Saddle–Node Bifurcation Leading to Survival Mosquitoes

A saddle–node bifurcation is demonstrated in a model of mosquito population growth. This bifurcation helps us understand the dynamics of two stages in the model: the aquatic stage (which includes the egg, larva, and pupa) and the nonaquatic stage (the mature mosquito). We calculated the basic offspring number using the next-generation matrix method and displayed it as the value of the saddle–node bifurcation. This means that the stable extinction state becomes unstable, while a survival state emerges as dominant in the dynamics, along with another coexistence state as a transition to surveillance. Numerical computations verify how factors such as limited logistic growth, the Allee effect, and the mortality density rate modify the mosquito dynamics.