Department of Mathematics, Pan African University Institute of Basic Sciences, Technology and Innovation, P.O. Box 62000-00200, Nairobi, Kenya.
Institute of Mathematical Sciences, Strathmore University, P.O. Box 59857-00200, Nairobi, Kenya.
Comput Math Methods Med. 2020 Mar 10;2020:5984095. doi: 10.1155/2020/5984095. eCollection 2020.
Influenza and pneumonia independently lead to high morbidity and mortality annually among the human population globally; however, a glaring fact is that influenza pneumonia coinfection is more vicious and it is a threat to public health. Emergence of antiviral resistance is a major impediment in the control of the coinfection. In this paper, a deterministic mathematical model illustrating the transmission dynamics of influenza pneumonia coinfection is formulated having incorporated antiviral resistance. Optimal control theory is then applied to investigate optimal strategies for controlling the coinfection using prevalence reduction and treatment as the system control variables. Pontryagin's maximum principle is used to characterize the optimal control. The derived optimality system is solved numerically using the Runge-Kutta-based forward-backward sweep method. Simulation results reveal that implementation of prevention measures is sufficient to eradicate influenza pneumonia coinfection from a given population. The prevention measures could be social distancing, vaccination, curbing mutation and reassortment, and curbing interspecies movement of the influenza virus.
流感和肺炎每年在全球人群中独立导致高发病率和死亡率；然而，一个明显的事实是，流感肺炎合并感染更为恶劣，这对公共卫生构成威胁。抗病毒药物耐药性的出现是控制合并感染的主要障碍。在本文中，我们建立了一个包含抗病毒药物耐药性的流感肺炎合并感染传播动力学的确定性数学模型。然后，应用最优控制理论，以患病率降低和治疗为系统控制变量，研究了控制合并感染的最优策略。庞特里亚金极大值原理用于刻画最优控制。使用基于龙格-库塔的前向-后向扫描方法对所得最优性系统进行数值求解。模拟结果表明，实施预防措施足以从给定人群中根除流感肺炎合并感染。预防措施可以是社交距离、疫苗接种、抑制突变和重配以及抑制流感病毒的种间运动。
