Mathematical Analysis of a Reaction‐Diffusion Pneumococcal Pneumonia Epidemic Model

Pneumococcal pneumonia, caused by Streptococcus pneumoniae , 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, is derived 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 treatment alone in controlling infections and curbing disease transmission, whereas elevated vaccine failure rates are observed to weaken the overall control efforts against pneumococcal pneumonia.