CN113571200A - Infectious disease propagation prediction method based on graph filter-vector autoregressive model - Google Patents

Infectious disease propagation prediction method based on graph filter-vector autoregressive model Download PDF

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CN113571200A
CN113571200A CN202110868810.9A CN202110868810A CN113571200A CN 113571200 A CN113571200 A CN 113571200A CN 202110868810 A CN202110868810 A CN 202110868810A CN 113571200 A CN113571200 A CN 113571200A
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蒋俊正
李文娟
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Abstract

The invention discloses an infectious disease propagation prediction method based on a graph filter-vector autoregressive model, which is characterized by comprising the following steps of: 1) constructing a graph model; 2) designing a prediction model; 3) optimally designing parameters of a graph filter; 4) and predicting the time-varying graph signal by using the optimized VAR model. The method has good practicability, can improve the accuracy of infectious disease prediction, and further improves decision basis for prevention.

Description

Infectious disease propagation prediction method based on graph filter-vector autoregressive model
Technical Field
The invention relates to the field of infectious disease prediction, in particular to an infectious disease propagation prediction method based on a graph filter-vector autoregressive model.
Background
Infectious diseases can be rapidly spread in a large range, so that great influence and harm are brought to human beings, and the infectious diseases further become one of the main factors endangering human health. Infectious atypical pneumonia in 2003, influenza a H1N1 in 2009, and novel coronavirus pneumonia outbreaks in 2019 are all examples of very typical infectious disease transmission. The spreading process is predicted according to the monitored infectious disease data and early warning is carried out in time, so that countermeasures are taken, and the harm of infectious diseases is greatly reduced. Infectious diseases are global public health problems threatening human society, so that the research related to prediction of transmission of infectious diseases is of great significance to prevention and control of infectious diseases.
At present, the models and methods for predicting infectious diseases are widely applied mainly to a propagation dynamics model, a markov model, a time series method, a multiple regression model, and the like. The classical susceptibility-infection (SI) model proposed by kermanck and Mckendrick can reasonably predict the transmission of infectious diseases from person to person; gomez et al propose a discrete markov chain method for contagious disease transmission based on contact, solving the problem of the number of people in contact during the transmission process that depends on one node; siregar et al have studied the onset of hemorrhagic fever of dengue fever under the influence of climate by adopting a time series regression method, provide the basis for prevention and control of dengue fever; vector Autoregressive (VAR) models, which are a type of multivariate regression model, are also often used in time series prediction problems. The infectious disease transmission process is mainly affected by human-to-human interaction in time and space, and the crowd flow between regions is a very critical influencing factor. However, in the conventional prediction method, much attention is paid to the time correlation between data as a time series, and the intrinsic topology of the data, that is, the correlation between regions is ignored. Therefore, how to better depict the relationship between data is also an important issue, and if infectious disease data is modeled as a graph signal and a region is modeled as a node on the graph, the time correlation between time series data and the correlation between regions can be well described.
Nowadays, Graph Signal Processing (GSP) is receiving attention from researchers as an emerging field. GSP models data on irregular discrete domains as graphs, and uses edges on the graph models to depict the relationship between data. In many practical applications, for example, data of a wireless sensor network may change with time, have a time-varying characteristic, and can be modeled as a time-varying graph signal. Tay et al denoise the time-varying image signal using an efficient image filter; isufi et al predict the time-varying graph signals by using an approximate time-vertex stationarity hypothesis and an extended VAR model, and solve the dimension problem existing in multivariate time sequence evolution prediction, but the method only considers the correlation between the prediction time and the previous time signals in the parameter estimation problem, and does not consider the correlation between each time before the prediction time and the previous time signals.
Disclosure of Invention
The invention aims to provide an infectious disease propagation prediction method based on a graph filter-vector autoregressive model, aiming at the defects of the prior art. The method has good practicability, can improve the accuracy of infectious disease prediction, and further improves decision basis for prevention.
The technical scheme for realizing the purpose of the invention is as follows:
the infectious disease propagation prediction method based on the graph filter-vector autoregressive model comprises the following steps:
1) constructing a graph model: infectious disease transmission time series data
Figure BDA0003188306260000021
Each row in the system represents one area, N areas are in total, each column represents the number of cases at a certain moment in all areas, and T is in totalpThe data of each moment takes the region as the nodes on the graph, and the nodes are connected by edges according to the characteristics of different data to construct the topological structure of the graph and transmit the infectious disease data
Figure BDA0003188306260000022
Modelling as a time-varying graph signal
Figure BDA0003188306260000023
Namely, the data at each moment is a graph signal;
2) designing a prediction model: when a Graph Filter-Vector Autoregressive (GF-VAR) model predicts infection propagation, a time-varying Graph signal X is predicted by the VAR model, then coefficients of the VAR model are designed by the aid of concepts of a Graph Laplace matrix and a Graph Filter, and the signal value at the time t can be representedShown as front TpFunction of the signal at 1 instant, TpAnd 2, modeling the time-varying graph signal by adopting a VAR model, wherein the expression is shown as formula (1):
Figure BDA0003188306260000024
wherein epsilontThe error vector is a random vector with mean value of 0 and positive definite covariance matrix, and the graph filter
Figure BDA0003188306260000025
As a coefficient matrix, aq,pIs the coefficient of the Laplace matrix of order p, and Q is the highest order of the Laplace matrix;
3) and (3) optimally designing parameters of the graph filter: analyzing the prediction model according to step 2), considering the correlation between each moment of the time-varying graph signal X and the previous moment, and using the parameter a of the GF-VAR model graph filterq,pIs expressed as an optimization problem as shown in equation (2):
Figure BDA0003188306260000031
equation (2) is summarized as an unconstrained optimization problem as shown in equation (3):
Figure BDA0003188306260000032
the inputs in the problem shown in equation (3) are the signal x and the Laplace matrix LGCan be solved to Q × (T)p-1) parameters aq,p；
4) Predicting a time-varying graph signal by using the optimized VAR model, and quantizing by using a normalized minimum mean square error root (rNMSE) formula to estimate the performance of the model, wherein the error formula is shown as a formula (4):
Figure BDA0003188306260000033
wherein xtThe true number of cases for the node at time t,
Figure BDA0003188306260000034
is the predicted number of cases.
The unconstrained optimization problem described in step 3) as shown in equation (3) can be transformed into a vector of coefficients for a graph filter
Figure BDA0003188306260000035
The least squares problem of (2) is shown in equation (5):
Figure BDA0003188306260000036
wherein b is,
Figure BDA0003188306260000037
C is defined as shown in formula (6):
Figure BDA0003188306260000038
the parameters involved in equation (6) are shown in equation (7):
Figure BDA0003188306260000041
the theoretical solution to the least squares problem in equation (5) is as shown in equation (8):
Figure BDA0003188306260000042
thereby obtaining Qx (T)p-1) map filter parameters aq,pAnd finally obtaining the graph filter.
The unconstrained optimization problem shown in the formula (3) in the step 3) is solved by adopting a convex optimization toolkit cvx, and then the convex optimization toolkit cvx is solved to obtain the graph filter.
Compared with the existing infectious disease prediction model and method, the technical scheme is that the graph filter is used as a coefficient matrix of the VAR model, the graph topology is embedded into the model, and the optimization problem of the parameters of the graph filter is proposed based on the correlation between each moment before the prediction moment and the previous moment signals.
Drawings
FIG. 1 is a graph comparing 6-step prediction errors of susceptible-infected SI data in examples;
FIG. 2 is a comparison of 6-step prediction error for susceptibility-infection but not disease-infection-recovery-susceptibility SEIRS data in the examples;
FIG. 3 is a graph comparing 10-step prediction errors of the data of the German novel coronavirus pneumonia COVID-19 in the example.
Detailed Description
The invention will be further elucidated with reference to the drawings and examples, without however being limited thereto.
Example (b):
the infectious disease propagation prediction method based on the graph filter-vector autoregressive model comprises the following steps:
1) constructing a graph model: infectious disease transmission time series data
Figure BDA0003188306260000043
Each row in the system represents one area, N areas are in total, each column represents the number of cases at a certain moment in all areas, and T is in totalpThe data of each moment takes the region as the nodes on the graph, and the nodes are connected by edges according to the characteristics of different data to construct the topological structure of the graph and transmit the infectious disease data
Figure BDA0003188306260000051
Modelling as a time-varying graph signal
Figure BDA0003188306260000052
Namely, the data at each moment is a graph signal;
2) designing a prediction model: when the GF-VAR model predicts the spread of infectious diseases, the VAR model is firstly adopted to predict a time-varying graph signal X, then the concept of a graph Laplace matrix and a graph filter is utilized to design the coefficient of the VAR model, and the signal value at the moment T can be represented as the previous TpFunction of the signal at 1 instant, TpAnd 2, modeling the time-varying graph signal by adopting a VAR model, wherein the expression is shown as formula (1):
Figure BDA0003188306260000053
wherein epsilontThe error vector is a random vector with mean value of 0 and positive definite covariance matrix, and the graph filter
Figure BDA0003188306260000054
As a coefficient matrix, the time correlation between time series data and the correlation between regions can be well described, graph topology is embedded into a model, aq,pThe coefficient of a p-order Laplace matrix is adopted, Q is the highest order of the Laplace matrix, the formula (1) is used as a one-step prediction result expression, and n-step prediction results can be obtained by performing iterative computation on the one-step prediction result expression for n times;
3) and (3) optimally designing parameters of the graph filter: analyzing the prediction model according to step 2), considering the correlation between each moment of the time-varying graph signal X and the previous moment, and using the parameter a of the GF-VAR model graph filterq,pIs expressed as an optimization problem as shown in equation (2):
Figure BDA0003188306260000055
equation (2) is summarized as an unconstrained optimization problem as shown in equation (3):
Figure BDA0003188306260000056
the inputs in the problem shown in equation (3) are the signal x and the Laplace matrix LGCan be solved to Q × (T)p-1) parameters aq,p；
4) Predicting a time-varying graph signal by using the optimized VAR model, and quantizing by using a normalized minimum mean square error root (rNMSE) formula to estimate the performance of the model, wherein the error formula is shown as a formula (4):
Figure BDA0003188306260000061
wherein xtThe true number of cases for the node at time t,
Figure BDA0003188306260000062
is the predicted number of cases.
The unconstrained optimization problem described in step 3) as shown in equation (3) can be transformed into a vector of coefficients for a graph filter
Figure BDA0003188306260000063
The least squares problem of (2) is shown in equation (5):
Figure BDA0003188306260000064
wherein b is,
Figure BDA0003188306260000065
C is defined as shown in formula (6):
Figure BDA0003188306260000066
the parameters involved in equation (6) are shown in equation (7):
Figure BDA0003188306260000067
the theoretical solution to the least squares problem in equation (5) is as shown in equation (8):
Figure BDA0003188306260000068
thereby obtaining Qx (T)p-1) map filter parameters aq,pAnd finally obtaining the graph filter.
The unconstrained optimization problem shown in the formula (3) in the step 3) is solved by adopting a convex optimization toolkit cvx, and then the convex optimization toolkit cvx is solved to obtain the graph filter.
Simulation experiment: simulations the performance of the proposed model was tested using mock-generated disease data (data generated by the susceptibility-infection (SI) model, data generated by the susceptibility-infection but not the pathogenesis-infection-recovery-susceptibility (SEIRS) model) and german new coronavirus pneumonia (COVID-19) data for simulated disease data based on flight network propagation at 487 days at 125 international airports: constructing graphs with the node number N being 125 and constructing a weight matrix W based on flight information by using SI data and SEIRS dataGAnd using the data from which the mean value within the sample has been subtracted as a signal, constructing a 6-neighbor graph in which the number of nodes is N100 for the german covi-19 data including 100 infected persons in 507 days of the region, and setting a parameter TpConstructing a weighted adjacency matrix W with 3 and Q with 5GNormalized Laplace matrix LnorSelecting successive TpData of dayxt：
Figure BDA0003188306260000071
As initial data, then, the optimization problem equation (3) is solved by the CVX toolkit to obtain Qx (T)p-1) parameters aq,pAnd finally, obtaining the parameter aq,pAnd data
Figure BDA0003188306260000072
Substituting the prediction model to obtain the predicted value
Figure BDA0003188306260000073
And will be
Figure BDA0003188306260000074
And one-step prediction of results
Figure BDA0003188306260000075
As new continuous TpData of day xtThen, the next time is predicted.
Comparing the method with a G-VARMA model and a GP-VAR model, and quantifying by a normalized minimum mean square error root rNMSE formula to evaluate the performance of the model, wherein the error is shown as a formula (4):
Figure BDA0003188306260000076
wherein xtThe true number of cases for the node at time t,
Figure BDA0003188306260000077
is the predicted number of cases.
In the simulation experiment process, the method of the embodiment is compared with a G-VARMA model and a GP-VAR model proposed by Isufi and the like, SI data and SEIRS data are subjected to 6-step prediction, German COVID-19 data are subjected to 10-step prediction, the prediction result of each data is visualized to obtain the prediction effect shown in figures 1, 2 and 3, different data are observed, and compared with the method, the GF-VAR model of the method of the embodiment has better stability, and the good prediction effect can be kept on different types of data.

Claims (3)

1. The infectious disease propagation prediction method based on the graph filter-vector autoregressive model is characterized by comprising the following steps of:
1) constructing a graph model: infectious diseasesPropagation time series data
Figure FDA0003188306250000011
Each row in the system represents one area, N areas are in total, each column represents the number of cases at a certain moment in all areas, and T is in totalpThe data of each moment takes the region as the nodes on the graph, and the nodes are connected by edges according to the characteristics of different data to construct the topological structure of the graph and transmit the infectious disease data
Figure FDA0003188306250000012
Modelling as a time-varying graph signal
Figure FDA0003188306250000013
Namely, the data at each moment is a graph signal;
2) designing a prediction model: firstly, a VAR model is adopted to predict a time-varying graph signal X, then the coefficient of the VAR model is designed by utilizing the concepts of a graph Laplacian matrix and a graph filter, and the signal value at the time T is assumed to be represented as the previous TpFunction of the signal at 1 instant, TpAnd (2) modeling the time-varying graph signal by adopting a VAR model, wherein the expression is shown as a formula (1):
Figure FDA0003188306250000014
wherein epsilontThe error vector is a random vector with mean value of 0 and positive definite covariance matrix, and the graph filter
Figure FDA0003188306250000015
As a coefficient matrix, aq,pIs the coefficient of the Laplace matrix of order p, and Q is the highest order of the Laplace matrix;
3) and (3) optimally designing parameters of the graph filter: filtering parameter a of GF-VAR model diagramq,pIs expressed as an optimization problem as shown in equation (2):
Figure FDA0003188306250000016
equation (2) is summarized as an unconstrained optimization problem as shown in equation (3):
Figure FDA0003188306250000017
the inputs in the problem shown in equation (3) are the signal x and the Laplace matrix LGSolved to Q × (T)p-1) parameters aq,p；
4) Predicting a time-varying graph signal by using the optimized VAR model, quantizing by adopting a normalized minimum mean square error root (rNMSE) formula, and evaluating the performance of the model, wherein the error formula is shown as a formula (4):
Figure FDA0003188306250000018
wherein xtThe true number of cases for the node at time t,
Figure FDA0003188306250000019
is the predicted number of cases.
2. The method of claim 1, wherein the unconstrained optimization problem of step 3) is transformed into a vector of coefficients for the graph filter as shown in equation (3)
Figure FDA0003188306250000021
The least squares problem of (2) is shown in equation (5):
Figure FDA0003188306250000022
wherein b is,
Figure FDA0003188306250000023
C is defined as shown in formula (6):
Figure FDA0003188306250000024
the parameters involved in equation (6) are shown in equation (7):
Figure FDA0003188306250000025
the theoretical solution to the least squares problem in equation (5) is as shown in equation (8):
Figure FDA0003188306250000026
thereby obtaining Qx (T)p-1) map filter parameters aq,pAnd finally obtaining the graph filter.
3. The infectious disease propagation prediction method based on graph filter-vector autoregressive model according to claim 1, wherein the unconstrained optimization problem in step 3) as shown in formula (3) is solved by using a convex optimization tool set cvx, and then the graph filter is obtained.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114978928A (en) * 2022-04-24 2022-08-30 重庆邮电大学 Dynamic message transmission method for social infection in coupling network with time-varying characteristic

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112700885A (en) * 2021-01-13 2021-04-23 大连海事大学 Method for identifying new coronavirus propagation model parameters based on Kalman filtering
CN112865748A (en) * 2021-01-13 2021-05-28 西南大学 Method for constructing online distributed multitask graph filter based on recursive least squares
CN113035368A (en) * 2021-04-13 2021-06-25 桂林电子科技大学 Disease propagation prediction method based on differential migration diagram neural network

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112700885A (en) * 2021-01-13 2021-04-23 大连海事大学 Method for identifying new coronavirus propagation model parameters based on Kalman filtering
CN112865748A (en) * 2021-01-13 2021-05-28 西南大学 Method for constructing online distributed multitask graph filter based on recursive least squares
CN113035368A (en) * 2021-04-13 2021-06-25 桂林电子科技大学 Disease propagation prediction method based on differential migration diagram neural network

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
朱莞琪;李娟生;孟蕾;杨玫;刘新凤;牛丽霞;于德山;蒋小娟;王琪;张蕾洁;: "基于向量自回归模型分析呼吸道病原感染与气象因素的动态关系", 中国卫生统计, no. 02 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114978928A (en) * 2022-04-24 2022-08-30 重庆邮电大学 Dynamic message transmission method for social infection in coupling network with time-varying characteristic

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