![]() ![]() The basic reproduction number \(R_0\) is the most important quantity in the study of epidemics model. The first reaction ( \(S\rightarrow E\)) is catalytic whereas the second ( \(S\rightarrow I\)) is auto catalytic reaction (Tomé and de Oliveira 2011). Susceptible individual becomes exposed or infected with rates that are proportional to the number of neighbouring infected individuals. Exposed and infected individuals remain forever in the same state. A susceptible individual (S) in contact with an infected individual either becomes exposed (E) or becomes infected (I) individual. The resulting models are of SEI, SEIR or SEIRS type, respectively, depending on whether the acquired immunity is permanent or not. In other words a susceptible individual first goes through a latent period (and is said to become exposed or in the class E) after infection before becoming infectious. However, many diseases incubate inside the hosts for a period of time before the hosts become infectious. A compartmental model based on these assumptions is called a SIR or SIRS model. Most of the literature of epidemic models assume that the disease incubation is negligible so that, once species becomes infected, each susceptible individual (S) instantaneously becomes infectious (I) and later recovers (R) with a permanent or temporary acquired immunity. Haque and Chattopadhyay ( 2007) investigated the role of transmissible diseases in a prey dependent predator–prey system with prey infection. ![]() Chattopadhyay and Arino ( 1999) considered a three species eco-epidemiological model and determined extinction criteria of species and found condition for Hopf-bifurcation in an equivalent two-dimensional model. In Rosenzweig prey–predator model, an epidemic threshold (above which an infected equilibrium or an infected periodic solution appear) was determined by Hadeler and Freedman ( 1989). ![]() Anderson and May ( 1986) were considered the disease factor in a predator–prey dynamics and found that the pathogen tends to destabilize the predator–prey interaction. They had reported the influence of mathematical models in disease spreading and their models are still relevant in many epidemic situations (Kermack and McKendrick 1932, 1933). The first mathematical description of contagious diseases has been formulated by Kermack and McKendric ( 1927). An epidemic model includes the specific property of population growth, the spread rules of infectious diseases, and the related ecological factors to construct mathematical models reflecting the dynamic properties of infectious diseases. Dynamics of transmissible disease in an ecological situation is remaining a major field of study due to its applications in real life. These mathematical models help to identify key parameters which determine the rich dynamics of an epidemiological system. In recent years significant progress has occurred in the theory and applications of epidemiology models in predator–prey systems (Kooi et al. An eco-epidemiological model is a combination of an ecological model and an epidemic model which may be a SI, SIS or SIR type. This study is aimed to introduce a new non-chemical method for controlling disease of prey population.Įco-epidemiology is a new branch of study in mathematical biology which incorporates both the ecological and epidemiological issues simultaneously. The main goal of this study is to show the non-trivial consequences of providing additional food for controlling infection in a diseased predator–prey system. Infection rate is also introduce in the system and the role of additional food is discussed. Effects of variation of latent period is presented. We compute the disease free regions in various parametric planes. However, in such case supply of suitable additional food can make the system disease free. Numerical simulation results establish that there exists a critical infection rate above which disease present in the system in absence of additional food. The impact of additional food on infected prey population is discussed. We discuss the existence and the local stabilityĬonditions of both the disease free and endemic equilibrium points. In this paper, we propose a susceptible-exposed-infected prey–predator model supplying additional food to predator.
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