Stability Analysis of the SIR-SI Model for Dengue Fever Transmission with Saturated Birth Rate

Abstract

The SIR-SI mathematical model for the problem of dengue virus spread which has been discussed in previous studies has not involved the saturated birth rate of mosquito. This discussion aims to construct and analyze the SIR-SI model which involves competition factors in mosquito population growth so that the model used to predict the number of dengue virus infections becomes more realistic. In addition, sensitivity analysis and numerical simulations of the models that have been constructed are also discussed. The method used is a literature study using theories derived from reputable articles. The results of this discussion show that the existence of an equilibrium point and its stability depends on the basic reproduction number. If the basic reproduction number is less than one, the number of cases of dengue fever infection will decrease. However, if the basic reproduction number is more than one, the number of cases of dengue infection will not decrease and even tend to be constant at a certain number. The average parameter of bites carried out by one mosquito in all humans () is the most dominant in increasing the spread of dengue disease in humans. On the other hand, mosquitoes' natural death rate parameter () is the most dominant in reducing the spread of dengue fever in humans. This information provides input and evaluation to decision-makers in solving the problem of the spread of dengue fever.