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Agent Based Simulators for Epidemic Modelling: Simulating Larger Models Using Smaller Ones

Daksh Mittal, Sandeep Juneja

TL;DR

This work introduces Shift-Scale-Restart (SSR), a principled algorithm to simulate large-city epidemics using smaller agent-based models by exploiting two pivotal regimes: an early multi-type branching process and a later mean-field limit. The authors establish rigorous coupling between the epidemic process and a branching process, proving that the small-model output can be shifted, scaled, and restarted to closely match the large-model trajectory, even under interventions and multiple strains. Theoretical analysis shows the transition from stochastic branching dynamics to deterministic mean-field behavior occurs around a population-size dependent time, justifying the SSR decomposition. Empirically, SSR achieves substantial runtime reductions (e.g., ~12.8×) with maintained accuracy across dense and sparse settings, parameter uncertainty, and variant scenarios, making large-scale scenario analysis and calibration more tractable for urban epidemiology.

Abstract

Agent-based simulators (ABS) are a popular epidemiological modelling tool to study the impact of various non-pharmaceutical interventions in managing an epidemic in a city (or a region). They provide the flexibility to accurately model a heterogeneous population with time and location varying, person-specific interactions as well as detailed governmental mobility restrictions. Typically, for accuracy, each person is modelled separately. This however may make computational time prohibitive when the city population and the simulated time is large. In this paper, we dig deeper into the underlying probabilistic structure of a generic, locally detailed ABS for epidemiology to arrive at modifications that allow smaller models (models with less number of agents) to give accurate statistics for larger ones, thus substantially speeding up the simulation. We observe that simply considering a smaller aggregate model and scaling up the output leads to inaccuracies. We exploit the observation that in the initial disease spread phase, the starting infections create a family tree of infected individuals more-or-less independent of the other trees and are modelled well as a multi-type super-critical branching process. Further, although this branching process grows exponentially, the relative proportions amongst the population types stabilise quickly. Once enough people have been infected, the future evolution of the epidemic is closely approximated by its mean field limit with a random starting state. We build upon these insights to develop a shifted, scaled and restart-based algorithm that accurately evaluates the ABS's performance using a much smaller model while carefully reducing the bias that may otherwise arise. We apply our algorithm for Covid-19 epidemic and theoretically support the proposed algorithm through an asymptotic analysis where the population size increases to infinity.

Agent Based Simulators for Epidemic Modelling: Simulating Larger Models Using Smaller Ones

TL;DR

This work introduces Shift-Scale-Restart (SSR), a principled algorithm to simulate large-city epidemics using smaller agent-based models by exploiting two pivotal regimes: an early multi-type branching process and a later mean-field limit. The authors establish rigorous coupling between the epidemic process and a branching process, proving that the small-model output can be shifted, scaled, and restarted to closely match the large-model trajectory, even under interventions and multiple strains. Theoretical analysis shows the transition from stochastic branching dynamics to deterministic mean-field behavior occurs around a population-size dependent time, justifying the SSR decomposition. Empirically, SSR achieves substantial runtime reductions (e.g., ~12.8×) with maintained accuracy across dense and sparse settings, parameter uncertainty, and variant scenarios, making large-scale scenario analysis and calibration more tractable for urban epidemiology.

Abstract

Agent-based simulators (ABS) are a popular epidemiological modelling tool to study the impact of various non-pharmaceutical interventions in managing an epidemic in a city (or a region). They provide the flexibility to accurately model a heterogeneous population with time and location varying, person-specific interactions as well as detailed governmental mobility restrictions. Typically, for accuracy, each person is modelled separately. This however may make computational time prohibitive when the city population and the simulated time is large. In this paper, we dig deeper into the underlying probabilistic structure of a generic, locally detailed ABS for epidemiology to arrive at modifications that allow smaller models (models with less number of agents) to give accurate statistics for larger ones, thus substantially speeding up the simulation. We observe that simply considering a smaller aggregate model and scaling up the output leads to inaccuracies. We exploit the observation that in the initial disease spread phase, the starting infections create a family tree of infected individuals more-or-less independent of the other trees and are modelled well as a multi-type super-critical branching process. Further, although this branching process grows exponentially, the relative proportions amongst the population types stabilise quickly. Once enough people have been infected, the future evolution of the epidemic is closely approximated by its mean field limit with a random starting state. We build upon these insights to develop a shifted, scaled and restart-based algorithm that accurately evaluates the ABS's performance using a much smaller model while carefully reducing the bias that may otherwise arise. We apply our algorithm for Covid-19 epidemic and theoretically support the proposed algorithm through an asymptotic analysis where the population size increases to infinity.
Paper Structure (53 sections, 10 theorems, 85 equations, 24 figures, 6 tables, 5 algorithms)

This paper contains 53 sections, 10 theorems, 85 equations, 24 figures, 6 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Agent Based Simulator
  4. Computing infection rate $\lambda_j(t)$
  5. Disease progression
  6. Public health safety measures (PHSMs)
  7. Speeding up ABS: The big picture and three key phenomena
  8. Shift-scale-restart algorithm
  9. Asymptotic Analysis
  10. Epidemic process dynamics
  11. Notation
  12. Dynamics
  13. The associated branching process dynamics
  14. Dynamics
  15. Coupling
  16. ...and 38 more sections

Key Result

Lemma 1

Consider $K$ define in (K_definition). There exist matrices $K_1 \in {\mathbb {R}^+}^{\hat{\eta}\times\hat{\eta}}$, $C\in{\mathbb {R}^+}^{(\eta-\hat{\eta})\times(\eta-\hat{\eta})}$ and $M \in {\mathbb {R}^+}^{(\hat{\eta})\times(\eta-\hat{\eta})}$ such that where $K_1 \in {\mathbb{R}^+}^{\hat{\eta}\times\hat{\eta}}$ is irreducible. Furthermore, $\rho(C) \leq \rho(K_1)$.

Figures (24)

  • Figure 1: Scaled number exposed in the smaller model match the larger model when we start with large, 12800 infections.
  • Figure 2: Scaled number exposed in smaller model do not match the larger model when we start with a few, 128 infections.
  • Figure 3: Smaller and larger model are essentially identical initially when we start with same no. of few, 100 infections.
  • Figure 4: Shift and scale smaller model (no. of exposed) matches the larger model under no intervention scenario.
  • Figure 5: Shift-scale-restart smaller model matches the larger one under real world intervention scenario over 250 days.
  • ...and 19 more figures

Theorems & Definitions (17)

  • Remark 1
  • Lemma 1
  • Theorem 1
  • Theorem 2
  • Lemma 2
  • Proposition 1
  • Remark 2
  • Remark 3
  • Corollary 1
  • Theorem 3
  • ...and 7 more