In this paper, we study the dynamics of soil-transmitted helminth infection. We formulate and analyse a deterministic compartmental model using nonlinear differential equations. The basic reproduction number is obtained and both disease-free and endemic equilibrium points are shown to be asymptotically stable under given threshold conditions. The model may exhibit backward bifurcation for some parameter values, and the sensitivity indices of the basic reproduction number with respect to the parameters are determined. We extend the model to include control measures for eradication of the infection from the community. Pontryagian’s maximum principle is used to formulate the optimal control problem using three control strategies, namely, health education through provision of educational materials, educational messages to improve the awareness of the susceptible population, and treatment by mass drug administration that target the entire population(preschool- and school-aged children) and sanitation through provision of clean water and personal hygiene. Numerical simulations were done using MATLAB and graphical results are displayed. The cost effectiveness of the control measures were done using incremental cost-effective ratio, and results reveal that the combination of health education and sanitation is the best strategy to combat the helminth infection. Therefore, in order to completely eradicate soil-transmitted helminths, we advise investment efforts on health education and sanitation controls.

中文翻译：

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土源性蠕虫感染最佳控制的数学模型。


在本文中，我们研究了土源性蠕虫感染的动态。我们使用非线性微分方程制定并分析确定性隔室模型。获得了基本繁殖数，并且在给定阈值条件下，无病平衡点和地方病平衡点都显示出渐近稳定。模型对于某些参数值可能会出现后向分叉，并确定基本再生数对于这些参数的敏感指数。我们扩展了该模型，包括消除社区感染的控制措施。庞特里亚吉安极大值原理提出了最优控制问题，采用三种控制策略，即通过提供教育材料进行健康教育、提高易感人群意识的教育信息以及针对整个人群（学前班）的大规模药物管理治疗。 - 和学龄儿童）以及通过提供清洁水和个人卫生来实现卫生。使用 MATLAB 进行数值模拟并显示图形结果。使用增量成本效益比来评估控制措施的成本效益，结果表明，健康教育和卫生设施相结合是对抗蠕虫感染的最佳策略。因此，为了彻底根除土源性蠕虫，我们建议在健康教育和卫生控制方面进行投资。