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

Multiple waves of COVID-19: a pathway model approach

A generalized pathway model, with time-dependent parameters, is applied to describe the mortality curves of the COVID-19 disease for several countries that exhibit multiple waves of infections. The pathway approach adopted here is formulated explicitly in time, in the sense that the model's growth rate for the number of deaths or infections is written as an explicit function of time, rather than in terms of the cumulative quantity itself. This allows for a direct fit of the model to daily data (new deaths or new cases) without the need of any integration. The model is applied to COVID-19 mortality curves for ten selected countries and found to be in very good agreement with the data for all cases considered. From the fitted theoretical curves for a given location, relevant epidemiological information can be extracted, such as the starting and peak dates for each successive wave. It is argued that obtaining reliable estimates for such characteristic points is important for studying the effectiveness of interventions and the possible negative impact of their relaxation, as it allows for a direct comparison of the time of adoption/relaxation of control measures with the peaks and troughs of the epidemic curve.

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.

Mathematical Models Supporting Control of COVID-19

Mathematical models have played an important role in the management of the coronavirus disease 2019 (COVID-19) pandemic. The aim of this review is to describe the use of COVID-19 mathematical models, their classification, and the advantages and disadvantages of different types of models. We conducted subject heading searches of PubMed and China National Knowledge Infrastructure with the terms "COVID-19," "Mathematical Statistical Model," "Model," "Modeling," "Agent-based Model," and "Ordinary Differential Equation Model" and classified and analyzed the scientific literature retrieved in the search. We categorized the models as data-driven or mechanism-driven. Data-driven models are mainly used for predicting epidemics, and have the advantage of rapid assessment of disease instances. However, their ability to determine transmission mechanisms is limited. Mechanism-driven models include ordinary differential equation (ODE) and agent-based models. ODE models are used to estimate transmissibility and evaluate impact of interventions. Although ODE models are good at determining pathogen transmission characteristics, they are less suitable for simulation of early epidemic stages and rely heavily on availability of first-hand field data. Agent-based models consider influences of individual differences, but they require large amounts of data and can take a long time to develop fully. Many COVID-19 mathematical modeling studies have been conducted, and these have been used for predicting trends, evaluating interventions, and calculating pathogen transmissibility. Successful infectious disease modeling requires comprehensive considerations of data, applications, and purposes.