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