A discrete-time dynamical system of wild mosquito population with Allee effects

Abstract

We study a discrete-time dynamical system of wild mosquito population with parameters: $\beta$ - the birth rate of adults; $\alpha$ - maximum emergence rate; $\mu >0$ - the death rate of adults; $\gamma$ - Allee effects. We prove that if $\gamma \ge \frac{\alpha (\beta -\mu )}{{\mu }^2}$ then the mosquito population dies and if $\gamma <\frac{\alpha (\beta -\mu )}{{\mu }^2}$ holds then extinction or survival of the mosquito population depends on their initial state.

arXiv comment13 pages, 2 figures