Mathematical Analysis of a Reaction-Diffusion Pneumococcal Pneumonia Epidemic Model

Abstract

Pneumococcal pneumonia, caused by Streptococcuspneumoniae, remains a significant health threat, particularly for children, the elderly, and immunocompromised individuals. This study presents a reaction-diffusion model using partial differential equations. The model ensures the positivity and boundedness of all solutions. The model also exhibits both disease-free and endemic equilibrium solutions. The effective reproduction number, Reisderived and conditions for the asymptotic stability of both the disease-free and endemic equilibrium are established. Sensitivity analysis highlights the parameters which are critical in the disease transmission. Numerical simulations confirm the global asymptotic stability of the equilibrium points. The findings further indicate that a combined strategy of vaccination and treatment is more effective than treat mental one in controlling infections and curbing disease transmission, where elevated vaccine failure rates are observed to weaken the overall control efforts again stpneumococcalpneumonia