Abstract
Some infectious diseases can cause individuals’ death, and aging factor is not negligible in the disease-induced death. In addition, incidence rate often plays a great role in modeling the spread of diseases. Hence, we consider two Susceptible–Infective–Recovered–Deceased–Susceptible (SIRDS) models with aging population factor and different incidence rates in this paper. The first model assumes the bilinear incidence rate, whereas the second model assumes the standard incidence rate. We investigate the dynamic properties of each model through both analytical and numerical approaches. Our results indicate that the dynamical properties of the first model are entirely dominated by the basic reproduction number, while additional condition is needed for the second one. Moreover, for the first model without vital dynamics and re-susceptibility, we derive an equation for the final size, analyze the solution of the implicit equation and identify some critical model parameters. Finally, numerical simulations are conducted to shed some light on the development of control strategies and to verify theoretical results.
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