An SIRS Pulse Vaccination Model with Nonlinear Incidence Rate and Time Delay

Kashkynbayev A. Yeleussinova M. Kadyrov S.
2023 Intercollegiate Biomathematics Alliance

Letters in Biomathematics
2023 #10 Issue 1 133 - 148 pp.

In this paper, we investigate the effectiveness of pulse vaccination as a control strategy for a time-delayed SIRS epidemic model with varying population size. The dynamics of the infectious disease are closely tied to the basic reproduction number, denoted as R₀ . Traditional epidemic models evaluate R₀ using the next generation matrix, but this approach is unsuitable for non-autonomous systems. As our study focuses on pulse vaccination strategies, our system naturally falls into the non-autonomous category. To address this, we adopt a general approach that derives R₀ in terms of spectral radii of Poincaré maps. Furthermore, we demonstrate the existence of an infectious-free periodic solution and establish its global attractiveness for R₀ < 1 while highlighting the persistence of the infectious disease for R₀ > 1. Lastly, we conduct a comprehensive sensitivity analysis for R₀ under the framework of the Holling type II functional response.

epidemic models , global attractiveness , pulse vaccination system (PVS) , spectral radius , the Poincaré map

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Department of Mathematics, Nazarbayev University, Astana, Kazakhstan
Department of Mathematics and Natural Sciences, SDU University, Kaskelen, Kazakhstan

Department of Mathematics
Department of Mathematics and Natural Sciences

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