Infectious disease transmission analysis method based on multimodal distribution optimization

Abstract

The invention discloses a multimodal distribution optimization-based infectious disease transmission analysis method, which comprises the following steps of: acquiring incubation period data and related characteristics of infectious disease cases, performing data preprocessing, dividing the data into a training set, a verification set and a test set, constructing a mixed density network (MDN) model for parameter learning and optimization, and finally performing prevention and control index analysis. And converting a multi-peak model result into a prevention and control decision basis, and completing infectious disease transmission analysis. According to the method, by constructing the dynamic mixed distribution model and combining crowd feature layering and data-driven parameter learning, single-peak distribution limitation is broken through, multi-peak distribution features caused by different propagation routes or crowd heterogeneity and the like are accurately captured, the adaptability and parameter estimation precision of the model to complex propagation scenes are improved, and the method is suitable for popularization and application. And a scientific basis is provided for formulating an infectious disease prevention and control strategy.

Description

Technical Field

[0001] This invention belongs to the field of epidemiology and public health data analysis technology, specifically relating to an infectious disease transmission analysis method based on multi-peak distribution optimization. Background Technology

[0002] Currently, when analyzing or predicting infectious disease data, statistical analysis, dynamic models, or neural networks can be used. In existing dynamic modeling, the incubation period and infective period are crucial for transmission analysis. The incubation period reflects the time from exposure to symptom onset, and its distribution characteristics influence the initiation and potential duration of transmission; for example, infectious diseases with long incubation periods are more likely to spread covertly. The infective period determines the timeframe for an individual's infectivity and is directly related to the duration and scale of transmission. However, it is often modeled as an exponential distribution, meaning that the probability of an individual leaving an exposed or infected state remains constant over time. This assumption ignores the fact that this probability changes over time, potentially leading to systematic biases in model predictions and policy recommendations. Therefore, overcoming biases in epidemiological parameter estimation and improving existing models through more realistic and historically dependent disease transmission dynamics has become a core issue.

[0003] The paper "Hong, H., Eom, E., Lee, H. et al. Overcoming bias in estimating epidemic parameters with realistic history-dependent disease spread dynamics. Nature Communications, 2024, (15): 8734-8747" proposes an inference method based on Bayesian Markov Chain Monte Carlo. This method not only estimates R-values ​​more accurately in the initial stage but also maintains robustness in the mid-stage of the epidemic and under different initial conditions. This study demonstrates the scalability of the method by providing a user-friendly computational package called IONISE, applicable to complex epidemic dynamics scenarios such as vaccination, variant transmission, and unreported cases. The paper "Ali, T. Comparing Methods for Estimating Gamma Distribution Parameters with Outliers Observation. Journal of Economics and Administrative Sciences, 2025, 31(145), pp. 163–174" proposes a method combining Hampel filter and median rank regression (HMRR). This method effectively handles outliers and, compared to existing statistical methods, estimates the shape and scale parameters of the Gamma distribution more accurately under different sample sizes and parameter values. It also demonstrates good robustness in both simulated and real-world data scenarios. This research provides a more effective parameter estimation tool for reliability analysis and has broad application prospects in system lifetime prediction and maintenance intervention planning.

[0004] However, the existing technologies mentioned above still have many shortcomings. Most current infectious disease transmission models employ a unimodal distribution assumption (such as exponential or gamma distribution), but the actual incubation period / infectious period of a disease often exhibits complex multimodal characteristics. In cases like COVID-19, different transmission routes lead to significant differences in the incubation period distribution, and traditional gamma distributions cannot capture these multimodal characteristics, resulting in biased model parameter estimation. Furthermore, in reality, infectious disease transmission is influenced by multiple factors, and existing methods rely on static data and fixed distribution assumptions, making it impossible to update parameters in real time. Therefore, a new method for analyzing infectious disease transmission is needed. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for analyzing the spread of infectious diseases based on multi-peak distribution optimization, offering a scientific basis for formulating infectious disease prevention and control strategies.

[0006] The technical solution adopted in this invention is: a method for analyzing the transmission of infectious diseases based on multi-peak distribution optimization, the specific steps of which are as follows:

[0007] S1. Collect incubation period data and related characteristics of infectious disease cases, then perform data preprocessing, and divide the preprocessed data into training set, validation set and test set;

[0008] First, incubation period data and related characteristics of infectious disease cases were systematically collected. These characteristics included population features and time-series features. Incubation period data recorded the number of days from exposure to the onset of symptoms. Population characteristics are identified through feature vectors. This includes: age Viral load Transmission routes Vaccination status Time-related features include: case report timestamps and their statistical observations within a preset sliding window.

[0009] in, Represents the real number field; This represents the total number of dimensions of the population characteristics after preprocessing; propagation pathways. Including: droplets, aerosols; vaccination status Includes: those who have been vaccinated and those who have not.

[0010] The collected data is then preprocessed, including cleaning and standardization, and different strategies are used to handle missing values ​​depending on the feature type.

[0011] Among them, continuous characteristics such as age and viral load are predicted by means or regression, while categorical characteristics such as transmission route and vaccination status are marked as "unknown" or inferred based on similarity.

[0012] For data points that deviate from the normal range, outlier detection is performed. The IQR value is calculated using the interquartile range (IQR) method, as shown in the following expression:

[0013] IQR ;

[0014] in, and Representing the 1st and 3rd quartiles, the outlier range is defined as follows: IQR IQR].

[0015] In the standardization process, continuous features such as age and viral load are normalized using Z-score, as shown in the following expression:

[0016] ;

[0017] in, Represents the normalized eigenvalues. Represents the original feature values. These represent the sample mean and standard deviation of the feature, respectively.

[0018] The classification features, such as transmission routes and vaccination status, are converted into one-hot codes. The cleaned and standardized data are then stratified by age, viral load, transmission route, and vaccination status to capture the differences in the incubation period or infectious period of infectious diseases across different strata, while also constructing interactive features.

[0019] Finally, the preprocessed data was divided into training, validation, and test sets according to the actual situation, and the synthetic minority oversampling technique SMOTE was used to separate the stratified samples whose proportions were lower than the total sample size. Interpolation is performed on the minority class samples to generate new synthetic samples, where This represents a pre-set constant, which is set according to the task requirements.

[0020] S2. Construct a hybrid density network (MDN) model, and input the training set, validation set and test set obtained in step S1 to learn and optimize parameters.

[0021] S21. Construct a hybrid density network (MDN) model;

[0022] The hybrid density network (MDN) model includes an input layer, a hidden layer, and an output layer.

[0023] The input layer data comes from the feature vectors preprocessed in step S1. , This indicates the actual number of feature dimensions of the data after preprocessing in step S1.

[0024] The hidden layer uses a multilayer perceptron (MLP) structure, and nonlinear feature transformation is achieved through the ReLU activation function, as shown in the following expression:

[0025] ReLU ;

[0026] in, , Indicates the depth of the hidden layer. Indicates the first The output of the hidden layer, Indicates the first The weight matrix of the hidden layer, Indicates the first The hidden layer's bias vector, where ReLU represents the activation function. And the hidden layer depth... The complexity of the features in step S1 is dynamically adjusted.

[0027] The output layer consists of three branches, which output the mixture weights, Gamma distribution parameters, and Lognormal distribution parameters, respectively, to construct a conditional mixture distribution to fit the multimodal distribution characteristics of the incubation period or infectious period of infectious diseases.

[0028] For the mixed weights, the weights of each mixed component are generated through Softmax normalization. That is, the Gamma distribution and the Lognormal distribution, expressed as follows:

[0029] ;

[0030] ;

[0031] in, Indicates through the weight matrix and bias Output of the last hidden layer Perform a linear transformation, then pass through an activation function. The resulting unnormalized mixed weight values, The amount of the mixed components is represented by an exponential transformation and a softmax function to ensure... This assigns a weight to each component in the mixture, and the sum of all weights is 1.

[0032] The Gamma distribution parameter The expression is as follows:

[0033] ;

[0034] in, and Let represent the shape parameter and rate parameter of the Gamma distribution, respectively, and ensure that they are greater than 0 through exponential transformation.

[0035] The Lognormal distribution parameters The expression is as follows:

[0036] ;

[0037] in, This represents the mean of a log-normal distribution. This represents the standard deviation, which is guaranteed to be greater than 0 through exponential transformation.

[0038] In multimodal distribution modeling, a mixture distribution model is constructed by combining Gamma and Lognormal distributions, i.e., a conditional mixture distribution. The expression is as follows:

[0039] ;

[0040] in, Indicates the number of days in the incubation period. This represents the coefficient for selecting the distribution type. Distribution parameters. The expression is obtained by mapping the unconstrained parameters output by the network, as follows:

[0041] [ = ;

[0042] =[ ];

[0043] in, This represents a mapping function.

[0044] S22. Perform model training, input the training set from step S1 and iteratively update the model parameters;

[0045] loss function The expression for the negative log-likelihood loss function combined with L2 regularization is as follows:

[0046] ;

[0047] in, This represents the total number of samples, i.e., the number of infected cases collected. Indicates the first The actual observed value of the latency period for each sample. Indicates the first Each sample corresponds to a vector containing multiple features. Indicates that under a given feature Under these conditions, the sample latency period is The probability, This represents the regularization coefficient, which is a pre-defined hyperparameter. For regularization terms, This indicates the number of network layers included in L2 regularization. This represents the square of the Frobenius norm of the matrix; This represents the square of the L2 norm of a vector. Indicates the first The weight matrix of a layer-regularized network. Indicates the first The bias vector of a layer-regularized network.

[0048] Regarding the parameter update mechanism, the hybrid density network (MDN) model uses the adaptive moment estimator Adam to perform gradient descent operations, adapting to the distribution of the synthetic samples generated by SMOTE in step S1, as shown in the following expression:

[0049] ;

[0050] ;

[0051] ;

[0052] in, This represents the set of parameters for the model. Indicates the number of iterations. Indicates the first Parameter values ​​at the next iteration This indicates the updated parameter value. This represents the learning rate. and They represent the first-order moment estimate and the second-order moment estimate, respectively. This represents the attenuation coefficient of the first moment. Represents the loss function Regarding parameters The gradient. This represents the attenuation coefficient of the second moment. It is an extremely small constant.

[0053] S23. Perform model validation and input the validation set from step S1 to fine-tune the hyperparameters.

[0054] Calculate the negative log-likelihood (NLL) of the validation set to measure the accuracy of the distribution fit, and the mean absolute error (MAE) to measure the prediction bias of the latency period. Adjust the hidden layer depth accordingly. Number of mixed components Regularization coefficient The model with the smallest NLL and smallest MAE is selected as the optimal model.

[0055] S24. Perform model testing, input the test set from step S1 to evaluate the generalization ability of the optimal model;

[0056] If the difference between the test set NLL and the validation set NLL is less than 5% and the MAE is less than 1 day, the model's generalization ability is acceptable; otherwise, the network structure should be adjusted or additional data should be provided.

[0057] The final output is the optimized latent conditional mixed distribution. .

[0058] S3. Based on step S2, conduct prevention and control indicator analysis and transform the results of the multi-peak model into a basis for prevention and control decision-making.

[0059] Furthermore, step S3 is specifically as follows:

[0060] First, optimize the latency distribution parameters in step S2. Embedding the classic propagation model, namely the SEIR model, to calculate the dynamic basic reproduction number. The propagation process is simulated, and the SEIR model expression is as follows:

[0061] ;

[0062] ;

[0063] ;

[0064] ;

[0065] in, Indicates susceptible population, Indicates a group of people in hiding. Indicates the infected population, This indicates the recovery population. This indicates the total number of people. = + + + . This represents the time-varying propagation rate. This indicates the rate at which infected individuals recover. The rate at which a latent individual becomes infected is calculated from the reciprocal of the average incubation period, as shown in the following expression:

[0066] ;

[0067] ;

[0068] in, This indicates the average incubation period.

[0069] If the incubation period exhibits a bimodal distribution, then the transmission rate... The weighted sum of the contributions of each subgroup is expressed as follows:

[0070] ;

[0071] in, and Let represent the propagation rate functions corresponding to the gamma distribution and the log-normal distribution, respectively.

[0072] Dynamic basic reproduction number The expression is as follows:

[0073] ;

[0074] in, Indicates the time-varying rate of recovery. Indicates the first day after infection Time is used to accumulate recovery risks; This indicates the duration of the entire infection period.

[0075] Combining the mixed distribution model from step S2, The expression is as follows:

[0076] ;

[0077] in, and Represent the gamma distribution and the log-normal distribution respectively. .

[0078] Then based on the dynamic basic reproduction number This proposes corresponding prevention and control policies, including the implementation of isolation policies, and restricting those with an incubation period exceeding a set threshold. Individuals are removed from the transmission chain.

[0079] Distribution of effective incubation period under quarantine policies Redefining, considering only incubation periods not exceeding [a certain threshold]. The expression for the day is as follows:

[0080] , ;

[0081] in, This represents the original latency distribution function. This indicates the distribution of the original latency period in arrive Integrate over the interval of days.

[0082] Effective transmission rate and effective reproduction number Due to changes in quarantine policies, the effective transmission rate The calculation expression is as follows:

[0083]

[0084] Effective reproduction number The calculation expression is as follows:

[0085]

[0086] Among them, when When the average number of new infections caused by each infected individual is less than 1, the disease transmission trend will gradually weaken; when Even then, the spread of the disease will continue.

[0087] Finally, by calculating and analyzing the effective transmission rate and effective reproduction number, the effectiveness of the isolation policy in controlling the spread of the disease is accurately assessed.

[0088] The beneficial effects of this invention are as follows: The method of this invention first collects incubation period data and related characteristics of infectious disease cases. After data preprocessing, the data is divided into training, validation, and test sets. Then, a hybrid density network (MDN) model is constructed for parameter learning and optimization. Finally, prevention and control indicators are analyzed, and the results of the multi-peak model are transformed into a basis for prevention and control decisions, thus completing the analysis of infectious disease transmission. This invention's method, by constructing a dynamic mixed distribution model (such as a Gamma-log-normal mixed model), combined with population characteristic stratification and data-driven parameter learning, overcomes the limitations of unimodal distribution, accurately captures multimodal distribution characteristics caused by different transmission routes or population heterogeneity, improves the model's adaptability to complex transmission scenarios and the accuracy of parameter estimation, and provides a scientific basis for the formulation of infectious disease prevention and control strategies. Attached Figure Description

[0089] Figure 1 This is a flowchart of an infectious disease transmission analysis method based on multi-peak distribution optimization according to the present invention.

[0090] Figure 2 This is a diagram illustrating the architecture design of a hybrid density network (MDN) model in an embodiment of the present invention. Detailed Implementation

[0091] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0092] like Figure 1 The flowchart of an infectious disease transmission analysis method based on multi-peak distribution optimization according to the present invention is shown below. The specific steps are as follows:

[0093] S1. Collect incubation period data and related characteristics of infectious disease cases, then perform data preprocessing, and divide the preprocessed data into training set, validation set and test set;

[0094] First, incubation period data and related characteristics of infectious disease cases were systematically collected. These characteristics included population features and time-series features. Incubation period data recorded the number of days from exposure to the onset of symptoms. Population characteristics are identified through feature vectors. This includes: age Viral load Transmission routes Vaccination status Time-related features include: case report timestamps and their statistical observations within a preset sliding window.

[0095] in, Represents the real number field (each dimension of the eigenvector takes the value of a real number); This represents the total number of dimensions of the population characteristics after preprocessing; propagation pathways. Including: droplets, aerosols; vaccination status Includes: those who have been vaccinated and those who have not.

[0096] The collected data is then preprocessed, including cleaning and standardization, and different strategies are used to handle missing values ​​depending on the feature type.

[0097] Among them, continuous characteristics such as age and viral load are predicted by means or regression, while categorical characteristics such as transmission route and vaccination status are marked as "unknown" or inferred based on similarity.

[0098] To avoid adverse effects, outlier detection is performed on data points that deviate from the normal range. The interquartile range (IQR) method is used to calculate the IQR value, as shown in the following expression:

[0099] IQR ;

[0100] in, and Representing the 1st and 3rd quartiles, the outlier range is defined as follows: IQR IQR].

[0101] In the standardization process, continuous features such as age and viral load are normalized using Z-score, as shown in the following expression:

[0102] ;

[0103] in, Represents the normalized eigenvalues. Represents the original feature values. These represent the sample mean and standard deviation of the feature, respectively.

[0104] The propagation pathway and vaccination status of the classification features are converted into one-hot codes, where the propagation pathway in this embodiment is... Split into .

[0105] To enhance multi-peak feature identification, the data was stratified according to transmission routes, i.e., the cleaned and standardized data were stratified by age, viral load, transmission route, and vaccination status to capture the characteristic differences in the incubation period or infectious period of infectious diseases under different strata (e.g., segmenting droplet transmission subsets). and aerosol propagation subset By analyzing their distribution patterns, we can accurately capture the characteristic differences in the incubation period or infectious period of infectious diseases under different transmission routes, providing strong support for the subsequent construction of more accurate infectious disease transmission models, calculation of relevant transmission indicators (such as transmission rate and reproduction number), and formulation of targeted prevention and control strategies. Simultaneously, we can construct interactive features (such as age × vaccination status). This allows us to capture nonlinear relationships and provide richer information for subsequent model mining of deeper data patterns.

[0106] Finally, in this embodiment, the preprocessed data is divided into training, validation, and test sets in a 7:2:1 ratio, and the synthetic minority class oversampling technique SMOTE is used to address the issue of stratified samples with a lower percentage of total samples. The minority class samples are interpolated to generate new synthetic samples, thereby increasing the number of minority class samples and making the class distribution of the dataset more balanced. This represents a pre-defined constant, set according to task requirements. This process ensures the stability and generalization ability of the model training, providing reliable input for subsequent multi-modal distribution modeling of hybrid density networks (MDNs).

[0107] S2. Construct a hybrid density network (MDN) model, and input the training set, validation set and test set obtained in step S1 to learn and optimize parameters.

[0108] S21. Construct a hybrid density network (MDN) model;

[0109] The inherent characteristics of the gamma distribution dictate that it can only describe unimodal, right-skewed distributions; it cannot accurately represent complex distributions such as multimodal distributions encountered in reality. To address this issue, this embodiment designs a hybrid density network (MDN) model architecture. In terms of network topology, a deep neural network is constructed to achieve a nonlinear mapping from the feature space to the distribution parameter space. For example... Figure 2 As shown, the hybrid density network (MDN) model includes an input layer, a hidden layer, and an output layer.

[0110] The input layer data comes from the feature vectors preprocessed in step S1. , This indicates the actual number of feature dimensions of the data after preprocessing in step S1.

[0111] The hidden layer uses a multilayer perceptron (MLP) structure, and nonlinear feature transformation is achieved through the ReLU activation function, as shown in the following expression:

[0112] ReLU ;

[0113] in, , Indicates the depth of the hidden layer. Indicates the first The output of the hidden layer, Indicates the first The weight matrix of the hidden layer, Indicates the first The bias vectors of the hidden layers, where ReLU represents the activation function, are used to introduce non-linearity and enhance the network's expressive power. The depth of the hidden layers... The depth of the hidden layer can be dynamically adjusted based on the complexity of the features in step S1. If the feature complexity is low, meaning the relationship between the original features and the interaction features is relatively simple and the patterns contained in the data are relatively singular, the depth of the hidden layer can be appropriately reduced. To avoid model overfitting; if the feature complexity is high, with many complex nonlinear relationships and multimodal distribution features, the depth of the hidden layer needs to be increased. This enables the model to have stronger feature extraction and expression capabilities.

[0114] The output layer consists of three branches, which output the mixture weights, Gamma distribution parameters, and Lognormal distribution parameters, respectively, to construct a conditional mixture distribution to fit the multimodal distribution characteristics of the incubation period or infectious period of infectious diseases.

[0115] For the mixed weights, the weights of each mixed component are generated through Softmax normalization. That is, the Gamma distribution and the Lognormal distribution, expressed as follows:

[0116] ;

[0117] ;

[0118] in, Indicates through the weight matrix and bias Output of the last hidden layer Perform a linear transformation, then pass through an activation function. The resulting unnormalized mixed weight values, The amount of the mixed components is represented by an exponential transformation and a softmax function to ensure... This assigns a weight to each component in the mixture, and the sum of all weights is 1.

[0119] The Gamma distribution parameter The expression is as follows:

[0120] ;

[0121] in, and Let represent the shape parameter and rate parameter of the Gamma distribution, respectively. An exponential transformation is used to ensure that these parameters are greater than 0.

[0122] The Lognormal distribution parameters The expression is as follows:

[0123] ;

[0124] in, This represents the mean of a log-normal distribution. This represents the standard deviation, which is also guaranteed to be greater than 0 through exponential transformation.

[0125] In multimodal distribution modeling, a mixture distribution model is constructed by combining Gamma and Lognormal distributions, i.e., a conditional mixture distribution. The expression is as follows:

[0126] ;

[0127] in, Indicates the number of days in the incubation period. This represents the distribution type selection coefficient, which determines the weights of the two distributions within each mixture component. The weighted sum of the mixed components can more flexibly fit complex real-world distributions. Distribution parameters The expression is obtained by mapping the unconstrained parameters output by the network, as follows:

[0128] [ = ;

[0129] =[ ];

[0130] in, This represents a mapping function.

[0131] The distribution parameters are obtained by dynamically generating parameter mappings from a neural network, which enables the distribution parameters to adaptively adjust with changes in the actual scene, thereby more accurately characterizing the multi-peak distribution features.

[0132] S22. Perform model training, input the training set from step S1 and iteratively update the model parameters;

[0133] loss function The design employs a negative log-likelihood loss function combined with an L2 regularization term to balance the model's fitting ability and generalization performance. The expression is as follows:

[0134] ;

[0135] in, This represents the total number of samples. In the context of infectious disease research, it can be the number of infected cases collected. Indicates the first The actual observed value of the latency period for each sample. Indicates the first Each sample corresponds to a vector containing multiple features. Indicates that under a given feature Under these conditions, the sample latency period is The probability, represents the regularization coefficient, which is a pre-defined hyperparameter used to adjust the relative importance between the negative log-likelihood loss and the regularization term. For regularization terms, This indicates the number of network layers included in L2 regularization. Represents a matrix (e.g.) The square of the Frobenius norm, which measures the size of all elements in the weight matrix; Represents the relationship between vectors (e.g.) The square of the L2 norm of the bias vector is used to measure the magnitude of the bias vector. Indicates the first The weight matrix of a layer-regularized network. Indicates the first The bias vector of a layer-regularized network, by constraining the weight matrix and the bias vector, the regularization term can prevent the model from overfitting the training data, and enable the model to have better generalization ability when facing new data.

[0136] Regarding the parameter update mechanism, the hybrid density network (MDN) model uses the adaptive moment estimator Adam to perform gradient descent operations, adapting to the distribution of the synthetic samples generated by SMOTE in step S1, as shown in the following expression:

[0137] ;

[0138] ;

[0139] ;

[0140] in, This represents the set of parameters of the model, which includes parameters such as weights and biases in the network. This indicates the number of iterations. During model training, iterations are performed continuously to optimize the parameters. Indicates the first The parameter values ​​at the next iteration, and This indicates the updated parameter value. This represents the learning rate, which determines the step size for each parameter update. and They represent the first-order moment estimate and the second-order moment estimate, respectively. This represents the attenuation coefficient of the first moment. Represents the loss function Regarding parameters The gradient indicates the direction of parameter updates. By calculating the gradient, we can determine how to adjust the parameters to reduce the value of the loss function. This represents the attenuation coefficient of the second moment. It is an extremely small constant, usually taking the value 10. -8 Adding it is to avoid calculation To ensure the stability of the calculation, the denominator may sometimes be zero.

[0141] S23. Perform model validation and input the validation set from step S1 to fine-tune the hyperparameters.

[0142] Calculate the negative log-likelihood (NLL) of the validation set to measure the accuracy of the distribution fit, and the mean absolute error (MAE) to measure the prediction bias of the latency period. Adjust the hidden layer depth accordingly. Number of mixed components Regularization coefficient The model with the smallest NLL and smallest MAE is selected as the optimal model.

[0143] S24. Perform model testing, input the test set from step S1 to evaluate the generalization ability of the optimal model;

[0144] If the difference between the test set NLL and the validation set NLL is less than 5% and the MAE is less than 1 day, it indicates that the model's generalization ability is qualified (no overfitting); otherwise, the network structure should be adjusted or supplemented with data.

[0145] The final output is the optimized latent conditional mixed distribution. (including) This provides the core input for calculating the prevention and control indicators in step S3.

[0146] S3. Based on step S2, conduct prevention and control indicator analysis and transform the results of the multi-peak model into a basis for prevention and control decision-making.

[0147] In this embodiment, step S3 is specifically as follows:

[0148] First, optimize the latency distribution parameters in step S2. Embedding the classic propagation model, namely the SEIR model, to calculate the dynamic basic reproduction number. The propagation process is simulated, and the SEIR model expression is as follows:

[0149] ;

[0150] ;

[0151] ;

[0152] ;

[0153] in, Indicates susceptible population, Indicates a group of people in hiding. Indicates the infected population, This indicates the recovery population. This indicates the total number of people. = + + + . The time-varying transmission rate is represented by a Bayesian time-varying coefficient model, which combines the time series and prior distribution of case data, and estimates the time-varying transmission rate through Markov chain Monte Carlo (MCMC) sampling. This indicates the rate at which infected individuals recover. The rate at which a latent individual becomes infected is calculated from the reciprocal of the average incubation period, as shown in the following expression:

[0154] ;

[0155] ;

[0156] in, This indicates the average incubation period.

[0157] If the incubation period exhibits a bimodal distribution, then the transmission rate... The weighted sum of the contributions of each subgroup is expressed as follows:

[0158] ;

[0159] in, and Let represent the propagation rate functions corresponding to the gamma distribution and the log-normal distribution, respectively.

[0160] Dynamic basic reproduction number The expression is as follows:

[0161] ;

[0162] in, The time-varying recovery rate is expressed using the same method as the time-varying propagation rate. Indicates the first day after infection Time is used to accumulate recovery risks; This indicates the duration of the entire infection period.

[0163] Combining the mixed distribution model from step S2, The expression is as follows:

[0164] ;

[0165] in, and Represent the gamma distribution and the log-normal distribution respectively. .

[0166] Then based on the dynamic basic reproduction number This proposes corresponding prevention and control policies, including the implementation of isolation policies, and restricting those with an incubation period exceeding a set threshold. Individuals are removed from the transmission chain. This measure alters the distribution of the incubation period in disease transmission models, thereby affecting transmission-related parameters.

[0167] Distribution of effective incubation period under quarantine policies Redefining, considering only incubation periods not exceeding [a certain threshold]. The expression for the day is as follows:

[0168] , ;

[0169] in, This represents the original latency distribution function. This indicates the distribution of the original latency period in arrive Integrating over this interval of days. This calculation method normalizes the distribution of the effective latency period, ensuring that... Within the interval, the sum of the probabilities of this distribution is 1.

[0170] Effective transmission rate and effective reproduction number Due to changes in quarantine policies, the effective transmission rate The calculation expression is as follows:

[0171]

[0172] This is based on the original transmission rate. Adjustments are made based on the original incubation period distribution. The ratio on the right reflects the proportion of the effective incubation period within the overall original incubation period distribution after the implementation of the isolation policy. This ratio is used to correct the original transmission rate, thus obtaining a new effective transmission rate.

[0173] Effective reproduction number The calculation expression is as follows:

[0174]

[0175] in, The basic reproduction number without isolation measures is represented by the ratio shown on the right, which yields the effective reproduction number after implementing isolation measures. The effective reproduction number is a key indicator for measuring the intensity of disease transmission. When this occurs, it means that on average, each infected individual causes fewer than one new infection, and the disease transmission trend will gradually weaken; when Even when the disease is under control, its spread will continue. By calculating and analyzing the effective transmission rate and effective reproduction number, we can accurately assess the effectiveness of isolation policies in controlling disease transmission, providing a scientific basis for optimizing and adjusting subsequent prevention and control policies.

[0176] In summary, this invention proposes a hybrid model that dynamically integrates Gamma and log-normal distributions. By adaptively adjusting the combination ratio of the two distributions, it overcomes the limitation of existing gamma distributions, which can only describe unimodal distributions. This model can effectively capture the multimodal incubation period characteristics caused by different infection routes (such as droplet transmission and contact transmission), and achieves accurate fitting of complex distribution patterns through parameter optimization algorithms (such as the EM algorithm), providing a more flexible distribution description tool for infectious disease transmission modeling. This invention also overcomes the limitation of fixed parameters in existing models by setting key parameters such as transmission rate and recovery rate as time-varying functions. By continuously updating parameters using data, it achieves dynamic simulation of the infectious disease transmission process, accurately fitting the multimodal data characteristics under mixed transmission scenarios, and significantly improving the model's ability to characterize and predict complex transmission situations.

[0177] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the implementation methods of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the present invention.

Claims

1. A method for analyzing the transmission of infectious diseases based on multi-peak distribution optimization, the specific steps of which are as follows: S1. Collect incubation period data and related characteristics of infectious disease cases, then perform data preprocessing, and divide the preprocessed data into training set, validation set and test set; First, systematically collect incubation period data and related characteristics of infectious disease cases, including population characteristics and time series characteristics; incubation period data records the number of days from exposure to the onset of symptoms. Population characteristics are identified through feature vectors. This indicates, including: age Viral load Transmission routes Vaccination status Time-related features include: case report timestamps and their statistical observations within a preset sliding window; in, Represents the real number field; This represents the total number of dimensions of the population characteristics after preprocessing; propagation pathways. Including: droplets, aerosols; vaccination status Includes: those who have been vaccinated and those who have not; The collected data is then preprocessed, namely, cleaned and standardized, and different strategies are used to handle missing values ​​depending on the feature type. Among them, continuous features such as age and viral load are predicted by means or regression, while categorical features such as transmission route and vaccination status are marked as "unknown" or inferred based on similarity. For data points that deviate from the normal range, outlier detection is performed. The IQR value is calculated using the interquartile range (IQR) method, as shown in the following expression: IQR ; in, and Representing the 1st and 3rd quartiles, the outlier range is defined as follows: IQR IQR]; In the standardization process, continuous features such as age and viral load are normalized using Z-score, as shown in the following expression: ； in, Represents the normalized eigenvalues. Represents the original feature values. These represent the sample mean and standard deviation of the feature, respectively. The classification features of transmission routes and vaccination status are converted into one-hot codes; then the cleaned and standardized data are stratified by age, viral load, transmission route and vaccination status to capture the characteristic differences of the incubation period or infectious period of infectious diseases under different strata, and at the same time construct interactive features. Finally, the preprocessed data was divided into training, validation, and test sets according to the actual situation, and the synthetic minority oversampling technique SMOTE was used to separate the stratified samples whose proportions were lower than the total sample size. Interpolation is performed on the minority class samples to generate new synthetic samples, where This represents a pre-defined constant, set according to task requirements; S2. Construct a hybrid density network (MDN) model, and input the training set, validation set and test set obtained in step S1 to learn and optimize parameters. S21. Construct a hybrid density network (MDN) model; The hybrid density network (MDN) model includes: an input layer, a hidden layer, and an output layer; The input layer data comes from the feature vectors preprocessed in step S1. , This indicates the actual number of feature dimensions of the data after preprocessing in step S1; The hidden layer uses a multilayer perceptron (MLP) structure, and nonlinear feature transformation is achieved through the ReLU activation function, as shown in the following expression: resume ; in, , Indicates the depth of the hidden layer. Indicates the first The output of the hidden layer, Indicates the first The weight matrix of the hidden layer, Indicates the first The bias vectors of the hidden layers, where ReLU represents the activation function; and the depth of the hidden layers. The complexity of the features in step S1 is dynamically adjusted. The output layer includes three branches, which output the mixture weights, Gamma distribution parameters, and Lognormal distribution parameters, respectively, to construct a conditional mixture distribution to fit the multimodal distribution characteristics of the incubation period or infectious period of infectious diseases; For the mixed weights, the weights of each mixed component are generated through Softmax normalization. That is, the Gamma distribution and the Lognormal distribution, expressed as follows: ； ； in, Indicates through the weight matrix and bias Output of the last hidden layer Perform a linear transformation, then pass through an activation function. The resulting unnormalized mixed weight values, The amount of the mixed components is represented by an exponential transformation and a softmax function to ensure... This ensures that each component in the mixture has a corresponding weight, and the sum of all weights is 1. The Gamma distribution parameter The expression is as follows: ； in, and Let represent the shape parameter and rate parameter of the Gamma distribution, respectively, and ensure that they are greater than 0 through exponential transformation; The Lognormal distribution parameters The expression is as follows: ； in, This represents the mean of a log-normal distribution. This represents the standard deviation, which is guaranteed to be greater than 0 through exponential transformation. In multimodal distribution modeling, a mixture distribution model is constructed by combining Gamma and Lognormal distributions, i.e., a conditional mixture distribution. The expression is as follows: ； in, Indicates the number of days in the incubation period. The coefficient representing the distribution type selection; distribution parameters. The expression is obtained by mapping the unconstrained parameters output by the network, as follows: [ = ； =[ ]； in, Represents a mapping function; S22. Perform model training, input the training set from step S1 and iteratively update the model parameters; loss function The expression for the negative log-likelihood loss function combined with L2 regularization is as follows: ； in, This represents the total number of samples, i.e., the number of infected cases collected. Indicates the first The actual observed value of the latency period for each sample. Indicates the first Each sample corresponds to a vector containing multiple features; Indicates that under a given feature Under these conditions, the sample latency period is The probability, This represents the regularization coefficient, which is a pre-defined hyperparameter. For regularization terms, This indicates the number of network layers included in L2 regularization. This represents the square of the Frobenius norm of the matrix; This represents the square of the L2 norm of a vector; Indicates the first The weight matrix of a layer-regularized network. Indicates the first The bias vector of a layer-regularized network; Regarding the parameter update mechanism, the hybrid density network (MDN) model uses the adaptive moment estimator Adam to perform gradient descent operations, adapting to the distribution of the synthetic samples generated by SMOTE in step S1, as shown in the following expression: ； ； ； in, Represents the set of parameters of the model; Indicates the number of iterations. Indicates the first Parameter values ​​at the next iteration This indicates the updated parameter value; Indicates the learning rate; and They represent the first-order moment estimate and the second-order moment estimate, respectively. This represents the attenuation coefficient of the first moment; Represents the loss function Regarding parameters The gradient; This represents the attenuation coefficient of the second moment; It is an extremely small constant; S23. Perform model validation and input the validation set from step S1 to fine-tune the hyperparameters. Calculate the negative log-likelihood (NLL) of the validation set to measure the accuracy of the distribution fit, and the mean absolute error (MAE) to measure the prediction bias of the latency period. Adjust the hidden layer depth accordingly. Number of mixed components Regularization coefficient The model with the smallest NLL and smallest MAE is selected as the optimal model; S24. Perform model testing, input the test set from step S1 to evaluate the generalization ability of the optimal model; If the difference between the test set NLL and the validation set NLL is less than 5% and the MAE is less than 1 day, the model's generalization ability is acceptable; otherwise, the network structure should be adjusted or additional data should be added. The final output is the optimized latent conditional mixed distribution. ; S3. Based on step S2, conduct prevention and control indicator analysis and transform the results of the multi-peak model into a basis for prevention and control decision-making.

2. The infectious disease transmission analysis method based on multi-peak distribution optimization according to claim 1, characterized in that, Step S3 is as follows: First, optimize the latency distribution parameters in step S2. Embedded propagation model, also known as SEIR model, calculates the dynamic basic reproduction number. The propagation process is simulated, and the SEIR model expression is as follows: ； ； ； ； in, Indicates susceptible population, Indicates a group of people in hiding. Indicates the infected population. Indicates the recovered population; This indicates the total number of people. = + + + Indicates the time-varying propagation rate; This indicates the rate at which infected individuals recover. The rate at which a latent individual becomes infected is calculated from the reciprocal of the average incubation period, as shown in the following expression: ； ； in, Indicates the average incubation period; If the incubation period exhibits a bimodal distribution, then the transmission rate... The weighted sum of the contributions of each subgroup is expressed as follows: ； in, and Let represent the propagation rate functions corresponding to the gamma distribution and the log-normal distribution, respectively; Dynamic basic reproduction number The expression is as follows: ； in, Indicates the time-varying rate of recovery. Indicates the first day after infection Time is used to accumulate recovery risks; Indicates the duration of the entire infection period; Combining the mixed distribution model from step S2, The expression is as follows: ； in, and Represent the gamma distribution and the log-normal distribution respectively. ; Then based on the dynamic basic reproduction number Propose corresponding prevention and control policies, set and implement isolation policies, and allow those with an incubation period exceeding a set threshold to be isolated. Individuals are removed from the transmission chain within a day; Distribution of effective incubation period under quarantine policies Redefining, considering only incubation periods not exceeding [a certain threshold]. The expression for the day is as follows: , ； in, This represents the original latency distribution function. This indicates the distribution of the original latency period in arrive Integrate over the interval of days; Effective transmission rate and effective reproduction number Due to changes in quarantine policies, the effective transmission rate The calculation expression is as follows: ； Effective reproduction number The calculation expression is as follows: ； Among them, when When the average number of new infections caused by each infected individual is less than 1, the disease transmission trend will gradually weaken; when At that time, the spread of the disease will continue; Finally, by calculating and analyzing the effective transmission rate and effective reproduction number, the effectiveness of the isolation policy in controlling the spread of the disease is accurately assessed.

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