In this paper, we propose a fractional-order prey-predator model with reserved area in the presence of the toxicity and competition. We prove different mathematical results like existence, uniqueness, non negativity and boundedness of the solution for our model. Further, we discuss the local and global stability of these equilibria. Finally, we perform numerical simulations to prove our results.

In this article, we consider a fractional $SEIR$ model, denoted by the $SEIQHR$ model, which aims to predict the outbreak of infectious diseases in general. In particular, we study the spread of COVID-19. The fractional order offers a flexible, appropriate, and reliable framework for pandemic growth characterization. Firstly, we analyze some elementary results of the model (boundedness and uniqueness of solutions). In addition, we establish certain conditions to ensure the local stability of the disease-free and endemic equilibrium points. Based on analytical and numerical results, we conclude that coronavirus infection (COVID-19) remains endemic, which requires long-term prevention and intervention strategies.