Lyapunov exponent and existence of T-periodic positive solution of stochastic Nicholson model with discrete and distributed delays

This article considers a generalized stochastic Nicholson model with harvesting term that includes discrete as well as distributed delays. The stochastic Nicholson model with discrete and distributed delays is a valuable tool for studying population dynamics in situations where both discrete and distributed time delays play a role. It has been applied to a variety of ecological and epidemiological systems, such as predator–prey interactions, disease transmission dynamics, and the management of invasive species. The delay, which is essential for the survival of the entire world, has been taken into account in order to make harvesting more realistic. We first demonstrated the existence of a positive solution across the entire domain before estimating the Lyapunov exponent. These estimates depend on the delay of the harvesting and noise. The next analysis consists of the existence of a positive T-periodic solution which concludes the fact that smaller white noise is required to produce a positive T periodic solution.