Impact of habitat destruction and its subsequent regeneration on the dynamics of a Holling type II prey-predator interacting species system with prey refuge

Here, we have studied the effects of habitat destruction and its regeneration effort on the dynamical behavior of prey-predator species system considering prey refuge with the help of mathematical model. In the formulation of the model, it is assumed that the habitat is destroyed due to anthropogenic activities, such as deforestation, overgrazing, mining, urbanization, intensive cultivation, and industrialization associated with human population growth and habitat destruction which have deleterious effects on the vital parameters of the prey-predator species system. We investigated how the dynamics of the prey and predator populations are influenced by changes in habitat destruction, control efforts, and subsequent regeneration of habitat. The stability analysis and bifurcation study of the mathematical model are carried out both analytically and numerically to understand the dynamical behavior of the system. With the help of numerical simulations and stability analysis, we analyze the environmental impact of habitat destruction, prey refuge, and habitat regeneration. It is observed from the stability analysis of the equilibrium points that the effects of habitat destruction will be apparent only when the level of habitat destruction becomes more than the critical value Dc. Furthermore, a sensitivity analysis of the interior equilibrium point is also carried out by using normalized forward sensitivity method to investigate the impact of model parameters. It is shown that as the growth rate of human population increases, the amount (proportion) of destroyed habitat increases causing decrease in the equilibrium densities of prey and predator populations. It is observed that stable coexisting behavior is changed to coexisting oscillatory behavior by taking coefficient measuring decrease in the natural availability of refuge for prey on account of habitat destruction as a bifurcation parameter. It is derived from the analysis of the model that as the effort rate for regenerating destructed habitat per unit amount of habitat destroyed increases, then initially, the prey and predator population both starts increasing but as the effort rate increases further, then the predator population tends to extinction on account of complete restoration of refuge habitat. Hence, for the coexistence of both the populations of prey and predator, it is suggested that the regeneration effort need not be applied beyond a specific limit.