A new model of the impact of chronic hepatitis C and its treatment on the development of tuberculosis: An optimal control and sensitivity analysis

Q3 Mathematics

Results in Control and Optimization Pub Date : 2025-05-19 DOI:10.1016/j.rico.2025.100574

Chaimae El Mourabit, Nadia Idrissi Fatmi

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Abstract

This study offers a mathematical model with eight compartments that explain how tuberculosis spreads among individuals afflicted with HCV. The novelty of this work comes through mathematical modeling of the dynamics of tuberculosis in HCV cases on the one hand and in patients receiving DAA treatment on the other. We analyze the formulated model by proving a solution’s existence and showing the system solution’s positivity and boundedness. Furthermore, the model is reconstructed as an optimal control issue, considering three controls (consciousness, treatment, and early detection) to decrease the prevalence of tuberculosis in HCV-infected people, utilizing Pontryagin’s maximum principle. Finally, numerical simulations are performed using MATLAB, and the outcomes validate that treatment combined with early detection and consciousness reduces the spread of tuberculosis among individuals affected with HCV compared to scenarios without control, leading to improved overall outcomes.

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慢性丙型肝炎及其治疗对结核病发展影响的新模型：最优控制和敏感性分析

这项研究提供了一个有8个区室的数学模型来解释结核病是如何在HCV患者中传播的。这项工作的新颖之处在于，一方面是通过对HCV病例和接受DAA治疗的患者的结核病动态进行数学建模。我们通过证明解的存在性和系统解的正性和有界性来分析模型。进一步，利用Pontryagin的最大值原理，将模型重构为一个最优控制问题，考虑意识、治疗和早期发现三个控制因素，以降低hcv感染者的结核病患病率。最后，使用MATLAB进行数值模拟，结果验证了与不加控制的情况相比，治疗结合早期发现和意识减少了HCV患者中结核病的传播，从而改善了总体结果。

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