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| 摘要: |
| 本文建立了一类具有性别结构的淋病 SIRS 传染病模型, 考虑了同性与异性的性行为对疾病传播动力学的影响. 首先, 证明了模型解的非负和有界性并计算出基本再生数R0. 其次当 R0<1, 证明了无病平衡点局部及全局渐近稳定. 当R0>1, 模型一致持续且存在正平衡点. 当疾病具有永久免疫力时, 通过构造 Lyapunov 函数证明了地方病平衡点的全局渐近稳定性. 最后, 通过数值模拟演示了理论结果的有效性, 利用敏感性分析讨论了参数对基本再生数的影响. 研究表明有效控制男性患者人数将在很大程度上减少淋病在人口中的总体流行. |
| 关键词: 淋病, 基本再生数, 性别结构, 全局渐近稳定, 一致持续 |
| DOI： |
| 分类号:O175.1 |
| 基金项目:国家自然科学基金项目 (12261087), 新疆维吾尔自治区自然科学杰出青年基金 (2022D01E41), 新疆维吾尔自治区天山英才领军人才项目(2023TSYCLJ0054) |
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| Study on a gonorrhea transmission SIRS model with sexed-structure |
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YANG HUAN,ZHANG LONG
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| Abstract: |
| In this paper, a gonorrhea transmission SIRS model with sexual structure is proposed to characterize the effects of homeosexual and heterosexual behaviour on the transmission dynamics of disease. First, the basic reproduction number R0 is computed and the non-negativity and boundedness of the solution are proved. Second, it is shown that when R0<1, the disease-free equilibrium is locally and globally asymptotically stable. When R0>1, the system is uniformly persistent and there is at least one positive equilibrium. Under the given conditions, the global asymptotic stability of endemic equilibrium is proved by constructing Lyapunov functions. Finally, the validity of the theoretical results is demonstrated by numerical simulations, and the effect of parameters on the basic regeneration number is analysed by sensitivity analysis. |
| Key words: Gonorrhea, Basic regeneration number, Sexual structure, Global stability, Uniform persistence |
