Bonyah Ebenezer, Khan Muhammad Altaf, Okosun K O, Islam Saeed
Department of Mathematics and Statistics, Kumasi Technical University, Kumasi, Ghana.
Department of Mathematics, Vaal University of Technology, Vanderbijlpark, South Africa.
PLoS One. 2017 Oct 4;12(10):e0185540. doi: 10.1371/journal.pone.0185540. eCollection 2017.
In this paper, we present and analyze an SEIR Zika epidemic model. Firstly, we investigate the model with constant controls. The steady states of the model is found to be locally and globally asymptotically stable. Thereafter, we incorporate time dependent controls into the model in order to investigate the optimal effects of bednets, treatments of infective and spray of insecticides on the disease spread. Furthermore, we used Pontryagin's Maximum Principle to determine the necessary conditions for effective control of the disease. Also, the numerical results were presented.
在本文中，我们提出并分析了一个寨卡病毒流行的SEIR模型。首先，我们研究了具有恒定控制措施的模型。发现该模型的稳态在局部和全局都是渐近稳定的。此后，我们将与时间相关的控制措施纳入模型，以研究蚊帐、感染治疗和杀虫剂喷洒对疾病传播的最佳效果。此外，我们使用庞特里亚金极大值原理来确定有效控制该疾病的必要条件。同时，还给出了数值结果。
