论文标题
在具有两个意识层面的流行病模型中，极限周期的马鞍节点分叉
Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness
论文作者
论文摘要
在本文中，我们研究了具有两种意识的人的流行病模型中极限周期分叉的出现。除了最有意识的个体的警报衰减率以及较知的人的创造率外，所有过渡率都是恒定的，这取决于疾病的患病率，以非线性的方式。对于ODE模型，极限循环的数值计算及其稳定性的研究是通过Poincaré图进行的。此外，还获得了足够的条件，以实现流过的平衡。这些疾病涉及疾病的传播性与意识之间的自然关系。最后，在非常低的进口案例速率下对模型的随机模拟用于确认ODE模型溶液中观察到的双稳定性（流行平衡和极限循环）的情况。
In this paper we study the appearance of bifurcations of limit cycles in an epidemic model with two types of aware individuals. All the transition rates are constant except for the alerting decay rate of the most aware individuals and the rate of creation of the less aware individuals, which depend on the disease prevalence in a non-linear way. For the ODE model, the numerical computation of the limit cycles and the study of their stability are made by means of the Poincaré map. Moreover, sufficient conditions for the existence of an endemic equilibrium are also obtained. These conditions involve a rather natural relationship between the transmissibility of the disease and that of awareness. Finally, stochastic simulations of the model under a very low rate of imported cases are used to confirm the scenarios of bistability (endemic equilibrium and limit cycle) observed in the solutions of the ODE model.
