Abu Hanifah Al Faruqy, Budi Priyo Prawoto
Dengue fever (DF) is a contagious viral disease transmitted by vectors, which frequently occurs, particularly in tropical regions worldwide. A new approach to preventing the spread of DF is the dissemination of mosquitoes carrying Wolbachia bacteria. Wolbachia is a bacterium naturally widespread and found in the reproductive tissues of several insects and arthropods. This article aims to construct a model for the spread of dengue fever with the presence of Wolbachia bacteria and determine the basic reproduction number (R0). By R0 we will find the stability analysis of the conducted model. The constructed model consists of six compartments: susceptible humans (Sh), infected humans (Ih), recovered humans (Rh), susceptible vectors (Sv), infected vectors (Iv), and vectors with Wolbachia (Wv). Based on the research, an SIR SIW model with a basic reproduction number using the Next Generation Matrix. By concern to spesific parameter, the case of R0 < 1 has been determined and its shows stable DFE equilibrium. The endemic condition, R0 > 1 shows stable. To make sure the results of the analytical calculation, numerical simulations are performed in this study. © 2025 Author(s).
Mathematics Departement, State University of Surabaya, Surabaya, Indonesia
