Dynamics of a stage-structured predator-prey model: cost and benefit of fear-induced group defense.

In the predator-prey system, predators can affect the prey population (1) by direct killing and (2) by inducing predation fear, which ultimately force preys to adopt some anti-predator strategies. However, the anti-predator strategy is not the same for all individual preys of different life stages. Also, anti-predator behavior has both cost and benefit, but most of the mathematical models observed the dynamics by incorporating its cost only. In the present study, we formulate a predator-prey model dividing the prey population into two stages: juvenile and adult. We assume that adult preys are only adapting group defense as an anti-predator strategy when they are sensitive to predation. Group defense plays a positive role for adult prey by reducing their predation, but, on the negative side, it simultaneously decreases their reproductive potential. A parameter, anti-predator sensitivity is introduced to interlink both the benefit and cost of group defense. Our result shows that when adult preys are not showing anti-predator behavior, with an increase of maturation rate, the system exhibits a population cycle of abruptly increasing amplitude, which may drive all species of the system to extinction. Anti-predator sensitivity may exclude oscillation through homoclinic bifurcation and avert the prey population for any possible random extinction. Anti-predator sensitivity also decreases the predator population density and produces bistable dynamics. Higher values of anti-predator sensitivity may lead to the extinction of the predator population and benefit adult preys to persist with large population density. Below a threshold value of anti-predator sensitivity, it may possible to retain the predator population in the system by increasing the fear level of the predator. We also observe our fear-induced stage-structured model exhibits interesting and rich dynamical behaviors, various types of bistabilities in different bi-parameter planes. Finally, we discuss the potential impact of our findings.

Cooperation delay induced chaos in an ecological system.

In the present paper, we investigate the impact of time delay during cooperative hunting in a predator-prey model. We consider that cooperative predators do not aggregate in a group instantly, but individuals use different stages and strategies such as tactile, visual, vocal cues, or a suitable combination of these to communicate with each other. We observe that delay in hunting cooperation has stabilizing as well as destabilizing effects in the system. Also, for an increase in the strength of the delay, the system dynamics switch multiple times and eventually become chaotic. We see that depending on the threshold of time delay, the system may restore its original state or may go far away from its original state and unable to recollect its memory. Furthermore, we explore the dynamics of the system in different bi-parameter spaces and observe that for a particular range of other parameter values, the system dynamics switch multiple times with an increase of delay in all the planes. Different kinds of multistability behaviors, the coexistence of multiple attractors, and interesting changes in the basins of attraction of the system are also observed. We infer that depending on the initial population size and the strength of cooperation delay, the populations can exhibit stable coexistence, oscillating coexistence, or extinction of the predator species.

Disease control through removal of population using Z-control approach.

Present study considers the situation where the removal of population is adopted as a prevention measure for isolating the susceptible population from an infected region to reduce the disease prevalence. To investigate the scenario, a dynamic error based method, Z-type control is applied in an SI type disease model with the aim of achieving a predetermined disease prevalence. The controlled system is designed by introducing a new compartment (the population in an infection-free region) in the uncontrolled system to capture the removal of susceptible population from the infected region to an infection free region. By performing numerical simulations, our study shows that using Z-control mechanism, the removal of susceptible to an infection free region can effectively achieve a predetermined disease prevalence. The removal rates required for achieving a specific reduction in infected population for different levels of disease endemicity are quantified. Furthermore, the global sensitivity analysis (PRCC) is also performed to have a more clear insights on the correlations of the control parameter with the model parameters.