In this paper, we propose a new SEIRS model and are concerned with stability and numerical solutions of the model. The model is generated under certain assumptions such as individuals are vaccinated or have a special treatment but do not carry lifelong immunity. After generating a new SEIRS model, we perturb the model into fractional time derivative form where Caputo type fractional-order derivative operators are employed. After showing existence and uniqueness of the non-negative solutions, we determine disease free steady-state point and basic reproduction number. We also determine endemic steady state points and study on stability of the fractional system in these equilibrium points. We solve fractional-order system approximately with an efficient Euler type numerical method. We conclude that the proposed system may serve as a kernel for understanding, analysis and computational solutions of a wide range of disease models in epidemiology.

在本文中，我们提出了一个新的SEIRS模型，并关注该模型的稳定性和数值解。该模型是在某些假设下生成的，例如个人已接种疫苗或接受特殊治疗，但没有终身免疫力。生成新的SEIRS模型后，我们将模型扰动为分数时间导数形式，其中使用了Caputo类型的分数阶导数算子。在显示出非负解的存在性和唯一性之后，我们确定无病稳态点和基本繁殖数。我们还确定地方性稳态点，并研究这些平衡点上分数系统的稳定性。我们使用有效的Euler型数值方法近似求解分数阶系统。