Study of a Prey-Predator Dynamics Under the Simultaneous Effect of Toxicant and Disease

Abstract

Abstract. A mathematical model is proposed to study the simultaneous effects of toxicant and infectious disease on Lotka-Volterra prey-predator system. It is considered in the model that only the prey population is being affected by disease and toxicant both, and the susceptible and infected prey populations are being predated by predator. All the feasible equilibrium of the model are obtained and the condition for the existence of interior equilibrium point is also been determined. The criteria for both local stability and instability involving ecotoxicological and epidemiological parameters are derived. The global stability of the interior equilibrium point is discussed using Lyapunov's direct method. The results are compared with the case when environmental toxicant is absent. Moreover, threshold conditions depending upon toxicant, disease and predation related parameters for the non-linear stability of the model is determined. Finally, the numerical verifications of analytic results are carried out.

Stability and Bifurcation of a Prey-Predator-Scavenger Model in the Existence of Toxicant and Harvesting

“…where 2 = −(̃+ 2̃2 +̃) < 0 and 2 = (̃+ 2̃2)(̃) +̃> 0. Therefore these eigenvalues have negative real parts and hence 2 is locally asymptotically stable if and only if the following condition holds: (19) Further, the Jacobian matrix evaluated at the predator free equilibrium point 3 = (̂, 0,̂) is given by…”

“…On the other hand, the effects of toxicants on ecological communities have become problems of major environmental concern due to the direct effects of food web systems, which in turn affects the human life. Accordingly, the effects of toxicants on the ecological systems are studied by many researches [18][19][20][21][22]. Therefore problems related to harvesting and toxicants in ecological systems have been drawing attention of many researchers and they are considered the main objective of this research work too.…”

Diseased Prey with Harvesting Predator in Prey-Predator System – An Analytical Study

“…al [10] analysed two models to study the prey-predator dynamics under the simultaneous effect toxic diseases. In the model they have proposed model in which prey-population.…”

Modeling and Analysis of a Single Species Population with Viral Infection in Polluted Environment

“…As a result ecologists acknowledge the importance of disease and parasite in the dynamics of the population [15][16][17][18][19]. Recently few interesting mathematical models with combined effects of disease and toxicant were studied [20][21][22], for competing and prey predator dynamics. Keeping in view of the above, in this paper, we have proposed a mathematical model by considering the combined effect of both the infection and the toxicant through food intake and environmental toxicant.…”