Tasman Hengki
Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia.
Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Indonesia, Depok 16424, Indonesia.
Math Biosci. 2015 Apr;262:73-9. doi: 10.1016/j.mbs.2014.12.005. Epub 2015 Jan 30.
This paper presents a mathematical model of malaria transmission considering the resistance of malaria parasites to the anti-malarial drugs. The model also incorporates mass treatment and insecticide as control strategies. We consider the sensitive and resistant strains of malaria parasites in human and mosquito populations. First, we investigated the existence and stability of equilibria of the model without control based on two basic reproduction ratios corresponding to the strains. Then, the Pontryagins Maximum Principle is applied to derive the necessary conditions for optimal control. Simulation results show the effectiveness of the optimal control to reduce the number of infected hosts and vectors.
本文提出了一个考虑疟原虫对抗疟药物耐药性的疟疾传播数学模型。该模型还纳入了群体治疗和杀虫剂作为控制策略。我们考虑了人类和蚊子群体中疟原虫的敏感株和耐药株。首先，我们基于对应于这些株的两个基本繁殖率，研究了无控制情况下模型平衡点的存在性和稳定性。然后，应用庞特里亚金极大值原理来推导最优控制的必要条件。模拟结果表明了最优控制在减少感染宿主和病媒数量方面的有效性。
