The mathematical modeling of the propagation of illnesses has an important role from both mathematical and biological points of view. In this article, we observe an SEIR-type model with a general incidence rate and a non-constant recruitment rate function. First, we observe the qualitative properties of different methods: first-order and higher-order strong stability preserving Runge-Kutta methods \cite{shu}. We give different conditions under which the numerical schemes behave as expected. Then, the theoretical results are demonstrated by some numerical experiments. \keywords{positivity preservation, general SEIR model, SSP Runge-Kutta methods}

翻译：疾病传播的数学建模在数学和生物学角度都具有重要作用。本文研究了一类具有一般发生率及非常量招募率函数的SEIR型模型。首先，我们分析了不同方法（一阶及高阶强稳定性保持龙格-库塔方法\cite{shu}）的定性性质。给出了数值格式行为符合预期的不同条件。随后，通过一些数值实验验证了理论结果。\keywords{正性保持，一般SEIR模型，SSP龙格-库塔方法}