海洛因和HIV同时感染和传播的动力学行为
Dynamics of Heroin and HIV Co-Infection and Co-Transmission
摘要: 本文建立了一个包括海洛因和HIV共同传播的具有双线性发生率的疾病模型，对该模型的分析不是一件易事。我们分别得到了吸食海洛因和HIV感染的基本再生数，以及它们的入侵再生数。当吸食海洛因和HIV感染的基本再生数都小于1时，唯一的无病平衡点总是存在并且是稳定的。当HIV感染(吸食海洛因)的基本再生数小于1时，HIV感染(吸食海洛因)的边界平衡点存在，并且其局部稳定的充分条件是海洛因使用者(HIV感染)的入侵再生数小于1。最后，我们得到了决定共存平衡点存在与否的关系式。
Abstract: We present an epidemic model with bilinear incidence that incorporates the joint dynamics of heroin and HIV, a model that is hard to analyze. We compute independent reproductive numbers for heroin use (Ru) and HIV (Rv). We also get the invasion reproductive number of heroin addiction () and HIV infection () respectively. We obtain that the only one disease-free equilibrium always exists and it is stable if max{Ru,Rv}<1. The boundary equilibrium of HIV infection exists if Rv>1 and it is locally stable if and only if . And we can get that the boundary equilibrium of heroin use exists if Ru>1 and it is locally stable if and only if . Finally, we manage to obtain some relations that can be used to determine the existence of coexistence equilibrium.
文章引用：程焕焕. 海洛因和HIV同时感染和传播的动力学行为[J]. 应用数学进展, 2021, 10(4): 1016-1025. https://doi.org/10.12677/AAM.2021.104110

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