|
| 摘要: |
| 本文研究了一类具有性别结构的淋病SIRS传染病模型稳定性的相关问题,考虑了同性与异性的性行为对淋病传播动力学的影响.首先证明了模型解的非负和有界性.其次,通过下一代矩阵的方法计算出基本再生数R0.此外,基于基本再生数并利用比较原理和持久性相关理论证明了当R0<1时,无病平衡点的全局渐近稳定性;当R0>1时,模型一致持续且存在正平衡点.进一步,当淋病具有永久免疫力时,通过构造Lyapunov函数的方法证明了地方病平衡点的全局渐近稳定性.最后利用数值模拟演示了理论结果的有效性,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 |
| 基金项目:国家自然科学基金项目资助(12261087),新疆维吾尔自治区自然科学杰出青年基金资助(2022D01E41),新疆维吾尔自治区天山英才领军人才项目资助(2023TSYCLJ0054). |
|
| STUDY ON A GONORRHEA TRANSMISSION SIRS MODEL WITH SEXED-STRUCTURE |
|
YANG Huan,WU Hao,DING Rui-di,ZHANG Long
|
| 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 nonnegativity and boundedness of the solutions for the model are proved. Second, the basic reproduction number R0 is computed by the next-generation matrix method. Furthermore, based on the basic reproduction number, and using the comparison principle and persistence related theory, it is proved that the disease-free equilibrium is globally asymptotically stable when R0 < 1 ; and that the model is uniformly persistent and has at least one positive equilibrium when R0 > 1. In addition, the global asymptotic stability of the endemic equilibrium is obtained by constructing the Lyapunov function when gonorrhea is permanently immune. Finally, the validity of the theoretical results is demonstrated by numerical simulations, It is shown that effective control of the male patient population would substantially reduce the overall prevalence of gonorrhea in the general population. |
| Key words: gonorrhea|basic regeneration number|sexual structure|global stability|uniform persistence |
