Bifurcation analysis of dengue hemorrhagic fever model with logistic growth rate in aquatic stage

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.