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

TL;DR

This paper analyzes a discrete-time mosquito population model with different birth and death rates, demonstrating conditions for population extinction or survival and deriving the long-term behavior of larvae and adults.

Contribution

It extends previous work by analyzing the case of unequal birth and death rates, providing conditions for population extinction or persistence.

Findings

Mosquito population dies out if birth rate is less than death rate.

Population survives with larvae growing unbounded if birth rate exceeds death rate.

Adult population stabilizes at a finite limit when the population survives.

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 ${\alpha\over \mu}$, where $\alpha>0$ is the maximum emergence rete.