标题： 一种考虑环境因素的人类和狗狂犬病传播动力学的数学与最优控制模型 显示英文标题

标题： A Mathematical and Optimal Control Model for Rabies Transmission Dynamics Among Humans and Dogs with Environmental Effects

摘要： 本研究提出一个确定性模型来研究狂犬病传播动力学，结合环境影响和控制策略，使用最优控制理论。 定性和定量分析表明，当有效繁殖数$\mathcal{R}_e < 1$时，无病平衡点是稳定的，而当$\mathcal{R}_e > 1$时，无病平衡点是不稳定的。 网格和等高线图说明$\mathcal{R}_e$与控制策略之间存在反比关系，包括犬类疫苗接种、健康促进和暴露后治疗。 增加干预措施会减少传播，而犬类之间的接触率较高会提高$\mathcal{R}_e$。 带有最优控制的数值模拟证实了综合策略的有效性。 疫苗接种和治疗被确定为在五年内实现狂犬病消除的关键干预措施。 显示英文摘要

摘要： This study presents a deterministic model to investigate rabies transmission dynamics, incorporating environmental effects and control strategies using optimal control theory. Qualitative and quantitative analyses reveal that the disease-free equilibrium is stable when the effective reproduction number $\mathcal{R}_e < 1$, and unstable when $\mathcal{R}_e > 1$. Mesh and contour plots illustrate an inverse relationship between $\mathcal{R}_e$ and control strategies, including dog vaccination, health promotion, and post-exposure treatment. Increased intervention reduces transmission, while higher contact rates among dogs raise $\mathcal{R}_e$. Numerical simulations with optimal control confirm the effectiveness of integrated strategies. Vaccination and treatment are identified as key interventions for achieving rabies elimination within five years.