Mathematical Modelling of Coexistence of Two Dengue Virus Serotypes with Seasonality Effect

Abstract

Dengue is a mosquito-borne disease which is endemic, particularly in the tropical and subtropical regions across the globe. Most of these regions have strong seasonal patterns in climatic factors such as rainfall and temperature, which are directly linked to dengue disease transmission through the mosquito population. These climatic factors have great influence on the mosquito survival, propagation and abundance. Several mathematical models have been used to forecast dengue burden in Madeira Island if two dengue virus serotypes coexist, but do not capture the seasonality effects on the dynamics of mosquito population. Hence, this study proposes a two-strain compartmental model to forecast the impact of seasonal variation on the transmission dynamics of dengue disease if two virus serotypes coexist in the Island. We derive the basic reproduction number, 0 = max{√01,√0j}, related to the model through the Next Generation Matrix operator. The diseasefree and boundary equilibrium points of the model are obtained, and we discuss the local and global stability of the disease-free equilibrium in terms of 0. It is found that the disease free-equilibrium is locally asymptotically stable whenever both 01,0j < 1, and unstable otherwise. The Comparison Theorem is used to prove the global asymptotic stability of the disease-free equilibrium. The results of our numerical simulation show that the presence of seasonal effect influences a high number of dengue infections in both human and mosquito populations.