College of Science, University of Shanghai for Science and Technology, Shanghai, People's Republic of China.
College of Mathematics and Information Science, Henan Normal University, Xinxiang, People's Republic of China.
J Biol Dyn. 2020 Dec;14(1):116-142. doi: 10.1080/17513758.2020.1726516.
We propose a model of a joint spread of heroin use and HIV infection. The unique disease-free equilibrium always exists and it is stable if the basic reproduction numbers of heroin use and HIV infection are both less than 1. The semi-trivial equilibrium of HIV infection (heroin use) exists if the basic reproduction number of HIV infection (heroin use) is larger than 1 and it is locally stable if and only if the invasion number of heroin use (HIV infection) is less than 1. When both semi-trivial equilibria lose their stability, a coexistence equilibrium occurs, which may not be unique. We compare the model to US data on heroin use and HIV transmission. We conclude that the two diseases in the US are in a coexistence regime. Elasticities of the invasion numbers suggest two foci for control measures: targeting the drug abuse epidemic and reducing HIV risk in drug-users.
我们提出了一个海洛因使用和 HIV 感染共同传播的模型。如果海洛因使用和 HIV 感染的基本再生数都小于 1，则存在唯一的无病平衡点，且该平衡点是稳定的。如果 HIV 感染（海洛因使用）的基本再生数大于 1，则 HIV 感染的半平凡平衡点（海洛因使用）存在，且该平衡点在入侵数（海洛因使用）小于 1 时是局部稳定的。当两个半平凡平衡点失去稳定性时，会出现共存平衡点，且该平衡点可能不唯一。我们将模型与美国的海洛因使用和 HIV 传播数据进行了比较。我们的结论是，美国的这两种疾病处于共存状态。入侵数的弹性表明控制措施有两个重点：针对吸毒流行和降低吸毒者的 HIV 风险。
