Mathematical Biosciences and Engineering, 2011, 8(2): 385-408. doi: 10.3934/mbe.2011.8.385.

Primary: 37G15, 37G35; Secondary: 39A11, 92B05.

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Periodically forced discrete-time SIS epidemic model with disease induced mortality

1. Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205
2. Department of Mathematics, Howard University, Washington, DC 20059

We use a periodically forced SIS epidemic model with disease induced mortality to study the combined effects of seasonal trends and death on the extinction and persistence of discretely reproducing populations. We introduce the epidemic threshold parameter, $R_0$, for predicting disease dynamics in periodic environments. Typically, $R_0<1$ implies disease extinction. However, in the presence of disease induced mortality, we extend the results of Franke and Yakubu to periodic environments and show that a small number of infectives can drive an otherwise persistent population with $R_0>1$ to extinction. Furthermore, we obtain conditions for the persistence of the total population. In addition, we use the Beverton-Holt recruitment function to show that the infective population exhibits period-doubling bifurcations route to chaos where the disease-free susceptible population lives on a 2-cycle (non-chaotic) attractor.
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Keywords Epidemics; infectives; periodic environments; susceptibles.

Citation: John E. Franke, Abdul-Aziz Yakubu. Periodically forced discrete-time SIS epidemic model with disease induced mortality. Mathematical Biosciences and Engineering, 2011, 8(2): 385-408. doi: 10.3934/mbe.2011.8.385


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