Mathematical Modeling of Epidemics: A Study on the Spread of Infectious Diseases

Abstract

Infectious diseases continue to be a major threat to international health and hence the need for best strategies for prediction, control and prevention. Mathematical modeling of epidemics is one of the most effective approaches to analyzing the processes that occur within a population and making related decisions. Towards this end, this paper offers a study of the mathematical modelling of epidemics with emphasis on the SIR model and its variants. In this paper, we examine how differential equations can be used to describe the spread of diseases and its control by tools like vaccination and isolation as well as changes in contact rates. The paper also consists of a section on validation and calibration using real world data and given simulation results. We showed that mathematical models can accurately show the likelihood of the spread of the infection and how interventions may best be applied.