Population Models With Delay in Dynamic Environment

TL;DR

This paper develops a delay differential equation model to analyze fish populations under periodic environmental changes and harvesting strategies, providing insights into population persistence and extinction conditions.

Contribution

It introduces a modified Getz type delay differential equation model incorporating periodic and rotational harvesting rates for fish populations.

Findings

Conditions for population extinction and persistence identified

Existence of global solutions established

Periodic solutions under seasonal variations demonstrated

Abstract

We study the combined effects of periodically varying carrying capacity and survival rates on the fish population in the ocean (sea). We introduce the Getz type delay differential equation model with a control parameter which describes how fish are harvested. We will modify and extend harvesting model of an exploited fish population to include periodic and rotational harvesting rates. We study the existence of global solutions for the initial value problem, extinction and persistence conditions, and the existence of periodic solutions.