Analytical Model for Childhood Pneumonia, a Case Study of Kenya
C. G. Ngari *
School of the Biological and Physical Sciences, Moi University, P.O.Box 3900-30100, Eldoret, Kenya.
G. P. Pokhariyal
School of Mathematics, University of Nairobi, P.O.Box 30197-00100 GPO, Nairobi, Kenya.
J. K. Koske
School of the Biological and Physical Sciences, Moi University, P.O.Box 3900-30100, Eldoret, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Pneumonia is an infection of the lungs that is caused by bacteria, viruses, fungi, or parasites. For a long time to the best of our knowledge there have not been reliable mathematical model for childhood pneumonia in Kenya. This research study developed a deterministic model based on the Susceptible-Vaccinated-Infected-Treated-Recovered-Susceptible compartment classes. The study used the partial differentiation of control reproduction number (RC) toinvestigate effects of; environment, efficacy of vaccination drug and treatment. Model analysis indicates the system lie in feasible region, it is bounded, has no backward bifurcation and there exists unique endemic equilibrium point when control reproduction number is greater than unity. Local and global stability of the equilibrium points indicated that control reproduction has to be maintained at less than unity to eradicate the disease. Sensitivity analysis of the control reproduction number indicates that improved vaccination drug’s efficacy, attaining herd immunity, higher treatment rates and lower effects of environment are the best intervention strategies to lower impact of the pneumonia of the children under the age of five years in Kenya.
Keywords: Control reproduction number, herd immunity, sensitivity analysis, disease free equilibrium point (DFE), endemic equilibrium point (EEP), local and global stability.