Stability Analysis and Simulation Results of an SIR Mathematical Model for the Dengue Fever

摘要

Dengue fever is a disease affecting people in more than 100 countries. Here we consider a host and vector model for the transmission of dengue fever. This SIR model consists of three compartments of susceptible, infective and removed for host (human) and two compartments of susceptible and infective for vector (dengue mosquitos). These five compartments yield five coupled nonlinear ordinary differential equations (ODEs). After non-dimensionalization, we have a system of three nonlinear ODEs. Reproductive number and two equilibrium points are calculated for various cases. Then we perform stability analysis based on the eigenvalues obtained at those equilibrium points. Simulation is carried out for susceptible, infective and removed by using Maple software and the results are presented in graphical forms for various scenarios.