A Mathematical Model of Dengue-Chikungunya Co-Infection in A Closed Population

Dengue disease has been a major health problem in many tropical and sub-tropical countries since the early 1900s. On the other hand, according to a 2017 WHO fact sheet, Chikungunya was detected in the first outbreak in 1952 in Tanzania and has continued increasing until now in many tropical and sub-tropical countries. Both these diseases are vector-borne diseases which are spread by the same mosquito, i.e. the female Aedes aegypti. According to the WHO report, there is a great possibility that humans and mosquitos might be infected by dengue and chikungunya at the same time. Here in this article, a mathematical model approach will be used to understand the spread of dengue and chikungunya in a closed population. A model is developed as a nine-dimensional deterministic ordinary differential equation. Equilibrium points and their local stability are analyzed analytically and numerically. We find that the basic reproduction number, the endemic indicator, is given by the maximum of three different basic reproduction numbers of a complete system, i.e. basic reproduction numbers for dengue, chikungunya and for co-infection between dengue and chikungunya. We find that the basic reproduction number for the co-infection sub-system dominates other basic reproduction numbers whenever it is larger than one. Some numerical simulations are provided to confirm these analytical results.