Abstract
AbstractThe present model is dealt with prey-predator interactions in two different patches where only prey species are allowed to disperse among the patches. Each of these two patches has different predator population but the predator in Patch-2 only is affected with a disease. The proposed model is biologically welldefined. Also, the feasibility of the equilibrium points and corresponding stability conditions are analysed. It is found that the disease among predator, even in one patch, makes an important role to control the whole system dynamics as it starts to oscillates by regulating the disease transmission rate. Moreover, the disease transmission rate has a stabilizing as well as destabilizing effect on the system dynamics. From the results, it is observed that a high dispersal rate decreases the count of infected predator in a patch in presence of prey dispersal. There is another interesting result: it is observed that the prey dispersal cannot destabilize the coexistence state, i.e., the system which is stable in absence of dispersal remains stable when the prey species disperse between two patches.
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