Impact of self-medication and hospitalization on pneumonia transmission: a mathematical modeling approach

Abstract

Pneumonia continues to pose a significant public health challenge, with treatment behaviors such as self-medication and hospitalization playing critical roles in disease control. This study developed a mathematical model to investigate the impact of these two treatment strategies on pneumonia transmission. The basic reproduction number (R₀) was computed using next generation matrix method, the disease-free equilibrium is locally and asymptotically when R₀<1 and unstable when   stable R₀> 1 revealing that  under effective hospitalization, while high reliance on self-medication promotes a stable endemic state. Sensitivity analysis showed that parameters representing the contact rate between susceptible and infected individuals and the progression from exposed to actively infected individuals increased disease spread, whereas hospitalization and vaccination rates reduced transmission. Numerical simulations confirmed that high rates of self-medication prolong infection and increase overall disease burden, while hospitalization and vaccination significantly reduce infections and accelerate recovery. Based on these findings, the study recommends improving access to hospitals, expanding vaccination coverage, and conducting public awareness campaigns to discourage self-medication.