: simulated mean population compliance C¯t C_t and the observed government restriction index RtRPR^RP_t; the dotted line marks the day on which the ABM starts. The results for each state were produced by the same calibration procedure (Section 3.1).Twelve panels arranged in three rows and four columns. Each column is a state. The top and middle rows compare simulated and observed positive and negative test counts; the bottom row shows simulated compliance together with the observed restriction index. (1) Occupation distribution: We use May 2019 employment estimates from the U.S. Bureau of Labor Statistics (BLS) (Bureau of Labor Statistics, 2019) to obtain the number of workers in each state by Standard Occupational Classification group. We use telework responses from the October 2022 BLS Current Population Survey (Bureau of Labor Statistics, 2023) to estimate the fraction of each occupational group capable of remote work. Specifically, we use the fraction reporting at least some hours of telework as a proxy for remote-work capability. We then use Arizona Executive Order 2020-12 (Office of the Arizona Governor, 2020), which defines essential services, to classify the occupational groups as essential or non-essential. Table 6 gives the estimated occupation distribution for Arizona. Essential services that can be performed remotely are included in the remote category. (2) Restriction index: We use the Oxford COVID-19 Government Response Tracker (OxCGRT) stringency index (Hale et al., 2021; Oxford COVID-19 Government Response Tracker (OxCGRT), 2024), rescaled to [0,1][0,1], as the government restriction index RtRPR^RP_t. This index summarizes containment and closure policies, including school and workplace closures, restrictions on public gatherings and internal movement, and international travel controls. (3) At-home and at-work mixing rates: We derive daily average contacts at home and at work from the contact surveys in (Feehan and Mahmud, 2021), which record the relationship between interacting individuals and the locations of their interactions. Table 5 lists the averages used for Arizona. We divide the daily averages by the population of the relevant state (e.g., 7.278 million for Arizona) to obtain rhomer_home and rworkr_work. (4) Agent sampling for interactions: After calculating the required numbers of necessary and voluntary interactions, |NIti||NI^i_t| and |VIti||VI^i_t|, we sample agent pairs at random until the interaction requirements are met, with no repetition within either interaction set. A pair may appear once in each of the necessary and voluntary interaction sets. (5) Time intervals: Both SIRTEM and the ABM use daily updates. SIRTEM starts on March 4, 2020, and the ABM starts on March 22, 2020, when the contact data needed to calculate rhomer_home and rworkr_work become available. (6) Transmission parameters: We use Optuna (Akiba et al., 2019) for Bayesian optimization of the transmission parameters. Occupation Share Examples Essential 56.26% Healthcare, food preparation, legal services Non-essential, non-remote 28.13% Entertainment, sales Remote 15.61% IT, business, management Table 6. Estimated occupation distribution used for Arizona. 5. Results We compare the simulated daily positive and negative test counts obtained with the calibrated transmission parameters against observations for Arizona, Florida, Minnesota, and Wisconsin. The top and middle rows of Figure 4 show daily positive and negative counts, respectively. The positive-test trajectories broadly reproduce the timing of the larger observed waves. The fit to negative-test counts varies across states, with substantial underestimation during parts of the Minnesota and Wisconsin simulations. Because observed data within the lookahead horizon are used to estimate the transmission parameters, these comparisons assess calibration fit rather than performance on held-out data. Compliance and restrictions. The bottom row of Figure 4 compares simulated mean compliance with the observed government restriction index. The trajectories show changes in compliance alongside changes in restrictions and test counts. The restriction index is supplied from historical data, so these comparisons do not establish that simulated infections cause policy changes or that changes in compliance cause the observed case trends. 6. Discussion Related Work. Related research addresses pandemic modeling, economic impacts, and policy optimization. Bhardwaj et al. (Bhardwaj et al., 2020) use reinforcement learning to design lockdown strategies that balance public health objectives and economic costs. OpenABM-Covid19 (Hinch et al., 2021) models non-pharmaceutical interventions, including contact tracing, using individual agents and contact networks. Duarte et al. (Duarte et al., 2021) review studies that integrate economics and epidemiology to inform pandemic policy, while Dobson et al. (Dobson et al., 2023) study the balance between economic and epidemiological interventions. Hunter et al. (Hunter et al., 2020) propose a hybrid model whose disease component switches between agent-based and equation-based representations according to the number of infections. ABM-SIRTEM contributes a coupling between population-level health dynamics and occupation-dependent welfare incentives that drive changes in agent compliance. Limitations and Future Work. The usefulness of the model depends on the assumptions and parameters used to represent a real population. We derive several inputs from observed data, but key hyperparameters, including those in Table 1, lack readily available ground-truth values. The welfare components are modeling proxies and have not been validated against independent economic or well-being measurements. Weekly transmission rates τtrτ^tr are fitted to historical observations and may absorb effects that are not explicitly represented in the model. Consequently, agreement with the calibration data does not establish out-of-sample forecasting performance or validate the inferred compliance trajectories. Forecasting future outbreaks requires additional evaluation without access to future observations. Future work will investigate forecasting under varying conditions and the optimization of the government restriction index to balance economic welfare against deaths, hospitalizations, and infections. 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