Modelling and optimal control of pneumonia disease with cost-effective strategies
Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
Informa UK Limited, trading as Taylor & Francis Group
Abstract
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.
Description
CITATION: Tilahun, G. T., Makinde, O. D. & Malonza, D. 2017. Modelling and optimal control of pneumonia disease with cost-effective strategies. Journal of Biological Dynamics, 11(S2):400-426, doi:10.1080/17513758.2017.1337245.
The original publication is available at https://www.tandfonline.com
The original publication is available at https://www.tandfonline.com
Keywords
Pneumonia, Pulmonary fibrosis, Pneumonia, Pneumococcal
Citation
Tilahun, G. T., Makinde, O. D. & Malonza, D. 2017. Modelling and optimal control of pneumonia disease with cost-effective strategies. Journal of Biological Dynamics, 11(S2):400-426, doi:10.1080/17513758.2017.1337245