title: Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models.
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.
authors.affiliation: Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA. franke@math.ncsu.edu
authors.forename: John E
authors.initials: JE
authors.lastname: Franke
authors.forename: Abdul-Aziz
authors.initials: AA
authors.lastname: Yakubu
mesh_terms: D001699:Biometry; D004194:Disease; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D006801:Humans; D008433:Mathematics; D015233:Models, Statistical; D009026:Mortality