Periodic Solutions for a Modified Delayed Heterogeneous Population-based Model

Abstract

This paper investigates the existence of periodic solutions for a modified delayed heterogeneous population-based disease model with multiple time delays. We extend the oscillatory result in the literature from a one-delay model to a five-delay model.
By means of the mathematical analysis method, we discuss the instability of the unique positive equilibrium point and the boundedness of the solutions. Two sufficient conditions to guarantee the periodic oscillation of the solutions are provided, and computer simulations are given to support the present criteria.