Data Sheet 1_A mathematical modeling and optimal control analysis of the effect of treatment-seeking behaviors on the spread of malaria.docx

Malaria, an infectious disease transmitted by mosquitoes and caused by the Plasmodium parasite, poses a significant global public health challenge, especially in areas lacking modern medical infrastructure. Traditional medicine often serves as either a primary or complementary treatment avenue. This study introduces a novel deterministic model that considers the impact of treatment seeking-behaviors on malaria transmission dynamics. Expanding upon the existing model, we incorporate distinct groups: individuals seeking treatment at health facilities and those self-treating with traditional remedies, which lack clinical validation. The study employs mathematical techniques for a comprehensive analysis of the model, including positivity, boundedness, existence and uniqueness, equilibrium, reproduction number, sensitivity, optimal control, and numerical simulations performed using MATLAB and the fourth-order Runge-Kutta method. Furthermore, we explore three time-dependent optimal control variables: antimalarial drug treatment, personal protective measures like ITNs, and promoting awareness to discourage inappropriate traditional medicine usage, all aimed at reducing disease transmission. Sensitivity analysis helps identify key parameters affecting malaria dynamics. Notably, increased utilization of health facilities for treatment significantly reduces the basic reproduction number, highlighting the importance of effective healthcare interventions. Numerical simulations underscore the vital role of treating infected individuals at health facilities in malaria eradication efforts. Optimal control analysis suggests that a combination of the three control strategies is most effective in combating malaria. This provides insights for public health policies to address the risk factors of using clinically not validated traditional medicine in malaria-endemic areas.

疟疾是由疟原虫（Plasmodium）寄生引发、经蚊虫叮咬传播的传染性疾病，对全球公共卫生构成严峻挑战，在缺乏现代医疗基础设施的地区尤为突出。传统医药常作为疟疾治疗的主要或辅助手段。本研究提出一种全新的确定性模型，用以探究就医行为对疟疾传播动力学的影响。本研究在现有模型基础上纳入两类明确群体：前往医疗机构就诊的患者，以及使用未经临床验证的传统疗法自行治疗的人群。本研究运用数学方法对该模型开展全面分析，涵盖解的正性、有界性、存在唯一性、平衡点、基本再生数、敏感性分析、最优控制以及采用MATLAB与四阶龙格-库塔法完成的数值模拟。此外，本研究设定三类时变最优控制变量：抗疟药物治疗、诸如经处理蚊帐（ITNs）之类的个人防护措施，以及开展宣传以劝阻不恰当使用传统医药的行为，所有策略均旨在降低疾病传播。敏感性分析可明确影响疟疾传播动力学的关键参数。值得注意的是，提升医疗机构就诊使用率可显著降低基本再生数，凸显了有效医疗干预措施的重要性。数值模拟结果证实，在医疗机构对感染者开展治疗在疟疾根除工作中发挥着关键作用。最优控制分析表明，联合使用上述三类控制策略在防控疟疾方面效果最佳。本研究结果可为公共卫生政策制定提供参考，以应对疟疾流行地区使用未经临床验证的传统医药所带来的风险因素。