The Impact of Protection Measures and Treatment on Pneumonia Infection: A Mathematical Model Analysis supported by Numerical Simulation

Abstract

In this study, we analyzed a nonlinear deterministic mathematical model for assessing the impacts of vaccination, other protection measures and treatment on the transmission of pneumonia in a population of varying size. Our model exhibits disease-free equilibrium, and endemic equilibrium point(s). Using center manifold criteria, we verified that the pneumonia model exhibits backward bifurcations R_P < 1 and the model shows the existence of more than one endemic equilibrium point where some of which are stable and others are unstable. Thus, the necessity of? R?_P<1, although essential, might not be enough to completely eradicate the disease from the community. Our examination of sensitivity analysis shows that the transmission rate ? plays a crucial role to change the qualitative dynamics of the pneumonia infection. Using data from published literature, numerical computations show that the numerical value of the effective reproduction number is R_P=8.31 at ? = 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.

A mathematical model for varicella-zoster and HIV co-dynamic supported by numerical simulations

“…It is also the infection of a single host by two or more pathogen variants (strains) or two or more distinct pathogen species. Co-infection with multiple pathogen strains is especially common in pneumonia, but it can occur in a variety of other diseases as well [7][8][9]. Super-infection is described as a subsequent infection with a different strain and the ensuing immune response [9].…”

“…Co-infection with multiple pathogen strains is especially common in pneumonia, but it can occur in a variety of other diseases as well [7][8][9]. Super-infection is described as a subsequent infection with a different strain and the ensuing immune response [9]. The concept of co-infection extends to the infection of a single host by multiple variants (strains) of a pathogen or even by different species of pathogens.…”

“…The successive introduction of diverse strains presents a distinct set of challenges and elicits responses within the host organism, thereby adding to the overall complexity of infectious diseases. [9].…”

COVID-19 and syphilis co-dynamic analysis using mathematical modeling approach

“…Mathematical modeling approach research done by scholars using a deterministic method [10,14], a stochastic method [7,22], or a fractional order method [23][24][25][26][27][28][29][30][31][32] has made a great contribution to linking the scientific approach with real-world physical situations and also for the decision-making process for solving real-world problems [33]. Different scholars have formulated and analyzed mathematical models on COVID-19 transmission [7, 8, 22, 24-26, 29, 30, 34-37], syphilis transmission [10,[17][18][19]23], and other infectious diseases transmission [20, 21,27,28,33,[38][39][40]; however, no one has done analysis on COVID-19 and syphilis co-infection transmission dynamics.…”