School of Computational and Communication Science and Engineering, The Nelson Mandela African, Institution of Science and Technology, P.O. Box 447, Arusha-, Tanzania.
Department of Computer Systems and Mathemmatics, Ardhi University, P.O. Box 35176, Dar es Salaam, Tanzania.
Comput Math Methods Med. 2020 Aug 1;2020:6721919. doi: 10.1155/2020/6721919. eCollection 2020.
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.
在本文中，我们研究了土壤传播性蠕虫感染的动力学。我们使用非线性微分方程来制定和分析确定性房室模型。得到了基本再生数，并且在给定的阈值条件下，证明了无病平衡点和地方病平衡点都是渐近稳定的。对于某些参数值，模型可能表现出后向分歧，并且确定了基本再生数对参数的敏感性指数。我们将模型扩展到包括从社区根除感染的控制措施。使用 Pontryagin 的最大原理，通过三种控制策略制定最优控制问题，即通过提供教育材料进行健康教育、通过提高易感人群的意识进行教育信息传播、以及针对全体人群（学龄前和学龄儿童）的大规模药物治疗和通过提供清洁水和个人卫生来进行卫生措施。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对控制措施的成本效益进行了评估，结果表明，健康教育和卫生措施的结合是对抗蠕虫感染的最佳策略。因此，为了彻底根除土壤传播性蠕虫，我们建议在健康教育和卫生措施方面投入努力。
