Dynamics of disease spread in a predator-prey system

Abstract

This paper discusses the dynamics of a communicable disease in a predator-prey system. It is assumed that a parasite is infectious and it spreads among preys according to a SIS (susceptible-infective-susceptible) model but not among predators, the predators stay healthy. Two predation response functions of Holling type II are used for both healthy and infected preys. The feasibility and stability conditions of the equilibrium points of the system are analyzed. The model has one trivial equilibrium and two free-disease positive equilibria; (i) in the absence of predator (and (ii) in the presence of predator. The threshold condition of is derived. If it is below threshold, becomes stable and if above threshold, it is unstable. The basic reproduction numbers for and are 170 Asrul Sani et al. also derived, called dan , respectively. These basic numbers serve as thresholds. If or , the equlibrium point or becomes asymptotically locally stable. If or , the equilibrium or is unstable.

Eco-Epidemiological Modelling and Analysis of Prey-Predator Population

“…Mathematical Modeling of prey-predator systems of interaction of species have a long history since original remarkable work was done by Lotka-Volterra Model in 1920 [1,3,5,6], and SIR model Compartment of systems of population is another vital area of research after pioneering work of Kermack and Mckendrick [1][2][3][5][6][7][8][9][10]. Anderson and May where the first who combined these two modeling systems, while Chattopadhyay and Arino were the first who used the term ''eco-epidemiology'' for such models [3,5,7].…”

“…The dynamics of disease in prey-predator systems now become an interesting area of research due to the fact that prey-predator interaction is rich and complex in nature [4,6,7,[11][12][13]. Several mathematical models have been proposed and studied on prey-predator systems [1][2][3][4][5][6][7][9][10][11][12]. Many studies focused on the study of disease in a prey only [1-5, 7, 12], other researchers were interested in the study of disease within the predator population only [14], and there are also some studies on diseases in both prey and predators [6,9,11] In this paper, we proposed and studied infectious disease on both prey and predator interaction of species with treatment given to infected prey and infected predator.…”

Mathematical Eco-Epidemiological Model on Prey-Predator System

“…Anderson R and May R. [6,7,10] were the first to propose an eco-epidemiological model by merging the Lotka-volterra prey-predator model [2,7,10] and the epidemiological SIR model which was introduced by Kermack and Mckendrick. [2,7,[12][13][14]. Many works have been devoted to study infectious disease on a prey-predator system [1][2][3][4][5][6][7][8][9][10].…”

“…Ecological populations suffer from various diseases. These diseases often play an important roles in regulating the population sizes [1,5,10,12,13]. Mathematical study of such populations has attracted attentions of both ecologists and mathematicians from several years past.…”

“…Mathematical study of such populations has attracted attentions of both ecologists and mathematicians from several years past. As a result numerous mathematical models have been developed, and these models have become essential tools in analyzing the interaction of different populations, particularly the interaction between prey and predator [10,12,15,17].…”