Shift, scale and restart smaller models to estimate larger ones: Agent based simulators in epidemiology

Daksh Mittal
Eeshan Modak
Friday, 6 May 2022, 16:30 to 17:30
A-201 (STCS Seminar Room)
Agent-based simulators are a popular epidemiological modelling tool to study the impact of various non-pharmaceutical interventions in managing an evolving pandemic. They provide the flexibility to accurately model a heterogeneous population with time and location varying, person specific interactions. To accurately model detailed behaviour, typically each person is separately modelled. This however, may make computational time prohibitive when the region population is large and when time horizons involved are large.  In this talk we review the agent based city simulator developed by IISC-TIFR to model Covid epidemic and dig deeper into the underlying probabilistic structure of the simulator (ABS) to arrive at modifications that allow smaller models to give accurate statistics for larger models. We exploit the observations 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. Soon after, once enough people have been infected, the future evolution of the pandemic is closely approximated by its mean field limit with a random starting state. We build upon these insights to develop a shift, scale and restart algorithm for the simulator that accurately evaluates the ABS's performance using a much smaller model. We provide theoretical support for the proposed approach through an asymptotic analysis where the population size increases to infinity.