A spatio-temporal modeling and prediction method for covid-19 based on dynamic population flow matrix spatial filter
By constructing a dynamic population flow matrix, the spatiotemporal modeling method for COVID-19 addresses the lack of consideration for spatial and temporal effects and population flow network relationships in existing models, achieving a more accurate description of the interaction between the COVID-19 pandemic and health risk factors and improving modeling accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- WUHAN UNIV
- Filing Date
- 2022-04-29
- Publication Date
- 2026-07-03
AI Technical Summary
Existing models of COVID-19 and health risk factors lack simultaneous consideration of spatial and temporal effects as well as population mobility networks, resulting in insufficient model prediction accuracy.
A spatiotemporal modeling method for COVID-19 based on a dynamic population flow matrix is constructed. By building a spatial adjacency matrix, a population flow network matrix, and a time matrix, Kronecker product operations and eigenvector selection are performed and incorporated into the regression model to consider the effects of spatial autocorrelation, temporal correlation, and population flow network.
This study improved the accuracy of describing the interaction between the COVID-19 pandemic and health risk factors, enhanced the accuracy of pandemic modeling, and provided an important reference for pandemic analysis and prevention.
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Figure CN115274129B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of geostatistics and spatial analysis applications, and specifically relates to a spatiotemporal modeling and prediction method for COVID-19 based on the spatial filter value of a dynamic population flow matrix. Background Technology
[0002] The emergence, outbreak, and spread of infectious diseases have a profound impact on human health and the economy. Researchers have conducted a series of studies on the temporal trends, milestone predictions, trajectory tracing, and health risk factors of novel coronavirus infection. Among these studies, clarifying the relationship between the spread of emerging infectious diseases and health risk factors is a prerequisite for achieving scientific early warning and prevention. Existing research results indicate that multiple factors can influence the spread rate of novel coronavirus infection. For example, the spread of novel coronavirus infection may be related to environmental factors such as temperature, precipitation, relative humidity, wind speed, and air quality, as well as population movement, public transportation, and government policies.
[0003] The outbreak of spatial epidemics and the spatial distribution of their health risk factors exhibit strong spatial correlations, and outbreaks of cases are highly likely to produce spatial clustering effects. Traditional statistical models, such as ordinary linear regression, do not account for the impact of spatial correlations on the results of studies on the relationship between novel coronavirus infection and health risk factors. While some spatial regression analysis models, such as spatial autoregressive models and geographically weighted regression models, incorporate spatial effects and consider the variance inflation effect caused by spatial autocorrelation, resulting in higher model fit and robustness, these models still offer advantages.
[0004] Compared to traditional spatial relationships, the adjacency relationships of population mobility networks also have a direct impact on the spread of the epidemic. With the development of transportation, the flow of people and the exchange of goods have become more convenient and frequent, and traditional spatial adjacency relationships (such as neighboring cities or provinces) may not fully reflect the degree of connection between research units. Taking popular cities as an example, interactions between other regions and these cities may overcome the original spatial distance, exhibiting a stronger scale of population flow than between spatially adjacent cities. However, most existing spatial regression models only consider spatial relationships, with relatively few studies modeling the impact of population mobility network connections.
[0005] The spread of the epidemic also exhibits a strong temporal correlation. The development of the epidemic not only interacts with current health risk factors but is also influenced by past epidemic conditions and health risk factors, demonstrating temporal autocorrelation and time lag effects. Currently, most analyses of the temporal trends of COVID-19 are based on time series frameworks, using a specific country or region as the study area and historical data on novel coronavirus infection to simulate the incidence levels at different stages. Taking the classic infectious disease transmission dynamics (SEIR) model as an example, initial parameters are set by referencing empirical models, and the spread is predicted by adjusting parameters using existing historical epidemic data. The effectiveness of intervention strategies is then evaluated by estimating the corresponding parameters. Some scholars have also used deep learning methods to predict the trends and turning points of COVID-19. While models based on infectious disease transmission dynamics and deep learning frameworks can improve the accuracy of time series simulation and prediction in infectious disease research, their complex underlying principles reduce the interpretability of the models. Furthermore, these time series models only consider the influence of temporal effects and do not simultaneously consider the influence of spatial effects.
[0006] In summary, the modeling of COVID-19 transmission and health risk factors lacks simultaneous consideration of spatial and temporal effects as well as population flow network relationships. Therefore, there is an urgent need to provide a spatiotemporal modeling and prediction method for COVID-19 based on the spatial filter value of a dynamic population flow matrix, which can provide basic support for the description and prediction of the spatiotemporal relationship between COVID-19 transmission and health risk factors. Summary of the Invention
[0007] The purpose of this invention is to provide a spatiotemporal modeling and prediction method for COVID-19 based on the spatial filter value of a dynamic population flow matrix, thereby simultaneously addressing the impact of spatial and temporal effects on the model during the modeling of COVID-19 and health risk influencing factors, more accurately describing the interaction relationship of COVID-19 health risk influencing factors, and improving the modeling accuracy of COVID-19 while considering spatiotemporal relationships.
[0008] This invention provides a method for spatiotemporal modeling and prediction of COVID-19 based on spatial filtering of a dynamic population flow matrix, comprising the following steps:
[0009] Step 1, Data Acquisition and Processing, includes acquiring COVID-19 data and data related to the spread of COVID-19, preprocessing and filtering data products for subsequent modeling;
[0010] Step 2, construct the spatial adjacency matrix, including constructing the adjacency matrix W based on the spatial adjacency relationship of the spatial units, where the matrix unit values represent the spatial adjacency weights between the research units;
[0011] Step 3: Construct an adjacency matrix for the population flow network. This includes obtaining population flow data between research units at various time points during the pandemic, and assigning a matrix to each time point based on the strength of population flow relationships.t Construct the adjacency matrix of the corresponding population flow network The matrix element values represent the values at time nodes. t The strength of population flow interactions between research units;
[0012] Step 4: Construct the temporal adjacency matrix, including expanding the one-dimensional time series into a two-dimensional adjacency matrix T, and the matrix element values... Corresponding to the time node i With time nodes j Temporal adjacency weights between them;
[0013] Step 5, spatiotemporal expansion of spatial adjacency relationships, includes performing a Kronecker product operation on the spatial adjacency matrix W constructed in Step 2 and the temporal adjacency matrix constructed in Step 4, and performing a temporal tensor expansion on the spatial adjacency matrix to obtain the spatiotemporal adjacency matrix WT, where the matrix element values represent the time nodes. t The strength of population flow interactions between research units;
[0014] Step 6, Spatiotemporal expansion of the adjacency relationships in the population flow network, including the process of applying the adjacency relationships of each time node in Step 3. t The adjacency matrix of the constructed population flow network Perform a Kronecker product operation with the temporal adjacency matrix constructed in step 4 to obtain the spatiotemporal adjacency matrix of population flow. T; Sum all the calculated spatiotemporal population flow adjacency matrices to obtain the final overall spatiotemporal population flow adjacency matrix FT;
[0015] Step 7, extraction and screening of spatiotemporal feature vectors, includes centering the spatiotemporal adjacency matrices WT and FT obtained in steps 5 and 6 to obtain centered spatiotemporal matrices WCT and FCT; calculating eigenvalues and eigenvectors of the centered matrices; initially screening the feature vectors according to a preset threshold, and then further screening the initially screened feature vectors using a stepwise method, and finally incorporating them into the modeling process as spatiotemporal influencing factors and spatiotemporal influencing factors of population flow.
[0016] Step 8: Construct a COVID-19 regression model based on the spatiotemporal filter of the dynamic population flow matrix, including the data selected in Step 1 and the spatiotemporal feature vectors selected in Step 7. Spatiotemporal feature vector of population flow It is added as an independent variable to the regression model to model, predict, and evaluate COVID-19 data.
[0017] Furthermore, in step 1, the data related to the spread of COVID-19 includes, but is not limited to, population density, population age structure, education level, GDP, population activity intensity, temperature, air pressure, wind speed, precipitation, and altitude.
[0018] Furthermore, in step 2, the spatial adjacency weight matrix can be established using Rock adjacency, Bishop adjacency, or Queen adjacency; or a distance-based spatial weighting method can be used instead of adjacency relationships.
[0019] Furthermore, in step 3, the interaction characteristics of unit population flow differ at different time points. Therefore, an adjacency matrix of the population flow network is constructed for all time points within the study period. t=0,1,2…,p, where p represents the time dimension in spatiotemporal modeling.
[0020] Furthermore, in step 4, the time weight is defined as follows: selecting n days before and after is defined as adjacent and the weight is set to 1; time exceeding n days before and after is defined as non-adjacent and the weight is set to 0; or a weight calculation method based on time distance can be used.
[0021] Furthermore, in steps 5 and 6, the spatiotemporal expansion of the matrix includes two types: spatiotemporal co-generation expansion and spatiotemporal lag expansion. Spatiotemporal co-generation expansion only considers the relationship between the research unit and itself at different time points, without considering the impact it has on other units at different time points. Spatiotemporal lag expansion considers not only the relationship between the research unit and itself at different time points, but also the impact of the research unit on other units at different time points.
[0022] Furthermore, in step 8, the modeling process includes the following steps:
[0023] The establishment of the regression model includes using the set of health impact factors X related to the spread of COVID-19 selected in step 1 and the set of spatiotemporal feature vectors obtained after stepwise screening in step 7 as independent variables, and the COVID-19 infection rate as the dependent variable IFR to establish a regression model.
[0024] Model accuracy evaluation includes selecting statistical indicators such as model goodness of fit, root mean square error, and maximum likelihood value to evaluate the model accuracy.
[0025] The present invention provides a spatiotemporal modeling and prediction method for COVID-19 based on the spatial filter value of a dynamic population flow matrix. It simultaneously considers spatial autocorrelation effect, temporal autocorrelation and time lag effect, as well as the interaction effect of the dynamic population flow network, thereby more accurately describing the interaction between the COVID-19 pandemic and health risk influencing factors, and improving the modeling accuracy of COVID-19 pandemic under the premise of considering spatiotemporal relationships. Attached Figure Description
[0026] Figure 1 This is a flowchart of an embodiment of the present invention.
[0027] Figure 2 This is a flowchart of the data preprocessing process according to an embodiment of the present invention.
[0028] Figure 3 This is a schematic diagram of the adjacency matrix of the population flow network in step 3 of the embodiment of the present invention.
[0029] Figure 4 This is a schematic diagram of the spatiotemporal co-generation relationship and spatiotemporal lag relationship in step 5 of the embodiment of the present invention. Detailed Implementation
[0030] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.
[0031] The core problem this invention addresses is the strong spatial and temporal correlation between health risk factors and the spread of COVID-19. Among these, population mobility networks are particularly crucial for modeling the spread of COVID-19. In modeling COVID-19 and its health risk factors, the spatial autocorrelation and temporal correlation effects do not meet the underlying assumptions of existing models, and the influence of population mobility networks in the modeling process is largely lacking. This invention constructs a spatiotemporal regression model of COVID-19 based on the spatial filter value of a dynamic population mobility matrix. By considering population mobility network relationships, it addresses the impact of spatial autocorrelation, population mobility network correlation, and temporal correlation effects on modeling, thereby improving the accuracy of COVID-19 and health risk factor modeling and providing important reference for the analysis and prevention of COVID-19 and other infectious diseases.
[0032] This invention supplements the network autocorrelation caused by spatial units overcoming spatial distance by introducing a population flow network matrix, and introduces a time matrix to spatiotemporally extend the spatial adjacency matrix and the population flow network matrix. By decomposing and filtering the features of the spatiotemporal matrix, spatiotemporal feature vectors of space and population flow are obtained and added to the model, thereby improving the predictive accuracy of spatiotemporal modeling of the COVID-19 pandemic.
[0033] See Figure 1 The present invention provides a method for spatiotemporal modeling and prediction of COVID-19 based on spatial filtering of a dynamic population flow matrix, comprising the following steps:
[0034] Step 1: Data Acquisition and Processing. See Figure 2 This includes the following steps:
[0035] Step 1.1: Data Acquisition and Preprocessing. Collect daily COVID-19 infection numbers and health risk factor data related to the spread of COVID-19 (environmental data, etc.), including but not limited to population density, population age structure, education level, GDP, population activity intensity, temperature, air pressure, wind speed, precipitation, and altitude. Perform descriptive statistical analysis on all variables in the dataset, and handle outliers and null values. Depending on the specific situation, interpolation methods can be selected for imputation or direct removal, ensuring that the data has a uniform temporal and spatial resolution to avoid unnecessary errors caused by outliers and null values.
[0036] Step 1.2: Normality Test and Transformation. Use a histogram to test whether the data is normally distributed or approximately normally distributed. If the data is severely skewed, use the Box-Cox method to transform the data to a normal distribution. The Box-Cox transformation formula is as follows:
[0037]
[0038] Where y represents the number of COVID-19 infections. These are the Box-Cox transformation parameters estimated using the maximum likelihood method. The transformed data meets the null hypothesis that the data follows a normal distribution, as required by the modeling process.
[0039] Step 1.3: Data Normalization. The set of independent variables (health risk factors) is normalized to ensure the data distribution is between 0 and 1, facilitating model coefficient analysis and comparison. The normalization formula is as follows:
[0040]
[0041] in It is the normalized factor X. and These are the maximum and minimum values of factor X, respectively.
[0042] Step 1.4: Correlation and Multicollinearity Tests. The Pearson coefficient is used to test the correlation between the dependent and independent variables. The VIF value is used to test for multicollinearity among the independent variables. If the VIF value is less than 10, there is no significant multicollinearity among the independent variables, and all variables are retained and added to the subsequent modeling. If the VIF value is greater than 10, multicollinearity exists. Variables with VIF values greater than 10 are removed sequentially according to their VIF values, and the VIF values are recalculated until all remaining variables have VIF values less than 10. These remaining variables are then retained and added to the subsequent modeling, thus avoiding overfitting caused by multicollinearity.
[0043] Step 2: Construct the spatial adjacency matrix. Construct the adjacency matrix W based on the spatial adjacency relationships of the spatial units. The values of the matrix units represent the spatial adjacency weights between the units under study.
[0044] Common methods for establishing spatial adjacency weight matrices include Rock adjacency, Bishop adjacency, and Queen adjacency; in addition to adjacency relationships, distance-based spatial weighting methods can also be used.
[0045] Taking Queen's adjacency as an example, each cell has an adjacency relationship with cells that share an edge or a point, with a weight value of 1, while non-adjacent cells have a weight value of 0.
[0046] Step 3: Construct the adjacency matrix of the population flow network. Based on each time point... t Constructing an adjacency matrix for population mobility networks based on the strength and weakness of internal population mobility relationships. This includes acquiring population flow data between research units at various time points during the pandemic, and analyzing the strength of population flows at each time point. t Construct the adjacency matrix of the corresponding population flow network The matrix element values represent the values at time nodes. t The strength of population flow interactions between research units.
[0047] The interaction characteristics of unit population flow differ at different time points, necessitating the construction of adjacency matrices for the population flow network at all time points within the research period. (t=0,1,2…,p), where p represents the time dimension in spatiotemporal modeling, which in this study is the number of days.
[0048] See Figure 3 Taking a celestial scale as an example, on day t, the inflow population from starting unit i to target unit j is: , The larger the value, the stronger the population interaction intensity between research units i and j on day t. (Population mobility network adjacency matrix) The cell value in the i-th row and j-th column is denoted as ,in .
[0049] Step 4: Construct the temporal adjacency matrix. Expand the one-dimensional time series into a two-dimensional adjacency matrix T, with matrix element values... Corresponding to the time node i With time nodes j The temporal adjacency weights between them. Taking the matrix weight calculation method based on temporal distance as an example, ,in For the first Day's time ID, number Heaven and the Di The time distance of days for =| j - i |, Matrix element value .
[0050] In step 4, the time weight can be defined by either defining n days before and after as adjacent and setting the weight to 1, or defining times exceeding n days before and after as non-adjacent and setting the weight to 0; or by using a weight calculation method based on time distance. In practice, n can be determined empirically or according to relevant regulations.
[0051] Step 5: Spatiotemporal expansion of spatial adjacency relationships. Perform a Kronecker product operation on the spatial adjacency matrix W constructed in Step 2 and the temporal adjacency matrix T constructed in Step 4 to perform a temporal tensor expansion of the spatial adjacency matrix, obtaining the spatiotemporal adjacency matrix WT. Spatiotemporal expansion of the matrix includes two methods: spatiotemporal co-occurrence expansion and spatiotemporal lag expansion. See [link to relevant documentation]. Figure 4 .
[0052] The spatiotemporal co-occurrence extension only considers the relationship between the research unit and itself at different time points, without considering the impact it has on other units at different time points. Spatiotemporal co-occurrence extension matrix The calculation formula can be expressed as follows:
[0053]
[0054] in It is a time unit matrix, and its dimensions are the same as those of the time adjacency matrix T; It is a spatial unit diagonal matrix, and its dimensions are the same as those of the spatial adjacency matrix W; This is the Kronecker product operator.
[0055] The spatiotemporal lag extension considers not only the relationship between the research unit and itself at different time points, but also the impact of the research unit on other units at different time points. Spatiotemporal lag extension matrix. The calculation formula can be expressed as follows:
[0056]
[0057] in It is a time-unit diagonal matrix with the same dimensions as the time adjacency matrix T; It is a spatial unit diagonal matrix, and its dimensions are the same as those of the spatial adjacency matrix W; This is the Kronecker product operator.
[0058] Step 6: Spatiotemporal expansion of adjacency relationships in the population flow network. The population flow network adjacency matrix constructed in Step 3 for each time node t (t=0,1,2…,m) is then... Perform a Kronecker product operation with the temporal adjacency matrix constructed in step 4 to obtain the spatiotemporal adjacency matrix of population flow. The spatiotemporal extension of the T matrix also includes the two methods described in step 5: spatiotemporal co-occurrence extension and spatiotemporal lag extension. Population flow spatiotemporal co-occurrence extension matrix Spatial-temporal lag extension matrix of population flow The calculation formulas are expressed as follows:
[0059]
[0060]
[0061] in It is a time unit matrix, and its dimensions are the same as those of the time adjacency matrix T; It is a spatial unit diagonal matrix, and its dimensions are the same as the population flow adjacency matrix. Consistent; The Kronecker product operator is used to calculate the adjacency matrix of all spatiotemporal population flows. Summing T (t=0,1,2…,p) yields the final overall population flow spatiotemporal adjacency matrix FT.
[0062] Step 7: Extraction and filtering of spatiotemporal feature vectors.
[0063] In this embodiment, the spatiotemporal adjacency matrices WT and FT obtained in steps 5 and 6 are centered to obtain centered spatiotemporal matrices WCT and FCT; eigenvalues and eigenvectors are calculated for the centered matrices; the eigenvectors are initially screened according to a preset threshold (preferably 0.25), and the stepwise method is used to further screen the initially screened eigenvectors, which are finally added to the modeling process as spatiotemporal influencing factors and spatiotemporal influencing factors of population flow.
[0064] Furthermore, the extraction and filtering of spatiotemporal feature vectors involves the following steps:
[0065] Step 7.1: Centering the spatiotemporal adjacency matrix. The spatiotemporal weight matrix WT and the population flow spatiotemporal weight matrix FT from Steps 5 and 6 are centered to obtain the symmetric spatiotemporal matrices WCT and FCT. The formula for centering the spatiotemporal adjacency matrix is as follows:
[0066]
[0067]
[0068] Where n represents the spatial dimension of the study area, i.e., the number of study units, and p represents the temporal dimension in spatiotemporal modeling, which in this study is the number of study days. I is an n×p-dimensional spatiotemporal identity matrix. It is an (n×p)×(n×p) dimensional matrix with all elements equal to 1. After symmetry transformation
[0069] Step 7.2: Calculation of spatiotemporal eigenvalues and eigenvectors. Calculate the eigenvalues and eigenvectors of the centered spatiotemporal weight matrices WCT and FCT obtained in Step 7.1, respectively, to obtain the eigenvalue set of WCT. = The set of eigenvectors corresponding to eigenvalues = , Eigenvalue set Arranged from largest to smallest, i.e. ; and the eigenvalue set of FCT = The set of eigenvectors corresponding to eigenvalues = eigenvalue set Arranged from largest to smallest, that is Where n represents the spatial dimension of the study area, i.e., the number of study units, and p represents the time dimension in spatiotemporal modeling, i.e., the number of study days in this study.
[0070] Step 7.3: Screening of Spatiotemporal Feature Vectors. First, the calculated spatiotemporal feature vectors and population flow spatiotemporal feature vectors are initially screened. Then, the initial screened feature vector set is further screened using a stepwise method. The specific steps are as follows:
[0071] Step 7.3.1: Preliminary screening of feature vectors. The feature vector set calculated in Step 7.2... and For initial screening with a threshold of 0.25, the eigenvalues corresponding to the eigenvectors must meet the following two requirements: 1. The eigenvalue is greater than 0; 2. The ratio of the eigenvalue to the largest eigenvalue in the set is greater than 0.25. / max ( >0.25, / max ( )>0.25, where i represents the i-th feature value in the feature vector set. The initially screened feature vectors can reflect different degrees of spatiotemporal clustering characteristics and population flow clustering characteristics. The larger the feature value, the stronger the clustering reflected by the corresponding feature vector.
[0072] Step 7.3.2: Feature vector stepwise selection. The feature vectors obtained in the initial screening in Step 7.3.1 are sorted by their eigenvalues from largest to smallest. Then, they are sequentially added to ordinary least squares regression models with the COVID-19 infection rate as the dependent variable and the factors from Step 1 as independent variables. The AIC value of each model is calculated. The regression model with the lowest AIC value is selected. Its corresponding spatiotemporal feature vector is Then divide the remainder The spatiotemporal feature vectors from outside are sequentially added to the regression model. The algorithm calculates the AIC of the regression equation and determines whether the AIC value decreases significantly. If the AIC value decreases significantly, the above operation is repeated. If the AIC value hardly decreases, the addition of spatiotemporal feature vectors to the regression model is stopped, and the added spatiotemporal feature vectors are recorded. These feature vectors are the final set of optimal spatiotemporal feature vectors selected. The stepwise method can effectively filter out variables that fail the significance test, thus avoiding interference from insignificant variables in the modeling process.
[0073] Step 8: Construct a COVID-19 regression model based on the spatiotemporal filter of a dynamic population flow matrix. The preferred implementation steps used in this example are as follows:
[0074] Step 8.1: Establishing the regression model. The set of health influencing factors related to the spread of COVID-19 selected in Step 1, X = Compared with the spatiotemporal feature vector set obtained after stepwise filtering in step 7 Using the COVID-19 infection rate as the independent variable and the IFR as the dependent variable, a regression model is established, and the formula is as follows:
[0075]
[0076] in Set of health influencing factors The corresponding parameters, Spatiotemporal feature vectors The corresponding parameters, The error is random, satisfying the null assumptions of independence and normal distribution. By substituting the independent variables and population movement data for subsequent time periods into the obtained model, the degree of change in the COVID-19 infection rate can be predicted based on changes in health influencing factors and population movement.
[0077] Step 8.2: Model accuracy evaluation. Select the goodness of fit after model adjustment. Statistical indicators such as root mean square error (RMSE) and maximum likelihood (AIC) are used to evaluate the accuracy of the model. The formulas for calculating these indicators are as follows:
[0078]
[0079]
[0080]
[0081] in Let it be the COVID-19 infection rate of the i-th research unit at time t. Taking a daily timescale as an example, it=1 represents the actual COVID-19 infection rate of the first research unit on day 1. Let be the predicted model value of the i-th unit at time t. df represents the overall average infection rate of COVID-19, p represents the number of independent variables, and df represents the degrees of freedom of the corresponding model. The number of study units is denoted by t, which represents the time dimension in spatiotemporal modeling, and in this study, it is the number of study days.
[0082] In specific implementation, the method proposed in the technical solution of this invention can be automatically executed by those skilled in the art using computer software technology. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of this invention and computer equipment including the computer program running the corresponding computer program, should also be within the protection scope of this invention.
[0083] In some possible embodiments, a COVID-19 spatiotemporal modeling and prediction system based on the spatial filter value of a dynamic population flow matrix is provided, including a processor and a memory. The memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute the COVID-19 spatiotemporal modeling and prediction method based on the spatial filter value of a dynamic population flow matrix as described above.
[0084] In some possible embodiments, a COVID-19 spatiotemporal modeling and prediction system based on the spatial filter value of a dynamic population flow matrix is provided, including a readable storage medium on which a computer program is stored. When the computer program is executed, it implements the COVID-19 spatiotemporal modeling and prediction method based on the spatial filter value of a dynamic population flow matrix as described above.
[0085] It should be understood that the above description of the preferred embodiments of the present invention is quite detailed, but it should not be considered as a limitation on the scope of protection of the present invention. Those skilled in the art, under the guidance of the present invention, can make substitutions or modifications within the scope of protection of the claims of the present invention, all of which fall within the scope of protection of the present invention. The scope of protection of the present invention shall be determined by the appended claims.
Claims
1. A COVID spatio-temporal modeling and prediction method based on dynamic population flow matrix spatial filter values, characterized in that, Includes the following steps: Step 1, Data Acquisition and Processing, includes acquiring COVID-19 data and data related to the spread of COVID-19, preprocessing and filtering data products for subsequent modeling; Step 2, construct the spatial adjacency matrix, including constructing the adjacency matrix W based on the spatial adjacency relationship of the spatial units, where the matrix unit values represent the spatial adjacency weights between the research units; Step 3, constructing the population flow network adjacency matrix, including obtaining the population flow data between the study units at each time node during the epidemic, and constructing the population flow network adjacency matrix F corresponding to each time node t according to the strength of the population flow relationship t , the matrix element value represents the strength of the population flow interaction between the study units at time node t; Step 4, constructing the time adjacency matrix, including expanding the one-dimensional time series into a two-dimensional adjacency matrix T, the matrix cell value T ij corresponding to the time adjacency weight between time node i and time node j; Step 5, the spatiotemporal expansion of spatial adjacency relationships, includes performing the Kronecker product operation on the spatial adjacency matrix W constructed in Step 2 and the temporal adjacency matrix constructed in Step 4, and performing a temporal tensor expansion on the spatial adjacency matrix to obtain the spatiotemporal adjacency matrix WT. The matrix element values represent the strength of population flow interaction between research units at time node t. Step 6, Spatiotemporal expansion of the population flow network adjacency relationship, including the population flow network adjacency matrix F constructed for each time node t in Step 3. t Performing the Kronecker product operation with the temporal adjacency matrix constructed in step 4 yields the spatiotemporal adjacency matrix F of population flow. t T; Sum all the calculated spatiotemporal population flow adjacency matrices to obtain the final overall spatiotemporal population flow adjacency matrix FT; Step 7, extraction and filtering of spatiotemporal feature vectors, including centering the spatiotemporal adjacency matrices WT and FT obtained in steps 5 and 6 to obtain centered spatiotemporal matrices WCT and FCT; calculating eigenvalues and eigenvectors of the centered matrices; The feature vectors are initially screened according to a preset threshold, and then the stepwise method is used to further screen the feature vectors after the initial screening. Finally, they are added to the modeling process as spatial and spatiotemporal influencing factors and population flow spatiotemporal influencing factors. Step 8, build a new coronavirus regression model based on the dynamic population flow matrix spatiotemporal filter value, including the data screened in step 1 and the spatial and temporal feature vector EV screened in step 7 WT , population flow spatiotemporal feature vector EV FT as an independent variable into the regression model, model and evaluate the new coronavirus data.
2. The method of claim 1, wherein the method is based on a dynamic population flow matrix spatial filter. In step 1, data related to the spread of COVID-19 include, but are not limited to, population density, population age structure, education level, GDP, population activity intensity, temperature, air pressure, wind speed, precipitation, and altitude.
3. The method of claim 1, wherein the method is based on a dynamic population flow matrix spatial filter. In step 2, the spatial adjacency weight matrix can be established using Rock adjacency, Bishop adjacency, or Queen adjacency; or a distance-based spatial weighting method can be used instead of adjacency relationships.
4. The method of claim 1, wherein the method is based on a dynamic population flow matrix spatial filter. In step 3, the interaction characteristics of unit population flow are different at different time points. Therefore, an adjacency matrix F of the population flow network is constructed for all time points within the study period. t t = 0, 1, 2, ..., p, where p represents the time dimension in spatiotemporal modeling.
5. The method of claim 1, wherein the method is based on a dynamic population flow matrix spatial filter. In step 4, the time weight is defined as follows: selecting n days before and after is defined as adjacent and the weight is set to 1; time exceeding n days before and after is defined as non-adjacent and the weight is set to 0; or a weight calculation method based on time distance can be used.
6. The method of claim 1, wherein the method is based on a dynamic population flow matrix spatial filter. In steps 5 and 6, the spatiotemporal expansion of the matrix includes two types: spatiotemporal co-occurrence expansion and spatiotemporal lag expansion. Spatiotemporal co-occurrence expansion only considers the relationship between the research unit and itself at different time points, without considering the impact it has on other units at different time points. Spatiotemporal lag expansion considers not only the relationship between the research unit and itself at different time points, but also the impact of the research unit on other units at different time points.
7. The new coronavirus spatio-temporal modeling and prediction method based on dynamic population flow matrix spatial filter value according to any one of claims 1-6, characterized in that: In step 8, the modeling process includes the following steps: The establishment of the regression model includes using the set of health impact factors X related to the spread of COVID-19 selected in step 1 and the set of spatiotemporal feature vectors obtained after stepwise screening in step 7 as independent variables, and the COVID-19 infection rate as the dependent variable IFR to establish a regression model. Model accuracy evaluation includes selecting statistical indicators such as model goodness of fit, root mean square error, and maximum likelihood value to evaluate the model accuracy.