AN INTRODUCTION-MATHEMATICAL MODELING IN POPULATION HEALTH BY USING SIR AND SEIR MODELS

Mathematical modeling serves as a corner stone in understanding and managing health issues at the population level. This study explores the application of compartmental models-specifically the susceptible -infectious-recovered (SIR) and Susceptible-Exposed-infectious-recovered (SEIR) frame works-to simulate disease transmission dynamics and guide public health interventions. By integrating real-world epidemiological data and differential equations, these models quantify the spread of infectious diseases such as influenza, COVID-19, and dengue. The inclusion of an "Exposed" compartment in SEIR enhances realism for pathogens with incubation periods, enabling more precise projections. Analytical techniques are applied to assess parameters such as transmission rate, recovery rate, and basic reproduction number (R₀). Results from model simulations provide insights into outbreak trajectory, peak infection periods, and the impact of interventions like vaccination, isolation, and contact reduction. This paper underscores the value of mathematical modeling in strategic planning and decision-making, offering a predictive lens to manage public health emergencies efficiently.