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Updated: Apr 17, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
Optimal vaccination in a stochastic epidemic model of two non-interacting populations
Edwin C Yuan1, David L Alderson2, Sean Stromberg3
1Physics Department, University of California Santa Barbara, Santa Barbara, California, United States of America; Applied Physics Department, Stanford University, Stanford, California, United States of America.
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.
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