A Mathematical Model of Treatment and Vaccination Interventions of Pneumococcal Pneumonia Infection Dynamics

Abstract

Streptococcus pneumoniae is one of the leading causes of serious morbidity and mortality worldwide, especially in young children and the elderly. In this study, a model of the spread and control of bacterial pneumonia under public health interventions that involve treatment and vaccination is formulated. It is found out that the model exhibits the disease-free and endemic equilibria. The disease-free equilibrium is stable if and only if the basic reproduction number and the disease will be wiped out of the population. For ${\mathcal{R}}_{\mathrm{0}}\ge \mathrm{1},$ the endemic equilibrium is globally stable and the disease persists. We infer the effect of these interventions on the dynamics of the pneumonia through sensitivity analysis on the effective reproduction number ${\mathcal{R}}_e,$ from which it is revealed that treatment and vaccination interventions combined can eradicate pneumonia infection. Numerical simulation to illustrate the analytical results and establish the long term behavior of the disease is done. The impact of pneumonia infection control strategies is investigated. It is revealed that, with treatment and vaccination interventions combined, pneumonia can be wiped out. However, with treatment intervention alone, pneumonia persists in the population.