Analysis of Pneumonia Transmission Dynamics in Under-Five Children Using an SEITR Model with Awareness and Vaccination

Abstract

Pneumonia remains one of the leading causes of mortality among children under five in Indonesia. This study investigates the transmission dynamics of pneumonia among the Indonesian under-five population using a compartmental SEITR (Susceptible–Exposed–Infected–Treated–Recovered) mathematical model incorporating caregiver awareness and vaccination. The study aims to analyze the equilibrium points and their stability, sensitivity of the model with respect to parameters affecting the basic reproduction number  and model behavior under various intervention scenarios through numerical simulations. The analysis includes the determination of equilibrium points, derivation of the basic reproduction number, local asymptotic stability analysis using linearization and the Routh–Hurwitz criterion, and sensitivity analysis. The results show that under the parameter values representing the Indonesian population, , and the analysis establishes the existence and stability conditions of the disease-free and endemic equilibria. Under these conditions, the disease-free equilibrium is unstable, whereas the endemic equilibrium is locally asymptotically stable, indicating that pneumonia tends to persist in the population. Sensitivity analysis reveals that the effective contact rate  is the most influential parameter in increasing , whereas the vaccination rate  has the greatest negative sensitivity effect . Numerical simulations demonstrate that increasing caregiver awareness to  with the vaccination rate maintained at  reduces  to , whereas increasing the vaccination rate alone without enhancing awareness is insufficient to achieve a disease-free state under the simulated scenarios. These findings indicate that increasing caregiver awareness, combined with vaccination, is an effective strategy for reducing pneumonia transmission among children under five.