Construction and empirical analysis of SEIRS infectious disease differential equation model with latent period

Infectious diseases have always been a focus of global public health attention. However, the current methods for analyzing and predicting the trend of infectious disease transmission are not comprehensive, resulting in significant discrepancies in the analysis results. To address this issue, a differential equation model of infectious diseases with latent periods is proposed for Susceptible-Exposed-Infectious-Recovered-Susceptible. On this basis, a staged model combined with logistic regression is established. Finally, in response to the problem of missing data related to infectious diseases in certain regions, LSTM networks and autoregressive integrated moving average models are used for prediction to assist differential equation models in disease transmission analysis. Through empirical analysis, it is known that the fitting degree between the results obtained from the infectious disease differential equation model proposed in the study and the actual results reaches 0.95, with a root mean square error of 0.03 and an average relative error of 3.5%. The prediction model proposed in the study achieves an accuracy of 92.72%, reaching convergence accuracy and convergence loss values after only 23 and 22 iterations. The differential equation model for infectious diseases proposed in the study can more accurately predict the spread trend of infectious diseases and provide scientific basis for public health decision-making.