Model Matematika SEIRS Penyebaran Penyakit Pneumonia pada Balita dengan Pengaruh Vaksinasi

Abstract

This research aims to establish a model for the spread of pneumonia in infants with SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) type, analyze the model, and determine the minimum proportion of vaccinations. This model is divided into four classes, namely susceptible, infected but not yet active, infected, and cured. The stability analysis of the model was carried out disease-free and endemic by showing the stability of asymptotes in both, meaning that the disease would not disappear but with complete vaccine administration it could reduce the number of pneumonia spreads. The basic reproduction number for disease-free and endemic simulations is greater than 1 if the vaccine is incomplete and less than 1 if the vaccine is given completely