The Impact of Protection Measures and Treatment onPneumonia Infection Model

Abstract

Pneumonia has been a major airborne transmitted disease and continues to pose a major public health burden in both developed and developing countries of the world. In this study, we constructed and analyzed a nonlinear deterministic compartmental mathematical model for assessing the community-level impacts of vaccination, other protection measures like practicing good hygiene, avoiding close contacts with sick people and limiting exposure to cigarette smoke, etc. and treatment on the transmission dynamics of pneumonia disease in a population of varying size. Our model exhibits two kinds of equilibrium points: pneumonia disease-free equilibrium point, and pneumonia endemic equilibrium point(s). Using center manifold criteria, we have verified that the pneumonia model exhibits backward bifurcations whenever its effective reproduction number [R]P < 1 and in the same region, the model shows the existence of more than one endemic equilibrium point where some of which are stable and others are unstable. Thus, for pneumonia infection, the necessity of the pneumonia effective reproduction number [R]P < 1, although essential, it might not be enough to completely eradicate the pneumonia infection from the considered community. Our examination of sensitivity analysis shows that the pneumonia infection transmission rate denoted by {beta} plays a crucial role to change the qualitative dynamics of pneumonia infection. By taking standard data from published literature, our numerical computations show that the numerical value of pneumonia infection model effective reproduction number is [R]P = 8.31 at {beta} = 4.21 it implies that the disease spreads throughout the community. Finally, our numerical simulations show that protection, vaccination, and treatment against pneumonia disease have the effect of decreasing pneumonia expansion.