# Infected Intermediate Predator and Harvest in Food Chain

• Ghassan Ezzulddin Arif Department of Mathematics College of education for Pure Sciences, Tikrit University, Iraq
• Sufyan Abaas Wuhaib Department of Mathematics Faculty of Computer Science and Mathematics, University of Tikrit, Iraq
• Marwa Fareed Rashad Department of Mathematics College of education for pure sciences Tikrit University , Iraq
Keywords: Food chain, Predator-Prey, Disease, stability and harvesting, Analytic function, Univalent function, Differential subordination, Superordination, Sandwich theorems

### Abstract

In this paper, a mathematical model consisting of the food chain model with disease in intermediate predator is proposed and discussed. The food chain model consists of four types: prey, intermediate predator, infected intermediate predator, and top predator. We studied the solutions for the original model and positive and bounded solutions in the sub models. Also found equilibrium points with sufficient and necessary conditions. By using Jacobian matrix and Lyapunov function to provide local and global stability. Can use the harvesting to control the disease and it can be used as tool to prevent disease transformation into an epidemic. Finally, some results were illustrated in numerical simulations.