Modeling the spread of dengue fever by using SIR model

Abstract

The establishment and spread of dengue fever is a complex phenomenon with many factors that interact with each other. This report present a study on a mathematical model, the SIR (Susceptible, Infected and Recovered) that serve as a framework for understanding the spread of the infectious dengue fever. We begin with a brief discussion of the origin and historical development of the disease. This is followed by a review on the relation between the three compartments, susceptible, infected and recovered. The modeling steps that lead to the SIR model using ordinary differential equation is explained in detail. The solution gives the basic reproduction number R_0, and this basic reproduction number is use to determine whether the dengue fever will dies out or persists in human population in the long run. The disease-free equilibrium point is determined and R_0 is used to determine whether the disease free equilibrium is stable or unstable. Establishing the endemic equilibrium point determines when the dengue fever will become calm.