Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models |
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Authors: | John E Franke Abdul-Aziz Yakubu |
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Institution: | Department of Mathematics, North Carolina State University, Raleigh, NC, 27695-8205, USA, franke@math.ncsu.edu. |
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Abstract: | The dynamics of simple discrete-time epidemic models without disease-induced mortality are typically characterized by global transcritical bifurcation. We prove that in corresponding models with disease-induced mortality a tiny number of infectious individuals can drive an otherwise persistent population to extinction. Our model with disease-induced mortality supports multiple attractors. In addition, we use a Ricker recruitment function in an SIS model and obtained a three component discrete Hopf (Neimark-Sacker) cycle attractor coexisting with a fixed point attractor. The basin boundaries of the coexisting attractors are fractal in nature, and the example exhibits sensitive dependence of the long-term disease dynamics on initial conditions. Furthermore, we show that in contrast to corresponding models without disease-induced mortality, the disease-free state dynamics do not drive the disease dynamics. |
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Keywords: | Basin of attraction Disease-induced mortality Multiple attractors |
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