Caputo fractional model for the predator–prey relation with sickness in prey and refuge to susceptible prey

Abstract

This research develops a model describing a relation between a predator and a prey where the prey species are divided into two classes i.e., susceptible prey species and the infected prey species. Furthermore, the susceptible prey species are also provided with a refuge. After this, the research expands the formulated model into a model with Caputo fractional derivative. A detailed analysis of the solution of Caputo fractional model for the predator–prey relation with a sickness in prey and a refuge to susceptible prey is done. Numerical solutions along with the simulations are briefed for the Caputo fractional model. Lastly, the phase portrait diagrams are also given for better understanding.

Keywords

• Predator–prey
• fractional derivative
• existence and uniqueness
• numerical solutions