On the modeling of an eco-epidemiological model using a new fractional operator

Abstract Having advanced numerical techniques in solving fractional problems is always one of the apparent needs in increasing the use of these tools in real-world problems. The major part of the progress made in this area has been due to development of effective numerical methods and techniques. In this article, we study a new approach to analyze the dynamics of an eco-epidemiological through a nonlinear fractional system of differential equations. Eco-epidemiology has become a significant topic of computational biology which connects ecology with epidemiology. In these models, the presence of a disease in one of populations in the environment brings major changes in the essential components of that system. For the model, the equilibrium points of the system are calculated. Then we present the convergence and uniqueness theorems of the solution obtained from the use of the fractional derivative operator. In another part of this research, the algorithm for implementing a numerical technique with high accuracy in approximating the numerical solutions of a fractional-order system is expressed. Using this algorithm, various numerical simulations are considered in the paper regarding to some parameters’ role in the model. Adding significant benefits from fractional-order derivatives to the model will be one of the achievements of this paper. A similar trend can be tested in the study of other models in eco-epidemiological problems.

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