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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Franke, J.E., Yakubu, AA. Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models. J. Math. Biol. 57, 755–790 (2008). https://doi.org/10.1007/s00285-008-0188-9
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DOI: https://doi.org/10.1007/s00285-008-0188-9