Dynamic Analysis of Threshold and Seasonal Impact in the SVEIRL Influenza Model

In this paper, a periodic seasonal influenza SVEIRL model is constructed to explore the mechanism by which seasonal influenza factors exert social impacts. Through dynamic analysis of the model and verification via numerical simulations, it is revealed that seasonal factors exhibit a significant positive correlation with both the basic reproduction number and the final epidemic scale. Using surveillance data from institutions including the Chinese National Influenza Center and the Public Health Science, the model is applied to simulate the trends of influenza epidemic in China. Under multi-dimensional scenarios that include different years, provinces, influenza subtypes, and the proportion of influenza-like cases in northern and southern regions of China, approximate values of seasonal factors for each scenario are calculated using methods such as genetic algorithms and parameter fitting. The findings reaffirm that the intensity of seasonal factors is positively correlated with the scale of influenza epidemics.