Application of Logistic Differential Equation Models in Early Warning of Infectious Diseases

Abstract Background: There is still a relatively serious disease burden of infectious diseases and the warning time for different infectious diseases before implementation of interventions is important. The logistic differential equation models can be used for predicting early warning of infectious diseases, the aim of this study is to compare the disease fitting effect of the logistic differential equation (LDE) model and the generalised logistic differential equation (GLDE) model, using the two models to calculate the early warning signals of different types of infectious diseases and to solve for disease early warning schedules throughout the year. Methods: Collecting the incidence of 22 infectious diseases in Jilin Province, China. The LDE and GLDE models were used to calculate the recommended warning week (RWW), the epidemic acceleration week (EAW) and warning removed week (WRW) for acute infectious diseases with seasonality, respectively. Results: Five diseases were selected for analysis based on screening principles: hemorrhagic fever with renal syndrome (HFRS), shigellosis, mumps, Hand, foot and mouth disease (HFMD), and scarlet fever. The GLDE model fitted the above diseases better (0.80 ≤ R2 ≤ 0.94, P < 0. 005) than the LDE model. The estimated warning durations (per year) of the LDE model for the above diseases were: weeks 12-23 and 40-50; weeks 20-36; weeks 15-24 and 43-52; weeks 26-34; and weeks 16-25 and 41-50. While the durations of early warning (per year) estimated by the GLDE model were: weeks 7-24 and 36-51; weeks 13-37; weeks 11-26 and 39-54; weeks 23-35; and weeks 12-26 and 40-50. Conclusions: Compared to the LDE model, the GLDE model provides a better fit to the actual disease incidence data. The RWW appeared to be earlier when estimated with the GLDE model than the LDE model. In addition, the WRW estimated with the GLDE model were more lagged and had a longer warning time.