Modeling the Existence of Basic Offspring Number on Basic Reproductive Ratio of Dengue without Vertical Transmission

Abstract

Dengue fever is a flavivirus of the family flaviviridae and transmitted to human after biting the infected vectors. The main vectors of dengue are Aedes aegypti and Aedes albopictus. There are four serotypes of dengue virus, viz. DEN-1, DEN-2, DEN-3, and DEN-4. The dengue virus, one of the virus that causes classical dengue fever (DF) and dengue haemorrhagic fever (DHF) is primarily found in the tropical and subtropical regions. Indonesia with the tropical climate has become an ideal land for dengue virus transmission. The wide clinical spectrum ranges from asymptomatic infections or mild illness, to the more severe forms of infection such as dengue hemorrhagic fever and dengue shock syndrome. The transmission of virus between mosquito can occur in two mechanisms, viz., horizontally and vertically. If the infected mosquito bite a human susceptible such that the human is infected, then this kind of transmission is called horizontal. The vertically transmission can occur from infected female mosquitoes to next generation. In this paper we build what is called Basic Offspring Number (Q0) based on the rate of change of aquatic mosquito and the total rate of change of mosquito population. Mathematical model is formulated to estimate the dynamics of the spread of disease dengue associated with basic offspring number Q0 (how the contribution of basic offspring number on basic reproductive ratio R0). The result shows that the existence of Q0 is significant toward R0.