Chaotic behaviors of the prevalence of an infectious disease in a prey and predator system using fractional derivatives

The risk of spread infectious diseases in the environment is always one of the main threats to the life of living organisms. This point can be assumed as a clear proof of the importance of studying such problems from various aspects such as computational mathematical models. In this contribution, we examine a mathematical model to investigate the prevalence of an infectious disease in a prey and predator system, including three subpopulations through a fractional system of nonlinear equations. The model characterizes a possible interaction between predator and prey where infectious disease outbreaks in a community. Further, the prey population is divided into two: susceptible and the infected population. This model involves the Caputo-Fabrizio derivative. One of the basic features of this type of derivative is the use of a non-singular (exponential) kernel, which increases its ability to describe phenomena compared to other existing operators. To the best of the author's knowledge, the use of fractional derivative operators for this model has not yet been investigated. Therefore, the presented results can be considered as new and interesting results for this model. In some of the acquired simulations, the chaotic behaviors are clearly detectable.