Modelling Vaccination and Treatment of Childhood Pneumonia and Their Implications
Cyrus Gitonga Ngari *
Department of Mathematics, Computing and Information Technology, University of Embu, P.O. BOX 6 – 60100, Embu, Kenya
*Author to whom correspondence should be addressed.
Abstract
This paper presents a deterministic model for pneumonia transmission and uses the model to assess the potential impact of the vaccination, treatment and efficacy of vaccination drugs in lowering the public health impact of the pneumonia disease. The model is based on the Susceptible-Vaccinated-Infected- Treated compartmental classes of children less than five years. There is possibility of the non-severely infected recovering from natural immunity. Model analysis indicates the system lie in the positive region, solution is bounded and there exist unique positive endemic equilibrium point whenever control reproduction number is greater than unity. Important epidemiological thresholds such as the basic and control reproduction number are determined. Disease-free point equilibrium points are determined. Local and Global stability of equilibrium points will be investigated. Sensitivity analysis of the reproduction numbers indicated higher vaccination drug efficacy vaccination, treatment and recoveries from natural immunity hold great promise in lowering pneumonia impact. Estimated numerical result indicated impact of treatment is positive. Numerical simulation was carried to predict the dynamics of the system.
Keywords: Deterministic model, vaccination, sensitivity and simulation