Mathematical Modeling of Pneumonia Spread in Toddlers with the Influence of Vaccination in Makassar City and Batik Motifs from the Simulation

Abstract

Pneumonia remains one of the leading causes of death in children under five years of age in Indonesia, especially in the city of Makassar. This study aims to model the dynamics of pneumonia transmission in toddlers by considering the effect of vaccination as a preventive intervention, using an SEIR (Susceptible–Exposed–Infected Recovered) mathematical model framework. Numerical simulations were conducted to analyze the temporal evolution of the population, with results showing that, without vaccination, the infected population increased sharply before reaching equilibrium. Conversely, the implementation of higher vaccination coverage significantly reduced the peak of infection and accelerated epidemic stabilization, emphasizing the important role of vaccination in controlling the spread of pneumonia. Furthermore, the simulation results were interpreted into batik motifs that adopted layered wave patterns with gradient colors, symbolizing the transition from susceptibility to recovery, and expressing the harmony between science and art.