考虑气候变率的疟疾传播建模与最优控制分析

IF 0.9 Q3 MATHEMATICS, APPLIED
Temesgen Duressa Keno, Lemessa Bedjisa Dano, Oluwole Daniel Makinde
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引用次数: 0

摘要

在本文中,我们提出了一个非线性确定性数学模型疟疾传播动力学纳入气候变化作为一个因素。首先,我们展示了解的有限区域和非负性,这表明该模型具有生物学相关性和数学上的良好定姿。采用新一代矩阵法确定了基本再现数,并研究了模型参数的灵敏度,确定了影响最大的参数。利用雅可比矩阵和李雅普诺夫函数说明平衡位置的局部稳定性和全局稳定性。如果基本繁殖数小于1,则无病平衡点是局部和全局渐近稳定的,否则发生地方性平衡。该模型具有正向分岔和后向分岔。此外,我们应用最优控制理论描述了包含三个控制的最优控制模型,即使用处理过的蚊帐、使用抗疟药物治疗感染者和室内残留喷洒策略。引入庞特里亚金极大值原理,得到了最优控制问题的必要条件。最后,通过优化系统的数值模拟和成本-效果分析表明,处理过的蚊帐与治疗相结合是减少疟疾的最优、成本最小的策略。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Modeling and Optimal Control Analysis for Malaria Transmission with Role of Climate Variability

Modeling and Optimal Control Analysis for Malaria Transmission with Role of Climate Variability

In this paper, we present a nonlinear deterministic mathematical model for malaria transmission dynamics incorporating climatic variability as a factor. First, we showed the limited region and nonnegativity of the solution, which demonstrate that the model is biologically relevant and mathematically well-posed. Furthermore, the fundamental reproduction number was determined using the next-generation matrix approach, and the sensitivity of model parameters was investigated to determine the most affecting parameter. The Jacobian matrix and the Lyapunov function are used to illustrate the local and global stability of the equilibrium locations. If the fundamental reproduction number is smaller than one, a disease-free equilibrium point is both locally and globally asymptotically stable, but endemic equilibrium occurs otherwise. The model exhibits forward and backward bifurcation. Moreover, we applied the optimal control theory to describe the optimal control model that incorporates three controls, namely, using treated bed net, treatment of infected with antimalaria drugs, and indoor residual spraying strategy. The Pontryagin’s maximum principle is introduced to obtain the necessary condition for the optimal control problem. Finally, the numerical simulation of optimality system and cost-effectiveness analysis reveals that the combination of treated bed net and treatment is the most optimal and least-cost strategy to minimize the malaria.

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