具有异质空间扩散的梅毒模型的阈值动力学分析与仿真

数学物理学报 ›› 2024, Vol. 44 ›› Issue (5): 1352-1367.

具有异质空间扩散的梅毒模型的阈值动力学分析与仿真

吴鹏¹(),方诚^2,^*()

¹杭州电子科技大学理学院杭州 310018
²浙江财经大学数据科学学院杭州 310018

收稿日期:2023-07-11 修回日期:2024-04-16 出版日期:2024-10-26 发布日期:2024-10-16
通讯作者: *方诚, E-mail: fangcheng12@zufe.edu.cn
作者简介:吴鹏, E-mail: hzpengwu@163.com
基金资助:
国家自然科学基金(12201557);国家自然科学基金(12001483);浙江省教育厅一般项目(Y202249921);安徽省自然科学基金(2108085MA10)

Dynamical Analysis and Numerical Simulation of a Syphilis Epidemic Model with Heterogeneous Spatial Diffusion

Wu Peng¹(),Fang Cheng^2,^*()

¹School of Sciences, Hangzhou Dianzi University, Hangzhou 310018
²School of Data Sciences, Zhejiang University of Finance and Economics, Hangzhou 310018

Received:2023-07-11 Revised:2024-04-16 Online:2024-10-26 Published:2024-10-16
Supported by:
NSFC(12201557);NSFC(12001483);Foundation of Zhejiang Provincial Education Department(Y202249921);Anhui Provincial Natural Science Foundation(2108085MA10)

摘要/Abstract

摘要：

为了研究个体扩散和空间异质环境对梅毒传播的影响, 该文构建了一类具异质空间反应扩散梅毒动力学模型. 首先, 研究了模型的适定性问题, 包括解的全局存在性、系统的耗散性和解半流吸引子存在性; 其次利用下一代再生算子定义推导出模型的基本再生数 $R_0$ 的泛函表达式; 再次, 讨论了系统解关于阈值-$R_0$ 的动力学行为, 具体地, 当 $R_0>1$ 时, 无病平衡态是全局稳定的, 当 $R_0>1$ 时, 系统是一致持久的. 在特殊情形下, 还证明了系统常数正平衡点的存在唯一性和全局稳定性. 最后, 通过数值模拟验证了理论结果并分析了空间因素对梅毒传播的影响. 数值结果表明: (1) 加强对隐性梅毒感染者的治疗可以有效地降低梅毒在人群中传播的风险; (2) 忽略空间异质性将会低估梅毒的流行趋势. 另外, 个体扩散率对梅毒传播的影响同样也是不容忽视的.

关键词: 梅毒, 反应扩散模型, 空间异质, 基本再生数, 阈值动力学, 数值模拟

Abstract:

To study the effects of individual diffusion and spatial heterogeneity on the transmission of syphilis, we construct a heterogeneous spatial reaction diffusion model of syphilis. Firstly, the well posed problem of the model is studied, including the global existence of the solution, the dissipativity of the system and the existence of the attractor for the semiflow; Secondly, based on the definition of the next generation regeneration operator, we derive the functional expression of the basic regeneration number $R_0$; Thirdly, we discussed the dynamical behaviors of the solution regarding the threshold-$R_0 $, specifically, when $R_0>1$, the disease-free steady state is globally stable, when $R_0>1 $, the system is uniformly persistent. In special cases, we also prove the existence, uniqueness, and global stability of the positive equilibrium of the system. Finally, the theoretical results were validated and the influence of spatial factors on the transmission of syphilis was analyzed through numerical simulation. Our numerical results indicate that: (1) strengthening the treatment of early latent syphilis carriers can effectively reduce the risk of syphilis transmission among population; (2) Ignoring spatial heterogeneity will underestimate the epidemic trend of syphilis. In addition, the impact of individual diffusion rate on the transmission of syphilis cannot be ignored.

Key words: Syphilis, Reaction-diffusion model, Spatial heterogeneity, Basic reproduction number, Threshold dynamics, Numerical simulation

中图分类号:

O175.23

吴鹏, 方诚. 具有异质空间扩散的梅毒模型的阈值动力学分析与仿真[J]. 数学物理学报, 2024, 44(5): 1352-1367.

Wu Peng, Fang Cheng. Dynamical Analysis and Numerical Simulation of a Syphilis Epidemic Model with Heterogeneous Spatial Diffusion[J]. Acta mathematica scientia,Series A, 2024, 44(5): 1352-1367.

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