As global living standards improve and medical technology advances, many infectious diseases have been effectively controlled. However, certain diseases, such as the recent COVID-19 pandemic, continue to pose significant threats to public health. This paper explores the evolution of infectious disease modeling, from early ordinary differential equation-based models like the SIR framework to more complex reaction-diffusion models that incorporate both temporal and spatial dynamics. The study highlights the importance of numerical methods, such as the Runge-Kutta method, implicit-explicit time-discretization techniques, and finite difference methods, in solving these models. By analyzing the development and application of these methods, this research underscores their critical role in predicting disease spread, informing public health strategies, and mitigating the impact of future pandemics.

翻译：随着全球生活水平的提高和医疗技术的进步，许多传染病已得到有效控制。然而，某些疾病，如近期爆发的新型冠状病毒肺炎（COVID-19）疫情，仍对公共卫生构成重大威胁。本文探讨了传染病建模的发展历程，从早期基于常微分方程的模型（如SIR框架）到更复杂的、同时包含时间和空间动态的反应-扩散模型。研究强调了数值方法（如龙格-库塔法、隐式-显式时间离散化技术和有限差分法）在求解这些模型中的重要性。通过分析这些方法的发展与应用，本研究阐明了它们在预测疾病传播、指导公共卫生策略以及减轻未来大流行影响方面的关键作用。