Mathematical modeling and analysis of pneumonia infection dynamics

Abstract

Pneumonia is one of the leading causes of death worldwide, especially among children below 5 years, the elderly above 65 years and people with weaker immune system. It is usually referred to as the “captain of the men of death" because of the great toll it exacted on humanity. In this work, we examined the dynamics of the pneumonia disease from a mathematical perspective via a deterministic SEIR model. This consists of investigating the equilibrium, basic reproduction number, stability analysis, and bifurcation analysis. It is observed that the pneumonia free equilibrium is locally asymptotically stable if the basic reproduction number is less than one, and the pneumonia endemic equilibrium is globally asymptotically stable in the invariant region if the basic reproduction number is greater than one. The sensitivity analysis revealed that the rate of transmission and the rate at which exposed individuals become infectious are the most sensitive parameters, and the bifurcation analysis via the centre manifold theory revealed the presence of forward bifurcation.