Optimal vaccination in a stochastic epidemic model of two non-interacting populations

TL;DR

This paper introduces a computational method to optimize vaccine distribution between two populations using a stochastic epidemic model, highlighting differences from traditional deterministic approaches especially at intermediate vaccine levels.

Contribution

It develops an efficient algorithm to compute the full probability distribution of epidemic sizes in a stochastic SIR model and applies it to optimize vaccine allocation.

Findings

Stochastic model provides more accurate optimal strategies than deterministic models.

Optimal vaccine allocation varies significantly between stochastic and deterministic models.

Intermediate vaccine quantities are particularly sensitive to stochastic effects.

Abstract

Developing robust, quantitative methods to optimize resource allocations in response to epidemics has the potential to save lives and minimize health care costs. In this paper, we develop and apply a computationally efficient algorithm that enables us to calculate the complete probability distribution for the final epidemic size in a stochastic Susceptible-Infected-Recovered (SIR) model. Based on these results, we determine the optimal allocations of a limited quantity of vaccine between two non-interacting populations. We compare the stochastic solution to results obtained for the traditional, deterministic SIR model. For intermediate quantities of vaccine, the deterministic model is a poor estimate of the optimal strategy for the more realistic, stochastic case.