Active Cases and Disease Extinction in the Stochastic SIR Model: Estimates with Probabilistic Guarantees

Abstract: SIR models, both deterministic and stochastic, provide a viable setup for studying epidemics. While the deterministic ones have been around for almost a century now, it hasn't still been possible to obtain analytical estimates for active infections in these setups. Also, these are not well-suited to answer questions relating to early termination. The stochastic variants, on the other hand, have indeed been amenable to such analyses. However, the current approaches are too complex; they involve using different approximations (by branching processes, ODEs, etc.) for different parts of the process.

In this work, we consider a discrete-time stochastic SIR model and take a fundamentally different route to overcome the known challenges in analyzing SIR models. Namely, our proofs rely on a sequence of stopping times based on jumps in the susceptible population. Their main advantage is that the number of recoveries between two successive stopping times is then a truncated geometric random variable. Our main results include probabilistic bounds for the number of active infections and the disease extinction time. We also obtain an estimate for the expected value of the largest epidemic size. This bound matches its analogue in the deterministic case asymptotically. 

This is ongoing work with Dr. Gal Dalal (nVidia, Israel) and Dr. Balazs Szorenyi (Yahoo Research, USA).

probability

Audience: advanced learners

Bangalore Probability Seminar

Series comments: The link to zoom meeting can be found on the seminar's google calendar - www.isibang.ac.in/~d.yogesh/BPS.html