Local Stability Analysis of Mathematic Model SEIHR-VW on Dengue Haemorrhagic Fever Transmission - Nolaika Arsiani Norramandhany; Widowati Widowati; Redemtus Heru Tjahjana ((IJCSAM) International Journal of Computing Science and Applied Mathematics, 2025)
Dengue fever is caused by the dengue virus (DENV) and is mainly transmitted by mosquitoes, particularly Aedes aegypti. In this study, we develop a mathematical model to describe and analyze how dengue spreads within a population. The mathematical model is expressed as a nonlinear system of differential equations and consists of seven compartments (SEIHRVW): susceptible, exposed, infected, hospitalized, and recovered humans, along with susceptible and infected mosquitoes. The model has two possible equilibrium points: a non-endemic and endemic equilibrium point. To better understand the dynamics of the model, we calculate the basic reproduction number (R0) using the Next Generation Matrix (NGM) method, and then the Routh-Hurwitz criterion method is applied to analyze the local stability of both equilibrium points. The results indicate that the nonendemic equilibrium point is asymptotically stable when R0 < 1, while the endemic equilibrium point becomes asymptotically stable when R0 > 1. In general, our analysis concludes that the proposed dengue transmission model is asymptotically stable at the endemic equilibrium point, with R0 = 3.85011.