Bifurcation analysis of dengue hemorrhagic fever model with logistic growth rate in aquatic stage - Herri Sulaiman; Fatmawati Fatmawati; Cicik Alfiniyah; Kumama Regassa Cheneke (Statistics, Optimization & Information Computing, 2025)
This work analyzes the transmission dynamics of dengue hemorrhagic fever (DHF) by incorporating the aquaticphase and logistic growth rate for mosquitoes population. The model accounts for human-mosquito interactions and exploresthe role of disease-induced mortality. We investigate the existence and stability of equilibria, particularly focusing on thephenomenon of backward bifurcation. Our analysis demonstrates that the disease-free equilibrium is globally asymptoticallystable when the basic reproduction number less than unity in the absence of disease-induced mortality. However, whendisease-induced mortality is considered, backward bifurcation emerges, leading to the coexistence of multiple equilibria inthe range basic reproduction number between critical reproduction number and one. A Lyapunov function approach confirmsthe global stability of the endemic equilibrium when basic reproduction number more than unity. Furthermore, we show thatneglecting disease-induced mortality eliminates backward bifurcation, ensuring a unique endemic equilibrium. Numericalsimulations support our theoretical findings, illustrating different stability behaviors under varying initial conditions.