We formulate and analyze a deterministic mathematical model for the transmission dynamics of schistosomiasis with treatment of both humans and bovines and mollu-sciciding of the contaminated environment. The model effective reproduction number is derived and analytical results show that the disease-free and endemic equilibria are both locally and globally asymptotically stable. Pontryagin’s Maximum Principle which uses both Lagrangian and Hamiltonian principles with respect to a time-dependent constant is used to establish the existence of the optimal control problem and to derive the necessary conditions for optimal control of the disease. Mollusciciding of the contaminated environment has a major impact on disease control. However, combining it with treatment could help mitigate the spread of the disease compared to applying each control measure individually. Numerical simulations are performed to support theoretical results.

中文翻译：

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人-牛血吸虫病模型的最优控制分析

我们制定并分析了血吸虫病传播动力学的确定性数学模型，包括对人和牛的治疗以及对受污染环境的杀软体动物。推导出模型有效繁殖数，分析结果表明，无病和地方病平衡是局部和全局渐近稳定的。Pontryagin 最大原理使用拉格朗日和哈密顿原理关于时间相关常数来确定最优控制问题的存在，并推导疾病最优控制的必要条件。受污染环境的软体动物杀灭对疾病控制具有重大影响。然而，与单独应用每种控制措施相比，将其与治疗相结合有助于减轻疾病的传播。进行数值模拟以支持理论结果。