Browsing by Author "Tilahun, Getachew Teshome"
- ItemModelling and optimal control of pneumonia disease with cost-effective strategies(Informa UK Limited, trading as Taylor & Francis Group, 2017) Tilahun, Getachew Teshome; Makinde, Oluwole Daniel; Malonza, DavidWe 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.
- ItemModelling and optimal control of typhoid fever disease with cost-effective strategies(Hindawi Publishing Corporation, 2017-09) Tilahun, Getachew Teshome; Makinde, Oluwole Daniel; Malonza, DavidWe propose and analyze a compartmental nonlinear deterministic mathematical model for the typhoid fever outbreak and optimal control strategies in a community with varying population.The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The model exhibits a forward transcritical bifurcation and the sensitivity analysis is performed.The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies, namely, the prevention strategy through sanitation, proper hygiene, and vaccination; the treatment strategy through application of appropriate medicine; and the screening of the carriers. The cost functional accounts for the cost involved in prevention, screening, and treatment together with the total number of the infected persons averted. Numerical results for the typhoid outbreak dynamics and its optimal control revealed that a combination of prevention and treatment is the best cost-effective strategy to eradicate the disease.