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一类具有感染意识和人口移徒的HIV/AIDS传染病模型
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Abstract:
本文首先建立了一个具有感染意识和不具有感染意识、人口移徒的HIV/AIDS传染病模型。接着给出了基本再生数的解析表达式，并证明了无病平衡点的全局渐近稳定性和疾病的一致持久性。然后根据四川省2004~2018年实际的艾滋病人数量，利用MCMC算法确定模型的最佳参数值，并得到了基本再生数R0 = 2.95 (95% CI: (0.85~5.25))。最后，数值模拟表明感染意识进展率和移徒对艾滋病传播有重要的影响。
First, this paper establishes an HIV/AIDS epidemic model considering migration, with and without infection awareness. Then, the expression of the basic regeneration number is given, and the global asymptotic stability of the disease-free equilibrium and the uniform persistence of the disease are proved. Next, according to the number of AIDS patients in Sichuan Province from 2004 to 2018, the MCMC algorithm is used to determine the optimal parameter value of such model, and the basic re-generation number is R0 = 2.95 (95% CI: (0.85~5.25)). Finally, numerical simulations show that the rate of infection awareness progression and migration has important effects on HIV transmission.
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