疟疾和媒介传播疾病的耦合模型

Coupled Models of Malaria and Vector-Borne Disease

摘要: 为了更好地理解寄生虫进化对媒介传播疾病的影响，本文建立了一个包含寄生虫和媒介传播疾病的嵌套模型，对该模型的分析不是一件易事，我们用常微分方程模型描述了宿主内寄生虫和红细胞的相互作用。在宿主内模型中，除了无病平衡点外，还存在一个边界平衡点和一个唯一共存平衡点。当宿主内平衡点稳定时，宿主外的易感个体的死亡率和感染率也是不变的。通过考虑寄生虫和红细胞的感染期，构造了一个年龄结构的媒介传播疾病模型。对于宿主间模型，无病稳态局部稳定性和共存稳态的存在性取决于基本再生数。

Abstract: In order to better understand the impact of parasite evolution on vector-borne disease, a nested model containing parasites and vector-borne disease is established in this paper. It is not easy to analyze this model. We use an ordinary differential equation model to describe the interaction between parasites and red blood cells in the host. In addition to disease-free equilibrium, there is a boundary equilibrium and a unique coexistence equilibrium in the host model. When equilibrium is stable, the mortality and infection rates of susceptible individuals remain unchanged on the between host. An age-structured vector-borne disease model is constructed by the infection periods of parasites and red blood cells. For the between model, the local stability of disease-free steady state and the existence of coexistence steady state depend on the basic reproduction number.