Dynamical system of a mosquito population with distinct birth-death rates

Abstract

We study the discrete-time dynamical systems of a model of wild mosquito population with distinct birth (denoted by $\beta$) and death (denoted by $\mu$) rates. The case $\mu =\beta$ was considered in our previous work. In this paper we prove that for $\beta <\mu$ the mosquito population will die and for $\beta >\mu$ the population will survive, namely, the number of the larvaes goes to infinite and the number of adults has finite limit $\frac{\alpha }{\mu }$, where $\alpha >0$ is the maximum emergence rete.

9 pages, 3 figures