提出了一种具有疫苗接种和有限医疗资源的离散流行病模型,以了解其潜在的动力学。该模型产生了一个非平滑的二维图,该图表现出令人惊讶的动力学行为阵列,包括前后分叉和周期加倍路径到混沌的现象,在不变区域中具有可行的参数。我们证明,除其他外,在免疫接种率低的情况下,随着疾病的传播率或基本繁殖次数逐渐增加,该模型产生上述现象,疫苗失败率高,医疗资源有限。最后,提供了数值模拟来说明我们的主要结果。
A discrete epidemic model with vaccination and limited medical resources is proposed to understand its underlying dynamics. The model induces a nonsmooth two dimensional map that exhibits a surprising array of dynamical behavior including the phenomena of the forward-backward bifurcation and period doubling route to chaos with feasible parameters in an invariant region. We demonstrate, among other things, that the model generates the above described phenomena as the transmission rate or the basic reproduction number of the disease gradually increases provided that the immunization rate is low, the vaccine failure rate is high and the medical resources are limited. Finally, the numerical simulations are provided to illustrate our main results.