SIR, SIRS, and SEIRS Models for Pertussis Cases in Eastern Visayas

Abstract

This study analyzed the effectiveness of the Susceptible-Infected-Recovered (SIR), Susceptible-Infected-Recovered-Susceptible (SIRS), and Susceptible-Exposed-Infected-Recovered-Susceptible (SEIRS) models in predicting pertussis incidence in Eastern Visayas, Philippines. The research aimed to compare the accuracy of these models using real-world data on weekly pertussis cases for the year 2024. The study utilized a mathematical modeling approach, employing differential equations to simulate disease transmission dynamics. Baseline parameter values for each model were obtained from existing literature, and these parameters were later refined through estimation techniques, specifically by using least squares optimization to fit the models to the observed data. The models were implemented using MS Excel, and their performance was evaluated using the Root Mean Square Error (RMSE) metric. The results of the study showed that the SIR model, with final estimated parameters β = 13.5968 and γ = 13.5496, provided the most accurate prediction of pertussis incidence the region, with the lowest RMSE of 9.07. In contrast, the SIRS and SEIRS models, while incorporating more complex disease dynamics such as waning immunity and an exposed period, exhibited higher RMSE values of 12.69 and 12.74, respectively, indicating less accurate predictions. These findings suggest that traditional models like SIR may be more practical for short-term pertussis forecasting in the context of Eastern Visayas in 2024. This study also highlighted the importance of model calibration and validation using local real-world data.