Stability and Sensitivity Analysis of Parameters in the SEIR-ASEI Model for the Transmission of Dengue Fever - Aprianti, Euis; Sonia, Sonia (Department of Mathematics, Universitas Negeri Gorontalo, 2025)
Dengue fever, which is transmitted by female Aedes mosquitoes, is caused by the dengue virus and remains a signiﬁcant health challenge in tropical countries, including Indonesia. This study developed an SEIR-ASEI type dengue fever transmission model by considering the aquatic phase of mosquitoes and incorporating logistic growth factors in aquatic sub-population. This study aims to analyze the stability of the model using the Vieta Theorem, and the Castillo-Chavez and Song Theorem through a bifurcation approach. The developed model has two equilibrium points, namely, the disease-free equilibrium point and the endemic equilibrium point. The stability of each equilibrium point depends on the value of the basic reproduction number, which is determined through the next-generation matrix. When R0 is less than one, the disease-free equilibrium remains locally asymptotically stable. Conversely, stability of the endemic state is assured when R0 exceeds one. An analysis of parameter sensitivity, using values associated with Aedes aegypti, was conducted to determine the factors that have the most signiﬁcant impact on disease transmission dynamics. The analysis results showed that adult mosquito mortality was the most sensitive parameter, but parameters in the aquatic phase also inﬂuenced changes in the basic reproduction number. Increasing aquatic mortality or reducing mosquito breeding sites could lower the R0 value, potentially reducing transmission rates. Therefore, controlling aquatic mosquitoes is an essential strategy in sustainable dengue prevention and control efforts.