Modeling on infectious diseases is significant to facilitate public health policymaking. There are two main mathematical methods that can be used for the simulation of the epidemic and prediction of optimal early warning timing: the logistic differential equation (LDE) model and the more complex generalized logistic differential equation (GLDE) model. This study aimed to compare and analyze these two models.

We collected data on (coronavirus disease 2019) COVID-19 and four other infectious diseases and classified the data into four categories: different transmission routes, different epidemic intensities, different time scales, and different regions, using R² to compare and analyze the goodness-of-fit of LDE and GLDE models.

Both models fitted the epidemic curves well, and all results were statistically significant. The R² test value of COVID-19 was 0.924 (p < 0.001) fitted by the GLDE model and 0.916 (p < 0.001) fitted by the LDE model. The R² test value varied between 0.793 and 0.966 fitted by the GLDE model and varied between 0.594 and 0.922 fitted by the LDE model for diseases with different transmission routes. The R² test values varied between 0.853 and 0.939 fitted by the GLDE model and varied from 0.687 to 0.769 fitted by the LDE model for diseases with different prevalence intensities. The R² test value varied between 0.706 and 0.917 fitted by the GLDE model and varied between 0.410 and 0.898 fitted by the LDE model for diseases with different time scales. The GLDE model also performed better with nation-level data with the R² test values between 0.897 and 0.970 vs. 0.731 and 0.953 that fitted by the LDE model. Both models could characterize the patterns of the epidemics well and calculate the acceleration weeks.

The GLDE model provides more accurate goodness-of-fit to the data than the LDE model. The GLDE model is able to handle asymmetric data by introducing shape parameters that allow it to fit data with various distributions. The LDE model provides an earlier epidemic acceleration week than the GLDE model. We conclude that the GLDE model is more advantageous in asymmetric infectious disease data simulation.

传染病建模对于促进公共卫生决策具有重要意义。有两种主要的数学方法可用于模拟流行病和预测最佳预警时机：逻辑微分方程（LDE）模型和更复杂的广义逻辑微分方程（GLDE）模型。本研究旨在比较和分析这两种模型。

我们收集了关于（冠状病毒病 2019）COVID-19 和其他四种传染病的数据，并将数据分为四类：不同的传播途径、不同的流行强度、不同的时间尺度和不同的地区，使用R²比较分析LDE和GLDE模型的拟合优度。

两种模型都很好地拟合了流行曲线，所有结果都具有统计学意义。这R^{COVID-19 的2}测试值为 0.924 (p< 0.001) 由 GLDE 模型拟合，0.916 (p< 0.001) 由 LDE 模型拟合。这R²检验值在 GLDE 模型拟合的 0.793 和 0.966 之间变化，对于具有不同传播途径的疾病，LDE 模型在 0.594 和 0.922 之间变化。这R²检验值在 GLDE 模型拟合的 0.853 和 0.939 之间变化，对于不同流行强度的疾病，LDE 模型在 0.687 和 0.769 之间变化。这R²检验值在 GLDE 模型拟合的 0.706 和 0.917 之间变化，对于不同时间尺度的疾病，在 LDE 模型拟合的 0.410 和 0.898 之间变化。GLDE 模型在国家级数据上的表现也更好R²测试值介于 0.897 和 0.970 之间与 LDE 模型拟合的 0.731 和 0.953。两种模型都可以很好地描述流行病的模式并计算加速周。

与 LDE 模型相比，GLDE 模型为数据提供了更准确的拟合优度。GLDE 模型能够通过引入形状参数来处理非对称数据，使其能够拟合具有各种分布的数据。LDE 模型提供了比 GLDE 模型更早的流行病加速周。我们得出结论，GLDE 模型在非对称传染病数据模拟中更具优势。