SUSCEPTIBLE VACCINATED INFECTED RECOVERED MODEL WITH THE EXCLUSIVE BREASTFEEDING AND ITS APPLICATION TO PNEUMONIA DATA IN INDONESIA - Widyaningsih, Purnami; Musta'in, Ghufron; Saputro, Dewi Retno Sari (BAREKENG: Jurnal Ilmu Matematika dan Terapan, 2025)
The spread of infectious diseases can occur directly or indirectly. Pneumonia is an infectious respiratory tract disease. Indonesia is among the top 10 countries in the world concerning deaths caused by pneumonia. The spread of infectious diseases can be prevented through vaccination and exclusive breastfeeding, which play a role in providing body immunity. This study aims to formulate an SVIR model with exclusive breastfeeding, apply it to pneumonia in Indonesia, and determine its spread pattern and interpretation regarding the target of free pneumonia by 2030. The methods used were literature and applied studies. Through literature studies, the characteristics of infectious diseases were identified, assumptions and parameters of the model were added, and relationships between variables were determined. The applied method was to estimate the parameters and initial values of the model based on annual data on pneumonia disease in Indonesia. The formulated model is a system of first-order nonlinear differential equations. The model is applied to pneumonia based on annual data from 2013 to 2022 in Indonesia, and its solution is determined using the fourth-order Runge-Kutta method. Based on the model solution and 2021-2022 data, a MAPE value of 15% is obtained, indicating that the model is sufficiently accurate in explaining the spread of pneumonia in Indonesia. The spread pattern of pneumonia in Indonesia from 2013 to 2030 indicates a downward. However, as of 2030, there are still 67,261 individuals infected, indicating that the target of pneumonia-free Indonesia has not been achieved. Simulation shows that with exclusive breastfeeding rate value = 0.438852 and Hib vaccination rate = 0.25 it is estimated that the target of free pneumonia in Indonesia in 2030 will be achieved. The free target can also be achieved by increasing the exclusive breastfeeding rate to 73.9% and the Hib vaccination rate to 0.22.