FRACTAL-FRACTIONAL SIRS MODEL FOR THE DISEASE DYNAMICS IN BOTH PREY AND PREDATOR WITH SINGULAR AND NONSINGULAR KERNELS

Abstract

In this study, we consider a mathematical model for the disease dynamics in both prey and predator by considering the Susceptible–Infected–Recovered–Susceptible (SIRS) model with the prey–predator Lotka–Volterra differential equations. Carrying capacity, predation, migration, and immunity loss are also taken into account for both species. Using the law of mass action, the physical model is transformed into a nonlinear coupled system of ODEs. The classical/integer order ODE system is then generalized through the fractal-fractional differential operators of power law and Mittag-Leffler kernels. For the model under consideration, we additionally check for positivity, boundedness, the basic reproduction number, and equilibrium points. Graphical results are obtained by use of a numerical approach, and the existence and uniqueness of the solution are also established theoretically. The graphical solutions has been displayed via 2D and 3D phase plots. It has been shown that when the fractional order reduces, the amplitude of the chaotic attractor dynamics shrinks, along with the range of limit cycles and periodic trajectories while a drop in the fractal dimension parameter causes an increase in the time period of the chaotic attractor dynamics. This study not only improves the understanding of epidemic breakouts in predator–prey systems, but also highlights the efficiency of fractal-fractional calculus in ecological modeling.