Model Matematika Penyebaran Penyakit Demam Berdarah Dengue

Abstract

Dengue disease was transmitted to human through infected mosquito Aedes Aegypti. It was found widely in the tropical regions of the world. Infection of dengue virus could be grouped into two mechanisms. The first mechanism was vertical transmission in mosquito body, where virus could be transmitted by female mosquito into her eggs. The second mechanism was transmission from mosquito into human body and conversely. In this study, mathematical models were used to study the behavior of the transmission of dengue disease. The mathematical model of the disease with assumption of healthy mosquito eggs was compared to the modified mathematical model of dengue disease assuming that some of mosquito eggs were infected by dengue virus. The seasonal influence, especially temperature, was considered in the analysis. The standard dynamical analysis was applied to both mathematical models. Numerical results showed that infected mosquito eggs influenced the spreading of dengue disease. There were bigger oscillation in the susceptible and infected human population, as well as in the infected mosquito, as a result of stronger seasonal influence during extrinsic incubation.