A Continuum Model Based on SIR Equations for Epidemic Spread Analysis

Abstract

To comprehend how epidemics develop and assess the efficacy of medical treatments, infectious disease modeling is crucial.  The SIR model, which separates the population into susceptible, infected, and recovered groups, is one example of the mathematical and statistical models that scientists and policymakers use to describe the dynamics of infection transmission among individuals within a society.  These models may also be expanded to incorporate other components, such vaccination, alterations in social behavior, and the results of medical treatments. This work focuses on analyzing the spread of Oropouche fever using the SEIR model with a protective factor that simulates the impact of interventions. The results demonstrate how interventions contribute to reducing the number of infections and delaying the peak of the epidemic. The work also examines the use of the SIRD model in two versions: the classic (without vaccination) and the modified (with vaccination). The numerical results clearly demonstrate the role of vaccination in reducing morbidity and mortality rates, highlighting the importance of mathematical modeling in designing effective strategies to combat epidemics.