A simulation of SIMV host - vector dengue model

Abstract

Dengue is an endemic infectious disease of the tropical countries. Moreover, dengue disease is a major problem in Indonesia, especially in North Kalimantan. This disease is caused by dengue virus. In this paper, we epidemic modeling to analyze the spread of dengue disease by choosing parameters that influence the transmission rate of dengue disease. SI model is a method that rewrite a real-world phenomena into a system of differential equations. We use Euler method to discretize the model. The resulted dynamical behavior of the discrete model is then analyzed, specifically we determine the existence and stability of equilibrium points. We found that this model is converged to its equilibrium points, so its consistent its the exact solution. We use computer simulation to show the trajectories of the numerical solutions plotted into the 2D planes. We found that the numerical simulation is not only illustrate the results, but also exhibit rich dynamics such as periodic solution and bifurcation.