Haramaya University, Department of Mathematics, Dire Dawa, Ethiopia.
Comput Math Methods Med. 2019 Sep 22;2019:2658971. doi: 10.1155/2019/2658971. eCollection 2019.
In this paper, we proposed a deterministic model of pneumonia-meningitis coinfection. We used a system of seven ordinary differential equations. Firstly, the qualitative behaviours of the model such as positivity of the solution, existence of the solution, the equilibrium points, basic reproduction number, analysis of equilibrium points, and sensitivity analysis are studied. The disease-free equilibrium is locally asymptotically stable if the basic reproduction number is kept less than unity, and conditions for global stability are established. Then, the basic model is extended to optimal control by incorporating four control interventions, such as prevention of pneumonia as well as meningitis and also treatment of pneumonia and meningitis diseases. The optimality system is obtained by using Pontryagin's maximum principle. For simulation of the optimality system, we proposed five strategies to check the effect of the controls. First, we consider prevention only for both diseases, and the result shows that applying prevention control has a great impact in bringing down the expansion of pneumonia, meningitis, and their coinfection in the specified period of time. The other strategies are prevention effort for pneumonia and treatment effort for meningitis, prevention effort for meningitis and treatment effort for pneumonia, treatment effort for both diseases, and using all interventions. We obtained that each of the listed strategies is effective in minimizing the expansion of pneumonia-only, meningitis-only, and coinfectious population in the specified period of time.
在本文中，我们提出了一种肺炎-脑膜炎合并感染的确定性模型。我们使用了一个由七个常微分方程组成的系统。首先，研究了模型的定性行为，如解的正定性、解的存在性、平衡点、基本再生数、平衡点分析和敏感性分析。如果基本再生数保持小于 1，则无病平衡点在局部渐近稳定，并且建立了全局稳定性的条件。然后，通过引入四种控制干预措施，如预防肺炎和脑膜炎以及治疗肺炎和脑膜炎疾病，将基本模型扩展到最优控制。利用庞特里亚金极大值原理得到最优系统。为了对最优系统进行模拟，我们提出了五种策略来检查控制效果。首先，我们考虑仅对两种疾病进行预防，结果表明，在规定的时间内，预防控制对降低肺炎、脑膜炎及其合并感染的蔓延有很大影响。其他策略包括预防肺炎和治疗脑膜炎、预防脑膜炎和治疗肺炎、治疗两种疾病以及使用所有干预措施。我们发现，列出的每种策略都能有效地将肺炎、脑膜炎和合并感染的人群在规定的时间内的扩张最小化。
