Exploring the complex dynamics of a diffusive epidemic model: Stability and bifurcation analysis.

The recent pandemic has highlighted the need to understand how we resist infections and their causes, which may differ from the ways we often think about treating epidemic diseases. The current study presents an improved version of the susceptible-infected-recovered (SIR) epidemic model, to better comprehend the community's overall dynamics of diseases, involving numerous infectious agents. The model deals with a non-monotone incidence rate that exhibits psychological or inhibitory influence and a saturation treatment rate.

Treatment of infected predators under the influence of fear-induced refuge.

In this research, we delve into the dynamics of an infected predator-prey system in the presence of fear and refuge, presenting a novel inclusion of treatment for infected individuals in this type of model. Through our analytical efforts, we establish a significant reproduction number that holds a pivotal role in determining disease extinction or persistence within the system. A noteworthy threshold value for this reproduction number delineates a boundary below which the infected population cannot endure in the system.

Effect of Fear, Treatment, and Hunting Cooperation on an Eco-Epidemiological Model: Memory Effect in Terms of Fractional Derivative.

In this paper, we have studied a fractional-order eco-epidemiological model incorporating fear, treatment, and hunting cooperation effects to explore the memory effect in the ecological system through Caputo-type fractional-order derivative. We have studied the behavior of different equilibrium points with the memory effect. The proposed system undergoes through Hopf bifurcation with respect to the memory parameter as the bifurcation parameter.

A systematic study of autonomous and nonautonomous predator-prey models for the combined effects of fear, refuge, cooperation and harvesting.

In the present study, we investigate the roles of fear, refuge and hunting cooperation on the dynamics of a predator-prey system, where the predator population is subject to harvesting at a nonlinear rate. We also focus on the effects of seasonal forcing by letting some of the model parameters to vary with time. We rigorously analyze the autonomous and nonautonomous models mathematically as well as numerically.