S-shaped growth curve model-based instant prediction method for morbidity trend of seasonal influenza

Abstract

The invention discloses a seasonal influenza incidence trend instant prediction method based on an S-shaped growth curve model. The method comprises the following steps: firstly, collecting an influenza monitoring historical data sequence, and intercepting basically unimodal epidemic period data in a segmented manner; secondly, fitting different S-shaped curve models for the data of each epidemic period, summarizing and analyzing parameter characteristics of different models, and determining an optimal model suitable for each epidemic period according to a goodness of fit index; secondly, during prediction, fitting the model by adopting a partial parameter constraint mode for early-stage short sequence data of an epidemic situation, and fitting the sequence data after reaching a peak by adopting a parameter free estimation mode; and finally, predicting a future value by adopting a curve trend extrapolation method, and evaluating a prediction effect after a new observation value is received. According to the method, after reasonable constraint is carried out on partial parameter values of the S-shaped growth curve model, fitting of observation values is carried out, the deviation of predicted values obtained through trend extrapolation is within an acceptable range, and the method can be expanded and applied to immediate prediction in the early stage of epidemic situations.

Description

Technical Field

[0001] The present invention relates to the technical field of infectious disease epidemic trend prediction, and in particular to a method for instantly predicting seasonal influenza incidence trends based on an S-shaped growth curve model. Background Art

[0002] Seasonal influenza (hereinafter referred to as influenza) is highly contagious and has potentially serious clinical consequences, posing a significant threat to public health. Predicting influenza incidence trends is a crucial basis for developing influenza prevention and control strategies. Conducting real-time forecasts during the influenza epidemic period can assess the current epidemic situation and quantify the incidence trend and intensity of the epidemic in the next phase. This helps relevant departments and the public make more informed decisions, better implement various intervention measures, and rationally allocate medical resources, ultimately improving public health and mitigating the impact of the epidemic.

[0003] Epidemic trend forecasting methods include those based on statistical models (such as generalized linear regression and ARIMA time series analysis), mechanistic models (such as transmission dynamics models), machine learning / artificial intelligence, and ensemble models. Commonly used models rely heavily on historical data, and machine learning / artificial intelligence models typically require large amounts of high-quality training data. Overall, influenza shows a clear seasonal increase each year, but significant variations exist in the onset, intensity, progression, and duration of epidemics across seasons. Traditional, commonly used models rely heavily on historical data, thus impacting the accuracy and reliability of their forecasts. In the early stages of an epidemic, when training samples are significantly scarce, the accuracy of the forecasts from various models is generally difficult to guarantee.

[0004] Sigmoid curves were previously used to characterize population size fluctuations under environmental capacity constraints. Their application in epidemic forecasting offers advantages such as not needing to consider transmission mechanisms, low reliance on historical data, and relatively robust results. Previous applications have primarily focused on analyzing concluded or prolonged epidemics, in which all model parameters can be freely estimated using data. For epidemics with a unimodal incidence curve, the S-shaped growth curve model offers significant advantages in fitting. However, in the early stages of an epidemic, when the effective sample size is small, curve models whose parameters are based entirely on free estimation can only guarantee a good fit for the training sample, but cannot guarantee effectiveness when extrapolating predictions. Summary of the Invention

[0005] To this end, the technical problem to be solved by the present invention is the applicability of the S-shaped growth curve in real-time prediction in the early stages of an epidemic. By setting reasonable constraints on the upper asymptote and inflection point time parameters, it is possible to fit small sample training data and then carry out effective extrapolation predictions. The prediction error will be significantly reduced as the time window is extended, so it can be expanded to be used in the early stages of an epidemic.

[0006] The present invention comprises the following steps:

[0007] Step 1. Collect historical influenza surveillance data and segment the data for the epidemic period that is basically single-peak;

[0008] Step 2. Fit different S-shaped growth curve models to the data of each epidemic period, and use a free estimation method for the model parameters;

[0009] Step 3. Summarize and analyze the parameter characteristics of different curve models and determine the optimal model suitable for each epidemic period based on the goodness of fit index;

[0010] Step 4. When implementing the forecast, for short series data from the early stage of the epidemic, the model is fitted using partial parameter constraints, while for series data after the peak, the model can be fitted using free parameter estimation;

[0011] Step 5. Use the curve trend extrapolation method to predict future values, and evaluate the prediction effect after receiving new observations. Dynamically update the model as time progresses and carry out the next prediction.

[0012] Compared with the prior art, the present invention has the following advantages:

[0013] In the early stages of an epidemic, when the sample size is extremely small and the epidemic trend is unclear, the commonly used quantitative prediction methods are not applicable or it is difficult to guarantee the accuracy of the prediction results. The application of existing S-shaped growth curve models in the field of epidemic prevention and control is seen in the fitting of data from epidemics that have subsided or lasted for a long time. The growth curve model uses a parameter free estimation method, and extrapolated predictions often produce errors far exceeding expectations, which is not suitable for application in the early stages of an epidemic. The prediction method established by the present invention reasonably constrains the values ​​of some parameters of the S-shaped growth curve model and then fits the observed values. The deviation of the predicted value obtained by the trend extrapolation method is within an acceptable range, so it can be expanded to real-time predictions in the early stages of an epidemic. Based on the real-time prediction of small sample sequences, the trend and scale of the epidemic can be predicted in the early stages of the epidemic, which is conducive to better implementation of public health intervention measures and mitigation of the adverse effects of the epidemic on society and the public. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to make the content of the present invention easier to understand, the following is a visual demonstration of the specific embodiments of the present invention.

[0015] Figure 1 This is a flow chart of the method for instantly predicting seasonal influenza incidence trends based on the S-shaped growth curve model of the present invention;

[0016] Figure 2This is the result of fitting three curve models simultaneously to the influenza activity in Zhejiang Province during the 2023-2024 epidemic season using parameter free estimation in an embodiment of the present invention;

[0017] Figure 3 This is the result of simulating real-time prediction of influenza activity in Zhejiang Province during the 2024-2025 epidemic season using a logistic curve model using parameter constraints in an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0019] Reference Figure 1 As shown, the embodiment of the present application provides a method for instantly predicting the incidence trend of seasonal influenza based on an S-shaped growth curve model, comprising the following steps:

[0020] S1: Collect historical influenza surveillance data series and segment the epidemic period data that are basically single-peak;

[0021] S2: Fit different S-shaped curves to the data of each epidemic period, and use a free estimation method for the parameters of the model;

[0022] S3: Summarize and analyze the parameter characteristics of various curve models. Determine the optimal model suitable for each epidemic period based on the goodness of fit index;

[0023] S4: When implementing forecasts, use partial parameter constraints to fit the model for short series data from the early stages of the epidemic. For series data after the peak, try fitting with free parameter estimation.

[0024] S5: Use the curve trend extrapolation method to predict future values. After receiving new observations, evaluate the prediction results, dynamically update the model over time, and carry out the next prediction.

[0025] Specifically, there are many types of S-shaped curve models. This application example selects three commonly used 4-parameter models: Logistic, Gompertz and Probit curve models. The expressions of the three curve models are:

[0026]

[0027]

[0028]

[0029] Among various Represents the cumulative value of the target variable at time t, such as the cumulative number of reported cases or influenza activity. The model parameters L are the lower asymptote; U is the upper asymptote; M is the time of inflection, which is the interval between t = 0 and the maximum value of new additions; and r is the growth rate. Normsdist() in the probit curve formula represents the value of the standard normal distribution function.

[0030] In this embodiment, the observed value is the influenza activity index collected on a weekly basis, and the data is derived from the Zhejiang Provincial Influenza Surveillance Information System. Influenza activity = ILI% × influenza virus detection positivity rate. In the influenza activity sequence recorded weekly from 2013 to 2024, data from each epidemic year with a single peak or approximately single peak in the autumn and winter epidemic curve were selected. Five relatively typical epidemic season observations were actually extracted, namely 2013-2014, 2017-2018, 2018-2019, 2019-2000 and 2023-2024. For the interception of the influenza epidemic season sequence in an epidemic year: when the observed values ​​for three consecutive weeks are greater than the median of the observed values ​​for that epidemic year, it indicates the entry into the epidemic period, and the first week is marked as t=1; when the observed values ​​for the last three consecutive weeks of the downward period of the epidemic curve are greater than the median of the observed values ​​for that epidemic year, it is considered the end of the epidemic period, and the last week is the end time of the epidemic period.

[0031] The raw data series represents the increments of influenza activity each week, accumulated period by period to form a cumulative series of observations. In step S2, three different S-shaped curve models are fitted to the series data from the same epidemic period. The parameter estimation method is nonlinear least squares, and no parameter constraints are specified during model fitting. Observation fitting can be performed using the drc package in R or the "Solver" analysis tool in Excel.

[0032] After fitting the data for each epidemic season, step S3 extracts parameter values ​​for different epidemic seasons and curve models. The maximum and minimum values ​​are primarily used to determine the parameter range, which is used to set the upper and lower bounds of the parameter constraints during fitting in step S4. For the logistic curve fit of the data from the five epidemic seasons, the U value range is (28.5-110.6) and the M value range is (5.9-13.7). In practical applications, integers wider than the upper and lower bounds can be used. In this example, U is set to (25-120) and M is set to (5-14).

[0033] For series of different epidemic seasons, the optimal model is determined based on indicators such as the root mean square error (RMSE) or the mean absolute percentage error (MAPE). The model with the smaller RMSE or MAPE value is the preferred model, and the types of curve models that fit the historical data series better are summarized. The calculation formulas for the two indicators are,

[0034] ;

[0035] .

[0036] In the above formula, are the observed value and fitted value at time t, respectively, and N is the sample size.

[0037] The preferred models for fitting the five epidemic periods in this example are: Logistic curve for 2013-2014, Probit curve for 2017-2018, Gompertz curve for 2018-2019, Probit curve for 2019-2000, and Logistic curve for 2023-2024. Figure 2 .

[0038] Step S4 fits the curve model for the early stages of a new influenza season, which will be used for further forecasting. The sample size of the observed sequence data collected at this time is very small, so the fitting process requires defining the ranges of the two parameters, U and M, according to the conditions in the previous steps. For larger sample sizes of sequence data after the peak of the epidemic, a free parameter estimation approach can be used for fitting.

[0039] Step S5 substitutes the parameter values ​​obtained by fitting under some parameter constraints into the corresponding formula to implement trend extrapolation prediction to obtain cumulative values, and obtains the predicted sequence of new values ​​after first-order difference, that is, the incidence intensity at different time points. Through the visual analysis of the predicted new value series, key nodes such as peak time and end time of the epidemic can be intuitively identified. Figure 3 .

[0040] The prediction performance of different curve models can be evaluated using metrics such as the RMSE (RMSE) and MAPE (Massive Error Proportional Error) of observed and predicted values, and the proportion of observed values ​​included in the 95% prediction interval. As new observations are collected over time, the performance of previous forecasts can be evaluated, and model fitting can be performed with extended time windows, while also updating trend extrapolation forecast results.

[0041] This example uses a logistic curve model to simulate and predict data from the 2024-2025 epidemic period. Analysis is performed in weeks 3, 5, 7, and 9 of the epidemic period. After collecting observations up to the aforementioned weeks, the logistic curve model is fitted using parameters U (25-120) and M (5-14). After obtaining estimates for all parameters, these estimates are inserted into the formula to obtain a cumulative series of values ​​for the entire epidemic period. The first-order difference results are the newly added series of influenza activity for each week. The observed data in this example are right-skewed, so an S-shaped curve model with shape parameters can be considered for practical applications.

[0042] The embodiments of the present invention are described in detail above, but the contents are only preferred embodiments of the present invention and should not be considered to limit the scope of the present invention. Any changes and improvements made within the scope of the present invention should still fall within the scope of the patent coverage of the present invention.

Claims

1. A method for real-time prediction of seasonal influenza incidence trends, characterized in that: The following steps are involved: Step 1. Collect historical influenza surveillance data and segment the data for the epidemic period that is basically single-peak; Step 2. Fit different S-shaped growth curve models to the data of each epidemic period, and use a free estimation method for the model parameters; Step 3. Summarize and analyze the parameter characteristics of different curve models and determine the optimal model suitable for each epidemic period based on the goodness of fit index; Step 4. When implementing the forecast, for short series data from the early stage of the epidemic, the model is fitted using partial parameter constraints, while for series data after the peak, the model is fitted using free parameter estimation; Step 5. Use the curve trend extrapolation method to predict future values, and evaluate the prediction effect after receiving new observations. Dynamically update the model as time progresses and carry out the next prediction.

2. The method for instant prediction of seasonal influenza incidence trend according to claim 1, characterized in that: The S-shaped growth curve model includes a Logistic model, a Gompertz model and a Probit model.

3. The method for instant prediction of seasonal influenza incidence trend according to claim 1, characterized in that: The step 1 comprises: Obtain influenza activity indicators recorded in time series from the Influenza Surveillance Information System; Select data from each epidemic season with a single-peak or nearly single-peak epidemic curve in autumn and winter; For the interception of an epidemic season sequence, the starting week when the observation values ​​for three consecutive weeks are greater than the median of the observation values ​​of the epidemic season is marked as the beginning of the epidemic period, and the ending week when the observation values ​​for the last three consecutive weeks of the downward period of the epidemic curve are greater than the median of the observation values ​​of the epidemic season is marked as the end of the epidemic period.

4. The method for instant prediction of seasonal influenza incidence trend according to claim 2, characterized in that: The step 2 includes: The nonlinear least squares method was used to fit different types of S-shaped curve models to the serial data of the same epidemic period; No parameter constraints are specified when fitting the model, and the parameters are freely estimated.

5. The method for instant prediction of seasonal influenza incidence trend according to claim 1, characterized in that: The step 3 includes: Extract parameter values ​​for different epidemic seasons and different curve models, and determine the parameter value range based on the maximum and minimum values; Determine the preferred model based on the root mean square error or mean absolute percentage error.

6. The method for instant prediction of seasonal influenza incidence trend according to claim 2, characterized in that: The step 4 comprises: For the series data with small sample size in the early stage of the epidemic, the value ranges of the two parameters, upper asymptote and inflection point time, are constrained; For serial data with large sample sizes after the epidemic peaks, the model is fitted using the parameter free estimation method.

7. The method for instant prediction of seasonal influenza incidence trend according to claim 6, characterized in that: The step 5 comprises: According to the model parameters obtained by fitting, the corresponding formula is substituted to perform trend extrapolation forecasting and obtain the cumulative value forecast sequence; Perform first-order difference on the cumulative value prediction sequence to obtain the prediction sequence of the newly added value; Predict new value-added sequences through visual analysis to identify peak times and end times of the epidemic; As time progresses, new observations are collected, the predictions are evaluated, and the model is updated dynamically.

8. The method for instant prediction of seasonal influenza incidence trend according to claim 1 or 7, characterized in that: The method further comprises the steps of evaluating and updating the prediction results: The prediction effect was evaluated using the root mean square error between the observed and predicted values, the mean absolute percentage error, and the proportion of the observed values ​​included in the 95% prediction interval. Dynamically adjust model parameters based on new observations and update prediction results to improve prediction accuracy and reliability.

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