Optimal parameterization of COVID-19 epidemic models

Zhang, Li; Huang, Jianping; Yu, Haipeng; Liu, Xiaoyue; Wei, Yun; Lian, Xinbo; Liu, Chuwei; Jing, Zhikun

At the time of writing, coronavirus disease 2019 (COVID-19) is seriously threatening human lives and health throughout the world. Many epidemic models have been developed to provide references for decision-making by governments and the World Health Organization. To capture and understand the characteristics of the epidemic trend, parameter optimization algorithms are needed to obtain model parameters. In this study, the authors propose using the Levenberg–Marquardt algorithm (LMA) to identify epidemic models. This algorithm combines the advantage of the Gauss–Newton method and gradient descent method and has improved the stability of parameters. The authors selected four countries with relatively high numbers of confirmed cases to verify the advantages of the Levenberg–Marquardt algorithm over the traditional epidemiological model method. The results show that the Statistical-SIR (Statistical-Susceptible–Infected–Recovered) model using LMA can fit the actual curve of the epidemic well, while the epidemic simulation of the traditional model evolves too fast and the peak value is too high to reflect the real situation. 摘要 现如今, æ–°å† è‚ºç‚Ž(COVID-19)严重威胁着世界各国人民的生命健康.许多流行病学模型已经被用于为政策制定者和世界卫生组织提供决策参考.ä¸ºäº†æ›´åŠ æ·±åˆ»çš„ç†è§£ç–«æƒ…è¶‹åŠ¿çš„å˜åŒ–ç‰¹å¾, 许多参数优化算法被用于反演模型参数.本文提议使用结合了高斯-牛顿法和梯度下降法的Levenberg–Marquardt(LMA)算法来优化模型参数.使用四个病例数相对较多的国家来验证这一算法的优势:ç›¸è¾ƒäºŽä¼ ç»Ÿæµè¡Œç—…å­¦æ¨¡åž‹æ¨¡æ‹Ÿæ›²çº¿è¿‡æ—©è¿‡å¿«çš„åˆ°è¾¾å³°å€¼, 应用LMAçš„Statistical-SIR(Statistical-Susceptible–Infected–Recovered)模型可以更好地拟合实际疫情曲线.