Stochastic predator–prey interactions with disease dynamics: fixed point and numerical investigations
摘要
This paper presents an analysis of the stochastic prey-predator model in which the prey is infected by a microparasite. Infection within a species may destabilize the ecosystem, and the diet of the species may be cut short. Thus, it is most necessary to incorporate the disease dynamics into the prey-predator dynamics. Further, sudden environmental changes may affect the prey-predator species population. It is because of this that the present model is used to study the reaction-diffusion prey-predator model with infected prey under the temporal noise in the Ito sense. The Brownian motion is incorporated into the model to include the stochasticity. Our primary interest is to determine the conditions under which populations coexist or one is driven to extinction, to investigate the impact of disease transmission rates and virulence on population sizes and dynamics, and to examine the effect of environmental variations and individual characteristics on the system’s dynamics. Existence of a solution is guaranteed through the application of fixed-point theory. To calculate the impact of disease on predator-prey interaction for different diffusion and environmental restrictions, we solve the problem numerically using the Implicit finite difference scheme. The scheme is consistent in the mean square sense as well as the von Neumann stable. Employing the numerical scheme and the consideration of the behavior of the solution reveals the intricate interaction among disease, hunting, and random environmental factors governing the density of predator-prey communities. The research brings to light the possible ecological impact of emerging diseases and environmental uncertainties on the balance of populations in ecosystems. The assessment of these numerical schemes increases the scope of available resources for modeling these types of ecosystems.