CN112669977B - Intervening SEIRD-CA infectious disease space-time diffusion simulation and prediction method - Google Patents
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Abstract
The invention relates to a space-time diffusion simulation and prediction method for an intervening SEIRD-CA infectious disease, belonging to the field of informatization. The method comprises the following steps: s1: establishing an intervening SEIRD module; s2: establishing a CA module; s3: establishing a space-time coupling module; s4: and (5) checking precision. The interventionalist SEIRD model is used to predict the number of infectious disease cases over time; the CA model maps the quantity prediction result to the grid space by integrating the space suitability probability, the constraint probability, the neighborhood probability, the random probability and the like of the infectious diseases; the space-time coupling module couples the two modules by constructing a constraint function to form CA iteration and conversion rules, and operation is completed.
Description
Technical Field
The invention belongs to the field of informatization, and relates to a space-time spread simulation and prediction method for infectious diseases of an intervening SEIRD-CA model.
Background
The pneumonic epidemic (COVID-19) caused by the novel coronavirus (SARS-CoV-2) has symptoms similar to those of severe acute respiratory syndrome (Severe Acute Respiratory Syndrome, SARS) and also presents a high degree of infectivity which SARS does not possess.
In the context of the new coronavirus (Corona Virus Disease 2019, covd-19), most research focused on time series modeling and prediction using statistical data, where epidemiological propagation models dominate. The time series model can predict the risk and approximate scale of outbreaks of the COVID-19 epidemic situation in various areas. The epidemic situation real-time map combines the epidemic situation process with the map, shows the space-time variation of the epidemic situation, and is a main mode for expressing the space-time spread of the epidemic situation. Spatial analysis is helpful to understanding the spread of infectious diseases, and based on related visual studies, spatial distribution of the infected person is found to have strong correlation with other spatial attributes. In the field of COVID-19 disease, most studies have been developed in terms of clinical and epidemiological characteristics of COVID-19, whereas the study of spatiotemporal modeling of COVID-19 has been limited. With the development of artificial intelligence and computer technology, network dynamics models represented by cellular automata are also used for the study of infectious diseases. The existing researches are mainly from the perspective of microscopic propagation, the influence of specific places on the propagation path of the simulated COVID-19 is emphasized, the data granularity requirement of microscopic models is high, and the uncertainty of the spatial distribution of the case calculated by the models is large.
Space tracing and accurate prediction of epidemic situation are still unsolved problems, and an intervening SEIRD-CA space-time coupling model is built for better simulating the space-time diffusion rule of the COVID-19. The model comprises an intervention SEIRD module, a CA module and a space-time coupling module. The interventionalist SEIRD model is used to predict the number of infectious disease cases over time; the CA model maps the quantity prediction result to the grid space by integrating the space suitability probability, the constraint probability, the neighborhood probability, the random probability and the like of the infectious diseases; the space-time coupling module couples the two modules by constructing a constraint function to form CA iteration and conversion rules, and the operation of the model is completed.
Disclosure of Invention
Accordingly, the present invention is directed to a method for simulating and predicting the space-time spread of infectious diseases in an interventional SEIRD-CA model.
In order to achieve the above purpose, the present invention provides the following technical solutions:
the method for simulating and predicting the space-time spread of infectious diseases of the intervening SEIRD-CA model comprises the following steps:
s1: establishing an intervening SEIRD model;
s2: establishing a CA module;
s3: establishing a space-time coupling module;
s4: and (5) checking precision.
Optionally, the S1 specifically is:
on the traditional SEIR model, R is subdivided into R and D, forming a new SEIRD model of infectious disease dynamics model intervention:
wherein S represents the number of people susceptible to infection and corresponds to the healthy number in the statistical data;
e represents the number of latent people and corresponds to the newly added suspected people in the statistical data;
i represents the number of infected people, and corresponds to the newly added number of diagnosed people in the statistical data;
r represents the number of healed people and corresponds to the accumulated number of healed people in the statistical data;
d represents the number of deaths, corresponding to the number of accumulated deaths in the statistics;
alpha represents the contact number of susceptible people, beta represents the probability of being infected by the contact suspected people, and alpha x beta represents the infectivity of the suspected people;
σ represents the probability of the latent population (E) being transformed into an infected population (I);
gamma represents the probability (i.e. cure rate) of the infected population (I) to a cured population (R);
kappa represents the probability (i.e., mortality) of the infected population (I) to the dead population (D).
Optionally, the S2 specifically is:
the overall probability of transition for each cell in the CA model depends on the suitability for epidemic development P s Neighborhood effect Ω and limiting factor P c ；
Optionally, the S3 specifically is:
the interventionalist SEIRD model generates the number of daily infectors and the CA model assigns the infectors; the space-time coupling module couples the two modules by constructing a constraint function to form CA iteration and conversion rules, and the operation of the model is completed.
Optionally, the S4 specifically is:
from the grid scale and the curve scale, the accuracy of the model is checked by using a mean square error MSE, a mean absolute error MAE and a root mean square error RMSE:
the mean square error MSE formula is as follows:
the mean absolute error MAE is formulated as follows:
the root mean square error RMSE is given by:
the invention has the beneficial effects that: the invention comprises an intervening SEIRD module, a CA module and a space-time coupling module. The interventionalist SEIRD model is used to predict the number of infectious disease cases over time; the CA model maps the quantity prediction result to the grid space by integrating the space suitability probability, the constraint probability, the neighborhood probability, the random probability and the like of the infectious diseases; the space-time coupling module couples the two modules by constructing a constraint function to form CA iteration and conversion rules, and the operation of the model is completed.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objects and other advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out in the specification.
Drawings
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in the following preferred detail with reference to the accompanying drawings, in which:
FIG. 1 is an SEIRD model of intervention;
FIG. 2 is a CA model;
FIG. 3 is a space-time coupling model;
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the illustrations provided in the following embodiments merely illustrate the basic idea of the present invention by way of illustration, and the following embodiments and features in the embodiments may be combined with each other without conflict.
Wherein the drawings are for illustrative purposes only and are shown in schematic, non-physical, and not intended to limit the invention; for the purpose of better illustrating embodiments of the invention, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the size of the actual product; it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numbers in the drawings of embodiments of the invention correspond to the same or similar components; in the description of the present invention, it should be understood that, if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc., that indicate an azimuth or a positional relationship based on the azimuth or the positional relationship shown in the drawings, it is only for convenience of describing the present invention and simplifying the description, but not for indicating or suggesting that the referred device or element must have a specific azimuth, be constructed and operated in a specific azimuth, so that the terms describing the positional relationship in the drawings are merely for exemplary illustration and should not be construed as limiting the present invention, and that the specific meaning of the above terms may be understood by those of ordinary skill in the art according to the specific circumstances.
Model 1 principle and method
1.1 SEIRD model principle of intervention
On the traditional SEIR model, R is subdivided into R and D, and government control measures are added to form a new infectious disease dynamics model Intervention SEIRD model, as shown in fig. 1:
wherein S represents the number of people susceptible to infection and corresponds to the healthy number in the statistical data;
e represents the number of latent people and corresponds to the newly added suspected people in the statistical data;
i represents the number of infected people, and corresponds to the newly added number of diagnosed people in the statistical data;
r represents the number of healed people and corresponds to the accumulated number of healed people in the statistical data;
d represents the number of deaths, corresponding to the number of accumulated deaths in the statistics;
alpha represents the contact number of susceptible people, beta represents the probability of being infected by the contact suspected people, and alpha x beta represents the infectivity of the suspected people;
σ represents the probability of the latent population (E) being transformed into an infected population (I);
gamma represents the probability (i.e. cure rate) of the infected population (I) to a cured population (R);
kappa represents the probability (i.e., mortality) of the infected population (I) to the dead population (D).
1.2 CA module
The CA module divides a research area into a plurality of homogeneous spaces, and learns the probability of occurrence of an infectious disease in different space positions in an observation period by establishing a correlation between space driving factors influencing disease transmission and disease distribution and by means of machine learning and other relevant algorithms, so as to form a space suitability probability map of the infectious disease. And simultaneously mapping the quantity prediction result to a grid space by integrating the space suitability, constraint probability, neighborhood probability, random probability and the like of the whole infectious disease (see fig. 2).
The spread of novel coronavirus epidemic has a close relationship with human activity. Taking elevation, gradient, land type and river as natural environment driving factors, taking hospitals, schools, hotels, shopping, dining, scenic spots, entertainment places, banks, station sites, railways, highways, main roads, secondary roads and population densities as social and economic driving factors, taking epidemic infected persons in the whole time range as labels, and carrying out regression to obtain a suitability probability layer (P) Suitability for use in a medical device )。
To achieve a daily spatial distribution of infected persons, the suitability probability layer is reclassified with the constraint probability layer (P Constraint ) The dot product yields a global probability layer (P Global situation ) According to the previous epidemic map, selecting a grid where a diagnostician is located according to the probability of the grid as a seed point (iJ) to obtain the ROI (P) of the seed point in the global probability layer Global ROI ) Dot product neighborhood probability layer (P) FIELD ) And randomly selecting an infection grid according to the grid probability, repeating the process, and completing one CA iteration when all the infected persons are distributed on the same day.
The overall probability of transition for each cell in the CA model depends on the suitability for epidemic development P s Neighborhood effect Ω and limiting factor P c 。
1.3 space-time coupling Module
The research utilizes the dynamic evolution characteristic of CA, uses CA for the space distribution simulation of novel coronavirus infected persons, and fully explores the space dynamic evolution rule. The interventionalist SEIRD model generates a daily number of infected persons and the CA model assigns the infected persons. The space-time coupling module couples the two modules by constructing a constraint function to form CA iteration and conversion rules, and the operation of the model is completed. (see FIG. 3).
So far, the time sequence simulation of the infectors and the CA model are realized through the intervention SEIRD model, and the spatial positions of the infectors are distributed in one day. Under the situation of investigation in the sealing city, assuming that the average latency period is 7 days, the number of the infected persons on the n+8th day is input by overlapping and combining the image layers of the infected persons on the n to the n+7th day, and then a daily epidemic map of the whole time period can be generated.
1.4 precision inspection
The present study examined the accuracy of the model from the grid scale and the curve scale, respectively, using Mean Square Error (MSE), mean Absolute Error (MAE), root Mean Square Error (RMSE):
the Mean Square Error (MSE) is given by:
the Mean Absolute Error (MAE) formula is as follows:
the Root Mean Square Error (RMSE) is given by:
2 data Source and data processing
2.1 data Source
The existing data about new crown epidemic situation mainly come from the statistical data published by authorities such as national health committee officials (http:// www.nhc.gov.cn /), world health organization (https:// www.who.int/westempoccic), MIDAS network and the like. The statistical data relates to newly added suspected, newly added diagnosed, accumulated death, accumulated cure, etc., which is mainly from the university of pittsburgh, usa, public health research institute public health dynamics laboratory (Public Health Dynamics Lab-PHDL) issuing an online portal for the modeling study of devid-19, which is maintained by the infectious disease etiology model coordination center (MIDAS Coordination Center-MCC). The trace data of the novel coronavirus diagnostic person are obtained by a Hualong network.
TABLE 1MIDASnetwork vid-19 statistics
Considering that spread of the COVID-19 has a close relationship with human activities, two types of natural environment and socioeconomic are selected as main driving factors for influencing spread of the COVID-19. The natural environment data used in this experiment included elevation, grade, land type, river. The elevation data is derived from ASTER GDEM, the land type data is derived from China national academy of sciences resource environment and data center, and the river data is derived from OSM. Socioeconomic data relates to class 14, where class 9 point of interest data for hospitals, schools, hotels, shopping, restaurants, scenic spots, banks, casinos, station sites are crawled by a Goldmap. The railway, expressway, main road and secondary road class 4 data are from a free street view map OSM (https:// www.openstreetmap.org), and the population density spatialization data are from World pop (WorldPop Data Portal).
TABLE 2 spatial model driver selection and data
2.2 data processing
All data were subjected to a consistency treatment (the unified study range was Chongqing city, and the unified projection coordinate system was WGS_1984_UTM_Zone48N) to construct a unified data set.
For POI data, firstly, a web crawler is adopted to climb 9 interest point data, which are closely related to human activities, in a Goldmap, including hospitals, schools, hotels, shopping, dining, scenic spots, banks, entertainment venues and station sites; then obtaining point data under a WGS-84 coordinate system through coordinate system conversion (GCJ-02- & gt WGS-84); then, the obtained product is imported into ARCGIS, nuclear density analysis is carried out on various POIs, the administrative scope data of Chongqing city is taken as a template, and a nuclear density analysis chart of each POI is obtained through mask extraction.
The land type data is subjected to reclassification and mask extraction operations. Because the distribution of the COVID infected persons has a certain correlation with the land types, the occurrence of the COVID-19 infected persons in water areas and unmanned areas is completely impossible, so the research reclassifies the land types into 3 types, wherein the unmanned areas such as the unused lands and the water areas are classified into one type, the cultivated lands, the woodlands and the grasslands are classified into one type, and the urban and rural domestic areas are classified into one type. The unmanned region serves as a constraint probability layer in the model construction process.
The elevation data comes from ASTER GDEM, and an elevation layer is obtained through mask extraction; and obtaining a gradient map layer through gradient calculation by means of ARCGIS.
Distance data from rivers, railways, highways, arterial roads and secondary roads are derived from OSM, and Euclidean distance layers of all traffic lines are obtained through Euclidean distance analysis in ARCGIS.
3.2 model correction and inspection
3.2.1 Compare scheme design
The study is based on the following assumptions:
(1) The result is affected and the difference is significant by using the infected person kernel density map, the actual number grid map and the 01 grid map with or without infected person as the neighborhood analysis map layer.
(2) In the simulation process, whether intervention measures are taken or not can have influence on the results and the differences are obvious.
(3) The 2 to 14 day latency in news stories was set to the median 7 days.
Selecting statistical data and point data of a COVID-19 infected person in a research period, designing five comparison schemes aiming at the two assumptions, and respectively carrying out comparison analysis on an actual epidemic map, wherein the specific scheme is as follows:
scheme one: the infected person nuclear density map is used as a neighborhood analysis map layer to combine an intervention SEIRD model (with intervention seal city and investigation).
Scheme II: the actual number grid graph is used as a neighborhood analysis graph layer to combine an intervention SEIRD model (with intervention for blocking city and checking).
Scheme III: the 01 grid graph with or without the infected person is used as a SEIRD model of the neighborhood analysis layer combined with intervention (with intervention for sealing city and checking).
Scheme IV: the actual number grid graph is used as a SEIRD model (no investigation in the sealing city) of the neighborhood analysis graph layer combined with the intervention.
Scheme five: the actual population grid graph is used as a neighborhood analysis graph layer to be combined with an interference-free SEIRD model (no dry pre-treatment).
Claims (2)
1. An intervening SEIRD-CA infectious disease space-time spread simulation and prediction method, characterized in that the method comprises the following steps:
s1: establishing an intervening SEIRD model;
s2: establishing a CA module;
s3: establishing a space-time coupling module;
s4: checking precision;
the S1 specifically comprises the following steps:
on the traditional SEIR model, R is subdivided into R and D and government control measures are added to form a new SEIRD model of infectious disease dynamics model intervention:
wherein S represents the number of people susceptible to infection and corresponds to the healthy number in the statistical data;
e represents the number of latent people and corresponds to the newly added suspected people in the statistical data;
i represents the number of infected people, and corresponds to the newly added number of diagnosed people in the statistical data;
r represents the number of healed people and corresponds to the accumulated number of healed people in the statistical data;
d represents the number of deaths, corresponding to the number of accumulated deaths in the statistics;
alpha represents the contact number of susceptible people, beta represents the probability of being infected by the contact suspected people, and alpha x beta represents the infectivity of the suspected people;
σ represents the probability of the latent population E being transformed into the infected population I;
gamma represents the probability of the infected crowd I to be converted into the cured crowd R, namely the cure rate;
kappa represents the probability of the infected population I to be converted into the dead population D, namely the mortality;
the step S2 is specifically as follows:
the overall probability of transition for each cell in the CA model depends on the suitability for epidemic development P s Neighborhood effect Ω and limiting factor P c ；
The step S3 is specifically as follows:
intervention SEIRD the number of infected individuals per day and the CA model assigns the infected individuals; the space-time coupling module couples the two modules by constructing a constraint function to form CA iteration and conversion rules, and the operation of the model is completed.
2. The method for spatiotemporal spread simulation and prediction of an intervening SEIRD-CA infectious disease of claim 1, wherein: the step S4 specifically comprises the following steps:
from the grid scale and the curve scale, the accuracy of the model is checked by means of the mean square error MSE, the mean absolute error MAE and the root mean square error RMSE:
the mean square error MSE formula is as follows:
the mean absolute error MAE is formulated as follows:
the root mean square error RMSE is given by:
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| KR101960504B1 (en) * | 2017-12-18 | 2019-07-15 | 세종대학교산학협력단 | Apparatus and method for epidemic spread prediction modeling |
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| KR101960504B1 (en) * | 2017-12-18 | 2019-07-15 | 세종대학교산학협력단 | Apparatus and method for epidemic spread prediction modeling |
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