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.

在分数问题中使用先进的数值技术始终是增加在实际问题中使用这些工具的明显需求之一。在这一领域取得进展的主要部分归功于有效数值方法和技术的发展。在本文中，我们研究了一种通过微分方程的非线性分数系统分析生态流行病学动态的新方法。生态流行病学已成为将生态学与流行病学联系起来的计算生物学的重要课题。在这些模型中，环境中某一种群中某种疾病的存在给该系统的基本组成部分带来了重大变化。对于模型，计算系统的平衡点。然后，我们介绍了使用分数导数算子获得的解的收敛性和唯一性定理。在本研究的另一部分中，表达了一种用于在近似分数阶系统的数值解时以高精度实现数值技术的算法。使用该算法，本文考虑了一些数值模拟，涉及一些参数在模型中的作用。将分数阶导数添加到模型中会带来很多好处，这将是本文的成就之一。在研究生态流行病学问题的其他模型时，也可以检验出类似的趋势。给出了一种在近似分数阶系统数值解中实现高精度数值技术的算法。使用该算法，本文考虑了一些数值模拟，涉及一些参数在模型中的作用。将分数阶导数添加到模型中会带来很多好处，这将是本文的成就之一。在研究生态流行病学问题的其他模型时，也可以检验类似的趋势。给出了一种在近似分数阶系统数值解中实现高精度数值技术的算法。使用该算法，本文考虑了一些数值模拟，涉及一些参数在模型中的作用。将分数阶导数添加到模型中会带来很多好处，这将是本文的成就之一。在研究生态流行病学问题的其他模型时，也可以检验类似的趋势。