AUTHOR=Li Zhuoyang , Lin Shengnan , Rui Jia , Bai Yao , Deng Bin , Chen Qiuping , Zhu Yuanzhao , Luo Li , Yu Shanshan , Liu Weikang , Zhang Shi , Su Yanhua , Zhao Benhua , Zhang Hao , Chiang Yi-Chen , Liu Jianhua , Luo Kaiwei , Chen Tianmu 

TITLE=An Easy-to-Use Public Health-Driven Method (the Generalized Logistic Differential Equation Model) Accurately Simulated COVID-19 Epidemic in Wuhan and Correctly Determined the Early Warning Time

JOURNAL=Frontiers in Public Health

VOLUME=Volume 10 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/public-health/articles/10.3389/fpubh.2022.813860

DOI=10.3389/fpubh.2022.813860

ISSN=2296-2565

ABSTRACT=Introduction: Modelling on infectious diseases is significant to facilitate public health policy making. 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 analyse these two models.
Methods: We collected data on (Corona Virus 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 the fit of LDE and GLDE models.
Results: 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 0.793-0.966 fitted by the GLDE model and varied between 0.594-0.922 fitted by the LDE model for diseases with different transmission routes. The R2 test values varied between 0.853-0.939 fitted by the GLDE model and varied form 0.687-0.769 fitted by the LDE model for diseases with different prevalence intensities. The R2 test value varied between 0.706-0.917 fitted by the GLDE model and varied between 0.410-0.898 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 0.897-0.970 versus 0.731-0.953 that fitted by the LDE model. Both models could characterize the patterns of the epidemics well and calculate the acceleration weeks. 
Conclusion: The GLDE model provides more accurate goodness of the 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 earlier epidemic acceleration week than GLDE model. We conclude that the GLDE model is more advantageous in asymmetric infectious disease data simulation.