Existence of solutions for a biological model using topological degree theory

TL;DR

This paper uses topological degree theory to prove the existence of positive T-periodic solutions in a biological delay differential equation model related to circadian oscillations in Drosophila.

Contribution

It introduces a novel application of topological degree theory to establish solutions in a biological model with feedback mechanisms.

Findings

Existence of positive T-periodic solutions proven.

Application to circadian rhythm models in Drosophila.

Advancement in mathematical methods for biological systems.

Abstract

Topological degree theory is a useful tool for studying systems of differential equations. In this work, a biological model is considered. Specifically, we prove the existence of positive T-periodic solutions of a system of delay differential equations for a model with feedback arising on Circadian oscillations in the Drosophila period gene protein.