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arXiv · 2512.20663

Multiple-Timescale Theory of the Susceptible-Infected-Recovered-Vaccinated Epidemic Model (SIRV) for High Basic Reproduction Number

Oleg B. Shiryaev
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Abstract

The susceptible-infected-recovered-vaccinated model (SIRV) of epidemic processes is treated for the combination of intercompartment transition rates yielding a high basic reproduction number, a condition corresponding to an intense epidemic. Multiple-timescale solutions to the SIRV model equations are presented, with the inverse of the basic reproduction number employed as the expansion parameter. The asymptotics emerge in implicit form but translate into an explicit approximation for the magnitude of the epidemic peak vs the vaccination rate. The findings are shown to agree thoroughly with the numerical results for the SIRV model. The latter becoming the susceptible-infected-recovered (SIR) one absent the vaccination, the asymptotic results are reduced to those for the SIR model accordingly, with the expressions for compartment sizes acquiring explicit form.

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Oleg B. Shiryaev. 2025-12-19. Multiple-Timescale Theory of the Susceptible-Infected-Recovered-Vaccinated Epidemic Model (SIRV) for High Basic Reproduction Number. https://arxiv.org/abs/2512.20663

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