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

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

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

Received  February 2010 Revised  August 2010 Published  April 2011

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