Dynamical Behavior of an eco-epidemiological Model involving Disease in predator and stage structure in prey

Lina Shihab Ahmed,Hassan Fadhil Al- Husseiny

doi:10.24996/ijs.2019.60.8.14

Abstract

An eco-epidemic model is proposed in this paper. It is assumed that there is a stage structure in prey and disease in predator. Existence, uniqueness and bounded-ness of the solution for the system are studied. The existence of each possible steady state points is discussed. The local condition for stability near each steady state point is investigated. Finally, global dynamics of the proposed model is studied numerically.

Highlights

There are many factors that affect each of prey and predator, for example, pollution of the environment, and lack of food, predation, fishing and others
In addition to the factors heir important factor is the spread of infectious diseases between the prey alone, predator, or both
The back of a great interest by researchers to study the effect of the spread of diseases, and this type for modeling is called eco-epidemiological, such as in 1986 Anderson and May [1] were the first who merged between it, ecology and epidemic systems, they created a prey-predator model with diseases

Summary

Introduction

There are many factors that affect each of prey and predator, for example, pollution of the environment, and lack of food, predation, fishing and others. The infected predator consumed the immature prey individuals according to lotka-volltera type of functional response with predation rate represent the disease transmission from susceptible predator to infected predator and contributes a portion of such food with conversion rate. The equations of system (2) are continuous and have continuous partial derivatives on the following positive 4th dim.space: These equations are Lipschizian on and the solution of system (2) exists and unique. Due to the fact that the conversion rate constant from prey population to predator population cannot exceeding the maximum predation rate constant from predator population to prey population, from the biological point of view, always we get: Where Since So that, represents prey specie which is growth logistically with carrying capacity(1), solve the differential equation with initial value ( ).

Exists under the following condition

Either and or

Which is negative if the following condition hold

It is easy to see that