School of Mathematics & Data Science, Shaanxi University of Science and Technology, Xi'an, 710021, China.
J Biol Phys. 2024 Nov 27;51(1):4. doi: 10.1007/s10867-024-09667-1.
In this paper, the dynamic behaviors of tuberculosis in the context of indirect environmental transmission are discussed by establishing the SEIRB epidemic model. The basic reproduction number is computed by employing the next-generation matrix approach. The global stability of disease-free equilibrium and endemic equilibrium is proved by constructing the Lyapunov function and the application of LaSalle's invariance principle. It shows that when the basic reproduction number is greater than 1, tuberculosis will spread among the population. When the basic reproduction number is less than 1, tuberculosis will disappear. Finally, an optimal control problem is constructed by using the extended model, which reveals the spread of tuberculosis can be effectively controlled by eliminating Mycobacterium tuberculosis in the environment and controlling tuberculosis patients at the same time. Numerical example results show the effectiveness of the optimization strategies.
本文通过建立 SEIRB 传染病模型，讨论了间接环境传播背景下结核病的动态行为。利用下一代矩阵方法计算了基本再生数。通过构造李雅普诺夫函数和应用拉塞尔不变原理，证明了无病平衡点和地方病平衡点的全局稳定性。结果表明，当基本再生数大于 1 时，结核病将在人群中传播。当基本再生数小于 1 时，结核病将消失。最后，通过使用扩展模型构建了一个最优控制问题，揭示了通过消除环境中的结核分枝杆菌和同时控制结核病患者，结核病的传播可以得到有效控制。数值实例结果表明了优化策略的有效性。
