Tilahun Getachew Teshome, Makinde Oluwole Daniel, Malonza David
a Pan African University Institute of Basic Sciences Technology and Innovation , Nairobi , Kenya.
b Faculty of Military Science , Stellenbosch University , Stellenbosch , South Africa.
J Biol Dyn. 2017 Aug;11(sup2):400-426. doi: 10.1080/17513758.2017.1337245. Epub 2017 Jun 14.
We propose and analyse a nonlinear mathematical model for the transmission dynamics of pneumonia disease in a population of varying size. The deterministic compartmental model is studied using stability theory of differential equations. The effective reproduction number is obtained and also the asymptotic stability conditions for the disease free and as well as for the endemic equilibria are established. The possibility of bifurcation of the model and the sensitivity indices of the basic reproduction number to the key parameters are determined. Using Pontryagin's maximum principle, the optimal control problem is formulated with three control strategies: namely disease prevention through education, treatment and screening. The cost-effectiveness analysis of the adopted control strategies revealed that the combination of prevention and treatment is the most cost-effective intervention strategies to combat the pneumonia pandemic. Numerical simulation is performed and pertinent results are displayed graphically.
我们提出并分析了一个用于不同规模人群中肺炎疾病传播动力学的非线性数学模型。利用微分方程的稳定性理论研究了确定性 compartmental 模型。获得了有效再生数，并建立了无病平衡点和地方病平衡点的渐近稳定性条件。确定了模型分岔的可能性以及基本再生数对关键参数的敏感性指标。利用庞特里亚金极大值原理，制定了具有三种控制策略的最优控制问题：即通过教育、治疗和筛查进行疾病预防。对所采用的控制策略进行的成本效益分析表明，预防和治疗相结合是抗击肺炎大流行最具成本效益的干预策略。进行了数值模拟，并以图形方式展示了相关结果。
