The study on the early warning period of varicella outbreaks based on logistic differential equation model

Using Baidu Index Data to Improve Chickenpox Surveillance in Yunnan, China: Infodemiology Study

BACKGROUND

Chickenpox is an old but easily neglected infectious disease. Although chickenpox is preventable by vaccines, vaccine breakthroughs often occur, and the chickenpox epidemic is on the rise. Chickenpox is not included in the list of regulated communicable diseases that must be reported and controlled by public and health departments; therefore, it is crucial to rapidly identify and report varicella outbreaks during the early stages. The Baidu index (BDI) can supplement the traditional surveillance system for infectious diseases, such as brucellosis and dengue, in China. The number of reported chickenpox cases and internet search data also showed a similar trend. BDI can be a useful tool to display the outbreak of infectious diseases.

OBJECTIVE

This study aimed to develop an efficient disease surveillance method that uses BDI to assist in traditional surveillance.

METHODS

Chickenpox incidence data (weekly from January 2017 to June 2021) reported by the Yunnan Province Center for Disease Control and Prevention were obtained to evaluate the relationship between the incidence of chickenpox and BDI. We applied a support vector machine regression (SVR) model and a multiple regression prediction model with BDI to predict the incidence of chickenpox. In addition, we used the SVR model to predict the number of chickenpox cases from June 2021 to the first week of April 2022.

RESULTS

The analysis showed that there was a close correlation between the weekly number of newly diagnosed cases and the BDI. In the search terms we collected, the highest Spearman correlation coefficient was 0.747. Most BDI search terms, such as "chickenpox," "chickenpox treatment," "treatment of chickenpox," "chickenpox symptoms," and "chickenpox virus," trend consistently. Some BDI search terms, such as "chickenpox pictures," "symptoms of chickenpox," "chickenpox vaccine," and "is chickenpox vaccine necessary," appeared earlier than the trend of "chickenpox virus." The 2 models were compared, the SVR model performed better in all the applied measurements: fitting effect, R²=0.9108, root mean square error (RMSE)=96.2995, and mean absolute error (MAE)=73.3988; and prediction effect, R²=0.548, RMSE=189.1807, and MAE=147.5412. In addition, we applied the SVR model to predict the number of reported cases weekly in Yunnan from June 2021 to April 2022 using the same period of the BDI. The results showed that the fluctuation of the time series from July 2021 to April 2022 was similar to that of the last year and a half with no change in the level of prevention and control.

CONCLUSIONS

These findings indicated that the BDI in Yunnan Province can predict the incidence of chickenpox in the same period. Thus, the BDI is a useful tool for monitoring the chickenpox epidemic and for complementing traditional monitoring systems.

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

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.

An Easy-to-Use Public Health-Driven Method (the Generalized Logistic Differential Equation Model) Accurately Simulated COVID-19 Epidemic in Wuhan and Correctly Determined the Early Warning Time

Introduction

Modeling on infectious diseases is significant to facilitate public health policymaking. There are two main mathematical methods that can be used for the simulation of the epidemic and prediction of optimal early warning timing: the logistic differential equation (LDE) model and the more complex generalized logistic differential equation (GLDE) model. This study aimed to compare and analyze these two models.

Methods

We collected data on (coronavirus disease 2019) COVID-19 and four other infectious diseases and classified the data into four categories: different transmission routes, different epidemic intensities, different time scales, and different regions, using R2 to compare and analyze the goodness-of-fit of LDE and GLDE models.

Results

Both models fitted the epidemic curves well, and all results were statistically significant. The R2 test value of COVID-19 was 0.924 (p &lt; 0.001) fitted by the GLDE model and 0.916 (p &lt; 0.001) fitted by the LDE model. The R2 test value varied between 0.793 and 0.966 fitted by the GLDE model and varied between 0.594 and 0.922 fitted by the LDE model for diseases with different transmission routes. The R2 test values varied between 0.853 and 0.939 fitted by the GLDE model and varied from 0.687 to 0.769 fitted by the LDE model for diseases with different prevalence intensities. The R2 test value varied between 0.706 and 0.917 fitted by the GLDE model and varied between 0.410 and 0.898 fitted by the LDE model for diseases with different time scales. The GLDE model also performed better with nation-level data with the R2 test values between 0.897 and 0.970 vs. 0.731 and 0.953 that fitted by the LDE model. Both models could characterize the patterns of the epidemics well and calculate the acceleration weeks.

Conclusion

The GLDE model provides more accurate goodness-of-fit to the data than the LDE model. The GLDE model is able to handle asymmetric data by introducing shape parameters that allow it to fit data with various distributions. The LDE model provides an earlier epidemic acceleration week than the GLDE model. We conclude that the GLDE model is more advantageous in asymmetric infectious disease data simulation.

Seasonal dynamics of varicella incidence in Bulgaria

Aim: Spatial and temporal distribution of varicella is heterogenic and insufficiently studied in Europe. The present study tries to fill the gap that exists about the seasonality of the infection in Bulgaria. Materials & methods: A 4-year retrospective study of the monthly and seasonal varicella epidemiology was performed at both national and district level. Results: In Bulgaria, varicella incidence peaked during winter (37% of the 2015–2018 cases), followed by spring (33%) and autumn (23%). Highly populated districts were more likely to follow this pattern, while less inhabited districts with smaller urbanized areas showed different periodicity of the infection. Conclusion: Winter peak in varicella incidence is positively associated with high accumulation of people in the large cities (>75,000 inhabitants).

Research about the optimal strategies for prevention and control of varicella outbreak in a school in a central city of China: based on an SEIR dynamic model

Varicella is an acute respiratory infectious diseases, with high transmissibility and quick dissemination. In this study, an SEIR (susceptible-exposed-infected-recovered) dynamic model was established to explore the optimal prevention and control measures according to the epidemiological characteristics about varicella outbreak in a school in a central city of China. Berkeley Madonna 8.3.18 and Microsoft Office Excel 2010 software were employed for the model simulation and data management, respectively. The result showed that the simulated result of SEIR model agreed well with the reported data when β (infected rate) equal to 0.067. Models showed that the cumulative number of cases was only 13 when isolation adopted when the infected individuals were identified (assuming isolation rate was up to 100%); the cumulative number of cases was only two and the TAR (total attack rate) was 0.56% when the vaccination coefficient reached 50%. The cumulative number of cases did not change significantly with the change of efficiency of ventilation and disinfection, but the peak time was delayed; when δ (vaccination coefficient) = 0.1, m (ventilation efficiency) = 0.7 or δ = 0.2, m = 0.5 or δ = 0.3, m = 0.1 or δ = 0.4 and above, the cumulative number of cases would reduce to one case and TAR would reduce to 0.28% with combined interventions. Varicella outbreak in school could be controlled through strict isolation or vaccination singly; combined interventions have been adopted when the vaccination coefficient was low.