Application of logistic differential equation models for early warning of infectious diseases in Jilin Province

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 effects of the logistic differential equation (LDE) model and the generalized logistic differential equation (GLDE) model for the first time using data on multiple infectious diseases in Jilin Province and to calculate the early warning signals for different types of infectious diseases using these two models in Jilin Province to solve the disease early warning schedule for Jilin Province 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.

Keywords: Early warning; Generalized logistic differential equation model; Infectious diseases; Jilin province; Logistic differential equation model; Mathematical model.

Fig. 1

Research and design technology roadmap. (n is the cumulative number of infectious disease cases; N is the upper limit of cumulative infectious disease cases; k is the correlation coefficient; c is a constant; λ is a shape parameter; SD is the standard deviation; EAW is epidemic acceleration week; RWW is recommended warning week; WRW is warning removed week)

Fig. 2

Overview of the incidence of 22 infectious diseases in Jilin Province, 2005–2019

Fig. 3

Fitted effectiveness of HFRS, shigellosis, mumps, HFMD and scarlet fever in Jilin Province, 2005–2019

Fig. 4

Early warning weeks for HFRS, shigellosis, mumps, HFMD and scarlet fever in Jilin Province in each year. (RWW is recommended warning week)

Fig. 5

Duration of warning for HFRS, shigellosis, mumps, HFMD and scarlet fever in Jilin Province. (EAW is epidemic acceleration week; RWW is recommended warning week; WRW is warning removed week)