CN114496287A - Quantitative evaluation method and system for space-time transmission risk of infectious disease caused by initial outbreak position - Google Patents

Quantitative evaluation method and system for space-time transmission risk of infectious disease caused by initial outbreak position Download PDF

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CN114496287A
CN114496287A CN202111503747.5A CN202111503747A CN114496287A CN 114496287 A CN114496287 A CN 114496287A CN 202111503747 A CN202111503747 A CN 202111503747A CN 114496287 A CN114496287 A CN 114496287A
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刘康
尹凌
薛建章
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Abstract

The invention discloses a quantitative evaluation method and a system for the space-time transmission risk of infectious diseases caused by an initial outbreak position, wherein firstly, a space-time transmission model of the infectious diseases is utilized to simulate the space-time transmission condition of the infectious diseases after the outbreak at different positions, and a simulation result is obtained; and then processing the simulation result into a space-time propagation risk quantitative evaluation index. The invention provides a systematic method and quantitative indexes for evaluating space-time propagation risks caused by different outbreak positions in a city, so as to help a government to make more prospective and space-accurate intervention and control measures and promote the application of a geographic information scientific theory and a method in the field of public health.

Description

Quantitative evaluation method and system for space-time transmission risk of infectious disease caused by initial outbreak position
Technical Field
The invention relates to the field of geographic information systems, in particular to a quantitative evaluation method and system for the space-time transmission risk of infectious diseases caused by initial outbreak positions, which are used for evaluating the space-time transmission risk caused by different initial outbreak positions in a city.
Background
Reviewing the historically large-scale, high infection rate epidemic and the current COVID-19 pandemic, it can be seen that urban internal infections are often outbreaked at a certain location and spread further into a larger spatial area. In addition, due to the difference of planning and self-development of each region of a city, the regions in the city have obvious spatial heterogeneity in the aspects of population, public facilities, functions and the like, so that a population flow network embedded in the space also has high structural heterogeneity (Liu et al, 2020; Hou et al, 2021), and finally, infectious diseases are exposed at different positions, so that different space-time transmission risks and control difficulties are generated. Therefore, quantitative evaluation of the space-time transmission risk caused by the initial outbreak position of the urban internal infectious disease is of great significance for prospective and accurate prevention and control.
Mathematical and computer modeling are important means to characterize the process of spatiotemporal transmission of infectious diseases. Differential equation models and intelligent body models are two types of models that are currently in common use. According to different disease transmission mechanisms, modeling factors and research perspectives, researchers have proposed a large number of infectious disease transmission model variants on the basis of the disease transmission model variants, and a vital planning tool is provided for policy makers and public health practitioners.
However, most of the current modeling research is aimed at predicting the spatiotemporal trend of infectious diseases in large-scale spaces such as countries, provinces/states, cities and the like (Yang et al, 2020), or simulating and evaluating the effects of interventions such as wearing masks, household isolation, close contact person tracking, travel limitation and the like (Ferguson et al, 2020; Lai et al, 2020; Yin et al, 2020; Zhou et al, 2020; Aleta et al, 2020), and the research is deep into the fine scale of the interior of the city, and the influence of the initial outbreak position on the spatiotemporal propagation risk of the infectious diseases is evaluated quantitatively and systematically.
In summary, the existing research and technologies mainly aim at predicting the spatial and temporal propagation trend of epidemic situations or simulating the effect of various intervention measures at the national/state/province/city level, and less deeply reach the fine scale inside cities. Meanwhile, current research lacks systematic methods and quantitative indicators to assess the risk of spatiotemporal propagation due to different outbreak locations.
[1]Kraemer,M.U.,Yang,C.H.,Gutierrez,B.,Wu,C.H.,Klein,B.,Pigott,D.M.,...&Scarpino,S.V.(2020).The effect of human mobility and control measures on the COVID-19epidemic in China.Science,368(6490),493-497.
[2]Liu,Y.,Yao,X.,Gong,Y.,Kang,C.,Shi,X.,Wang,F.,Wang,J.,Zhang,Y.,Zhao,P.,Zhu,D.,&Zhu,X.(2020).Analytical methods and applications of spatial interactions in the era of big data.Acta Geographica Sinica,75(7):1523-1538.
[3]Hou,X.,Gao,S.,Li,Q.,Kang,Y.,Chen,N.,Chen,K.,...&Patz,J.A.(2021).Intracounty modeling of COVID-19 infection with human mobility:Assessing spatial heterogeneity with business traffic,age,and race.Proceedings of the National Academy of Sciences,118(24).
[4]Aleta,A.,Martin-Corral,D.,y Piontti,A.P.,Ajelli,M.,Litvinova,M.,Chinazzi,M.,...&Moreno,Y.(2020).Modelling the impact of testing,contact tracing and household quarantine on second waves of COVID-19.Nature Human Behaviour,4(9),964-971.
[5]Yin,L.,Zhang,H.,Li,Y.,Liu,K.,Chen,T.,Luo,W.,...&Mei,S.(2021).A data driven agent-based model that recommends non-pharmaceutical interventions to suppress Coronavirus disease 2019 resurgence in megacities.Journal of the Royal Society Interface,18(181),20210112.
[6]Lai,S.,Ruktanonchai,N.W.,Zhou,L.,Prosper,O.,Luo,W.,Floyd,J.R.,...&Tatem,A.J.(2020).Effect of non-pharmaceutical interventions to contain COVID-19in China.nature,585(7825),410-413.
[7]Yang,Z.,Zeng,Z.,Wang,K.,Wong,S.S.,Liang,W.,Zanin,M.,...&He,J.(2020).Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions.Journal of thoracic disease,12(3),165.
[8]Zhou,Y.,Xu,R.,Hu,D.,Yue,Y.,Li,Q.,&Xia,J.(2020).Effects of human mobility restrictions on the spread of COVID-19in Shenzhen,China:a modelling study using mobile phone data.The Lancet Digital Health,2(8),e417-e424.
Disclosure of Invention
The invention aims to provide a method and a system for quantitatively evaluating the space-time transmission risk of infectious diseases caused by initial outbreak positions, and aims to overcome the defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
the quantitative assessment method for the spatiotemporal transmission risk of the infectious disease caused by the initial outbreak position comprises the following steps:
simulating the space-time transmission condition of the infectious disease after outbreak at different positions by using an infectious disease space-time transmission model to obtain a simulation result;
and processing the simulation result into a space-time propagation risk quantitative evaluation index.
Further, the construction process of the infectious disease space-time propagation model specifically comprises the following steps:
firstly, defining a basic evaluation unit according to research needs, and then processing the mobile phone positioning data into a plurality of types of data based on the basic evaluation unit, wherein the plurality of types of data based on the basic evaluation unit comprise: the number of resident population of each basic evaluation unit, the number of daily out population of each basic evaluation unit and the population flow among the basic evaluation units;
and constructing an infectious disease space-time transmission model based on susceptibility-latent-infection-removal according to several types of data based on a basic evaluation unit.
Further, the construction of the infectious disease spatiotemporal propagation model based on susceptibility-occult-infection-removal is specifically as follows:
dividing the resident population in each basic evaluation unit into susceptible population, latent population, infected population and removed population, wherein the infected population comprises dominant infectors and latent infectors;
based on pathogenesis and transmission mechanism, a space-time transmission model of infectious diseases which are susceptible, latent, infected and removed is constructed as follows:
Figure BDA0003402630810000041
Figure BDA0003402630810000042
Figure BDA0003402630810000043
Figure BDA0003402630810000044
Figure BDA0003402630810000045
wherein the content of the first and second substances,
Figure BDA0003402630810000046
i.e. the total resident population in the basic evaluation unit remains unchanged;
Nlthe number of resident population of the basic evaluation unit l;
Si(t)、Li(t)、
Figure BDA0003402630810000051
and Ri(t) the number of susceptible, occult, dominant infected, occult infected and removed persons within the basic evaluation unit i on day t, respectively,
Figure BDA0003402630810000052
and
Figure BDA0003402630810000053
the number of dominant and recessive infectors within the basal assessment unit l on day t, respectively;
beta is the effective infection rate of the dominant infected person (average number of infectious persons per day of the dominant infected person);
delta is the conversion rate from the latent period to the infectious period, and the value is the reciprocal of the latent period;
γ1movement of a dominantly infected personThe rate of division is the reciprocal of the infection period of the dominant infected person;
γ0the removal rate of a recessive infected person is the reciprocal of the infection period of the recessive infected person;
epsilon represents the ratio of the effective infection rate of recessive to dominant infected persons;
σ is the proportion of dominant infected persons;
hijindicates the number of persons from basic evaluation units i to j, h, throughout the dayljIndicates the number of persons from basic evaluation units l to j, h, throughout the dayijThe device consists of two parts: when i ≠ j, hijFor the number of persons from basic assessment unit i to j all day, when i ═ j, hijThe number of persons who did not leave the basic evaluation unit all day, on the basis of which h is calculatedijEach row of the matrix is normalized to ensure sigmajhij＝1,
Figure BDA0003402630810000055
∑lhljNlRepresenting the population number in the basic evaluation unit j when the population is mixed;
Figure BDA0003402630810000054
representing the number of infected persons in the basic evaluation unit j when mixed;
only beta is an unknown parameter in the model, and the beta estimation method is as follows:
1) taking different values of beta, operating a space-time transmission model of the infectious disease, and obtaining a corresponding daily newly-increased case quantity curve of the whole market;
2) estimating R0 from each daily new case curve using exponential growth, via R0 toolkit in R language, to obtain pairs of (β, R0) values;
3) and fitting the relation between the beta and the R0 to obtain the effective infection rate beta corresponding to the basic regeneration number R0 of the infectious disease.
Further, the specific process of simulating the space-time transmission condition of the infectious disease after the infectious disease is outbreak at different positions by using the infectious disease space-time transmission model is as follows:
determining the number of seeds initially placed in a single basic evaluation unit according to the research requirement;
for a certain basic evaluation unit, if the total population of the basic evaluation unit is smaller than the seed number, directly setting the seed number placed in the basic evaluation unit as the total population of the basic evaluation unit, otherwise, setting the seed number placed in the basic evaluation unit as the seed number, then performing propagation simulation, and recording the propagation condition of each day; and traversing all basic evaluation units in the infectious disease space-time transmission model, counting all simulation results, and obtaining the disease transmission condition of each basic evaluation unit as an initial outbreak position.
Further, the quantitative evaluation index of the spatio-temporal propagation risk specifically includes:
index 1: the total infected population in the city on day d;
respectively counting the total number of infected people in the whole market on the d day according to the simulation result of each basic evaluation unit serving as the basic evaluation unit for initially placing the seeds;
index 2: on day d, epidemic situation and the number of basic evaluation units are counted;
respectively counting the number of the total market epidemic situation and the number of the basic evaluation units on the d day for the simulation result of each basic evaluation unit as the basic evaluation unit for initially placing the seeds, and if the number of infected people in the basic evaluation unit is more than or equal to 1, determining that the basic evaluation unit is affected by the epidemic situation and counting the number of the infected people in the statistical range;
index 3: the spatial diffusion degree of epidemic situation on day d;
and respectively counting the spatial diffusion degree of the full-market epidemic situation on the d day according to the simulation result of each basic evaluation unit as the basic evaluation unit for initially placing the seeds.
Further, the calculation process of the spatial diffusion degree is as follows:
the position of the center of gravity of the infection is first calculated:
Figure BDA0003402630810000061
the degree of spatial diffusion is then calculated:
Figure BDA0003402630810000071
in the formula, N is the number of basic evaluation units.
The quantitative evaluation system for the spatiotemporal spread risk of the infectious disease caused by the initial outbreak position comprises a simulation module and an evaluation module, wherein:
a simulation module: the method is used for simulating the space-time transmission condition of the infectious disease after the infectious disease is outbreak at different positions by utilizing the infectious disease space-time transmission model to obtain a simulation result;
an evaluation module: and the method is used for processing the simulation result into a space-time propagation risk quantitative evaluation index.
Further, the construction process of the infectious disease space-time propagation model specifically comprises the following steps:
firstly, a prediction basic evaluation unit is defined according to research needs, and then mobile phone positioning data is processed into a plurality of types of data based on the basic evaluation unit, wherein the plurality of types of data based on the basic evaluation unit comprise: the number of resident population of each basic evaluation unit, the number of daily out population of each basic evaluation unit and the population flow volume among the basic evaluation units;
constructing an infectious disease space-time propagation model based on susceptibility-occult-infection-removal according to a plurality of types of data based on a basic evaluation unit, wherein the infectious disease space-time propagation model based on susceptibility-occult-infection-removal is specifically constructed as follows:
dividing the resident population in each basic evaluation unit into susceptible population, latent population, infected population and removed population, wherein the infected population comprises dominant infectors and latent infectors;
based on pathogenesis and transmission mechanism, a space-time transmission model of infectious diseases which are susceptible, latent, infected and removed is constructed as follows:
Figure BDA0003402630810000072
Figure BDA0003402630810000073
Figure BDA0003402630810000081
Figure BDA0003402630810000082
Figure BDA0003402630810000083
wherein the content of the first and second substances,
Figure BDA0003402630810000084
i.e. the total resident population in the basic evaluation unit remains unchanged;
Nlthe number of resident population of the basic evaluation unit l;
Si(t)、Li(t)、
Figure BDA0003402630810000085
and Ri(t) the number of susceptible, occult, dominant infected, occult infected and removed persons within the basic evaluation unit i on day t, respectively,
Figure BDA0003402630810000086
and
Figure BDA0003402630810000087
the number of dominant and recessive infectors within the basal assessment unit l on day t, respectively;
beta is the effective infection rate of the dominant infected person (average number of infectious persons per day of the dominant infected person);
delta is the conversion rate from the latent period to the infectious period, and the value is the reciprocal of the latent period;
γ1the removal rate of the dominant infected person is the reciprocal of the infection period of the dominant infected person;
γ0the removal rate of a recessive infected person is the reciprocal of the infection period of the recessive infected person;
epsilon represents the ratio of the effective infection rate of recessive to dominant infected persons;
σ is the proportion of dominant infected persons;
hijindicates the number of persons from basic evaluation units i to j, h, throughout the dayljIndicates the number of persons from basic evaluation units l to j, h, all dayijThe device is composed of two parts: when i ≠ j, hijFor the number of persons from basic assessment unit i to j all day, when i ═ j, hijThe number of people who do not leave the grid all day, on the basis of the number, hijEach row of the matrix is normalized to ensure sigmajhij＝1,
Figure BDA0003402630810000088
∑lhljNlRepresenting the population number in the basic evaluation unit j when the population is mixed;
Figure BDA0003402630810000089
representing the number of infected persons in the basic evaluation unit j when mixed;
only beta is an unknown parameter in the model, and the beta estimation method is as follows:
1) taking different values of beta, operating a space-time transmission model of the infectious disease, and obtaining a corresponding daily newly-increased case quantity curve of the whole market;
2) estimating R0 from each daily new case curve using exponential growth, via R0 toolkit in R language, to obtain pairs of (β, R0) values;
3) and fitting the relation between the beta and the R0 to obtain the effective infection rate beta corresponding to the basic regeneration number R0 of the infectious disease.
Further, the specific process of simulating the space-time transmission condition of the infectious disease after the infectious disease is outbreak at different positions by using the infectious disease space-time transmission model is as follows:
determining the number of seeds initially placed in a single basic evaluation unit according to the research requirement;
for a certain basic evaluation unit, if the total population of the basic evaluation unit is smaller than the seed number, directly setting the seed number placed in the basic evaluation unit as the total population of the basic evaluation unit, otherwise, setting the seed number placed in the basic evaluation unit as the seed number, then performing propagation simulation, and recording the propagation condition of each day; and traversing all basic evaluation units in the infectious disease space-time transmission model, counting all simulation results, and obtaining the disease transmission condition of each basic evaluation unit as an initial outbreak position.
Further, the quantitative evaluation index of the spatio-temporal propagation risk specifically includes:
index 1: the total infected population in the city on day d;
respectively counting the total number of infected persons in the whole market on the d day according to the simulation result of each basic evaluation unit as the basic evaluation unit for initially placing the seeds;
index 2: on day d, epidemic situation and the number of basic evaluation units are counted;
respectively counting the number of the total market epidemic situation and the number of the basic evaluation units on the d day for the simulation result of each basic evaluation unit as the basic evaluation unit for initially placing the seeds, and if the number of infected people in the basic evaluation unit is more than or equal to 1, determining that the basic evaluation unit is affected by the epidemic situation and counting the number of the infected people in the statistical range;
index 3: the spatial diffusion degree of epidemic situation on day d;
respectively counting the spatial diffusion degree of the full-market epidemic situation on the d day for the simulation result of each basic evaluation unit as the basic evaluation unit for initially placing the seeds; the calculation process of the spatial diffusion degree is as follows:
the position of the center of gravity of the infection is first calculated:
Figure BDA0003402630810000101
the degree of spatial diffusion is then calculated:
Figure BDA0003402630810000102
in the formula, N is the basic evaluation unit number.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention constructs an infectious disease space-time propagation model on the fine space granularity in a city, simulates the space-time propagation condition of the infectious disease after outbreak at different positions, and calculates the quantitative evaluation index of the space-time propagation risk of each basic evaluation unit so as to help show the space-time propagation risk of each basic evaluation unit more clearly, understand the mechanism of the infectious disease outbreak from bottom to top, help the government to make intervention and control measures with more foresight and space accuracy, and promote the application of the geographic information scientific theory and method in the public health field.
Drawings
The accompanying drawings are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.
FIG. 1 is a schematic diagram of the basic process of the present invention;
FIG. 2 is a graph showing the relationship between the effective infection rate β and the estimated value of R0;
FIG. 3 is a graph showing the results of 10,20,30 and 40 days of total infected population in the market, wherein (a) is day 10, (b) is day 20, (c) is day 30 and (d) is day 40;
FIG. 4 is a graph showing the results of epidemic and community numbers at days 10,20,30 and 40, wherein (a) is day 10, (b) is day 20, (c) is day 30 and (d) is day 40;
FIG. 5 is a graph showing the results of spatial spreading of epidemic situation at days 10,20,30 and 40, wherein (a) is day 10, (b) is day 20, (c) is day 30 and (d) is day 40.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Taking the SLIR model of COVID-19 with 649 communities in Shenzhen city as basic evaluation units as an example:
step 1: and constructing a space-time transmission model of the infectious disease.
The invention firstly needs to construct a space-time transmission model of the infectious diseases of the region to be researched.
Firstly, mobile phone positioning data is needed:
for the infectious disease space-time propagation model, a basic evaluation unit is planned according to research needs, and then mobile phone positioning data is processed into several types of data based on the basic evaluation unit for the infectious disease space-time propagation model.
Then, model expression form construction is carried out:
the Shenzhen city community is used as a basic evaluation unit for population division, and a population model based on susceptibility-Latent-infection-removal (SLIR) is constructed in consideration of the infection process of COVID-19.
And dividing the resident population in each basic evaluation unit into susceptible population, latent population, infection period population and removal population, wherein the infection period population comprises dominant infectors and latent infectors, only the infection period population is contagious, and the rest populations are not contagious.
Wherein, the latent period refers to the period from the invasion of pathogen into body to the occurrence of infectivity; the infection period refers to the period from infectivity to recovery, isolation or death, and has transmitting power. The population in the infection stage is divided into dominant infectors and recessive infectors, wherein the dominant infectors are attacked 1-2 days after entering the infection stage, which is 1.5 days in the embodiment. If the infection is not found in advance by means of close contact person tracking and the like, the dominant infected person is admitted and isolated about 6 days after the onset of disease in a natural state (referring to epidemic early data, corresponding to R0 ≈ 2.5), so that the infection period is about 1.5+6 days; the infection period for recessive infected persons is about 10 days.
Based on pathogenesis and transmission mechanism, a space-time transmission model of Infectious diseases of susceptibility-Latent-infection-removal (SLIR) is constructed as follows:
Figure BDA0003402630810000121
Figure BDA0003402630810000122
Figure BDA0003402630810000131
Figure BDA0003402630810000132
Figure BDA0003402630810000133
wherein the content of the first and second substances,
Figure BDA0003402630810000134
i.e. the total resident population in the community remains unchanged.
NlThe number of resident population of the basic evaluation unit l;
Si(t)、Li(t)、
Figure BDA0003402630810000135
and Ri(t) indicates the number of susceptible, occult, dominant infected, occult infected and removed persons within the basic evaluation unit i on day t, respectively (similarly,
Figure BDA0003402630810000136
and
Figure BDA0003402630810000137
the number of dominant and recessive infectors within the basal assessment unit l on day t), respectively);
beta is the effective infection rate of the dominant infected person, namely the average number of infectious people per day of a dominant infected person;
delta is the conversion rate from the latent period to the infection period, and the value is the reciprocal of the latent period, and the latent period is taken for 4.7 days in the embodiment;
γ1the removal rate of the dominant infected person is the reciprocal of the infection period of the dominant infected person, the infection period of the dominant infected person is reported according to the initial epidemic situation, and the period is taken for 7.5 days in the embodiment;
γ0the removal rate of the recessive infectors is the reciprocal of the infection period of the recessive infectors, and the infection period of the recessive infectors is 10 days in the embodiment;
epsilon represents the ratio of the effective infection rate of recessive infectors to dominant infectors, and the example is 0.12 by referring to the national CDC report;
σ is the proportion of dominant infected persons, and 75% is taken in the example;
hijrepresenting the number of persons from basic assessment Unit i to j throughout the day (similarly, h)ljRepresenting the number of people from basic assessment unit l to j throughout the day), consists of two parts: when i ≠ j, hijFor the number of persons from basic assessment unit i to j all day, when i ═ j, hijThe number of people who did not leave the grid throughout the day. On the basis, for hijEach row of the matrix is normalized to ensure sigmajhij＝1,
Figure BDA0003402630810000138
∑lhljNlRepresenting the population in the basic evaluation unit j when the population is mixed (i.e. resident who resides in the unit including the unit and other units);
Figure BDA0003402630810000141
representing the number of infected persons in the basic evaluation unit j when mixed;
the effective infection rate beta is calculated by the following method: a certain number of seed cases are given (the positions of the seed cases can be set according to population distribution), different values are taken for beta, the corresponding daily new curves are simulated, R0 is estimated from each daily new curve through an R0 toolkit of R language and by using an Exponential growth method (EG), and then the relation between beta and R0 is fitted to obtain the effective infection rate beta corresponding to the basic regeneration number R0 of COVID-19 which is approximately equal to 2.5. In the embodiment, given different effective infection rates β, 200 initial seed cases are set, and different daily new growth curves in Shenzhen city are obtained through simulation of the urban internal infectious disease spatio-temporal diffusion model, so as to estimate corresponding R0. FIG. 2 shows the relationship between the effective infection rate β and the estimated value of R0; given R0 equal to 2.5, the corresponding effective infection rate β value is obtained.
The spatiotemporal propagation model of infectious disease of this step includes, but is not limited to, the SLIR model exemplified herein, and other kinds of spatiotemporal propagation models of infectious disease constructed using other means or data sets are also possible. After the model of spatio-temporal transmission of infectious diseases is constructed, a transmission simulation of step 2 may be performed.
Step 2: simulating the space-time transmission condition of infectious diseases after outbreak at different positions.
After the infectious disease space-time propagation model is built, in order to specifically calculate the propagation risk of each community subsequently, a propagation model is used for simulating the space-time propagation condition of infectious diseases after outbreaks at all different positions, and the method comprises the following specific steps:
(1) the number of seeds initially placed in a single community is determined according to the research needs, and 30 initially infected seeds are taken in the embodiment.
(2) For a certain community, if the total population of the community is smaller than the number of the seeds, the number of the seeds placed in the community is directly set as the total population of the community, otherwise, the number of the seeds placed in the community is set as the number of the seeds determined in the step (1), for example, seeds are directly scattered according to the population of the community such as a Roc and a community where few people live in a plateau (the number of the people live is less than 30), and the number of the seeds determined in the interior communities such as the Nanshan Futian is set as the number of 30. And then carrying out propagation simulation, and recording the propagation condition of each day. The number of days for the specific simulation can be adjusted according to the research needs, and 40 days are simulated in the embodiment.
(3) The simulation described in (2) is performed separately for all communities in the model, as initial outbreak locations.
(4) And after all communities are traversed and simulated once, counting all simulation results to obtain the disease transmission condition of each community as an initial outbreak position.
And step 3: and calculating a space-time propagation risk quantitative evaluation index.
In order to quantitatively evaluate the space-time transmission risk of the infectious disease caused by the initial outbreak position, all simulation results in the step 2 are processed into the following 3 space-time transmission risk quantitative evaluation indexes:
index 1: cumulative infected persons in the whole market at day d (10, 20,30 and 40 days in the embodiment)
For the simulation results of each community as the community for initially placing the seeds, the total infected population in the whole market on the day d is counted respectively.
Index 2: epidemic situation spread on day d and the number of communities (10, 20,30,40 days in this example)
And respectively counting the total market epidemic situation and the number of communities on the d day according to the simulation result of each community as the community for initially placing the seeds. Because the SLIR model is a differential equation set model, the number of the infected persons possibly existing in the community is not an integer, so the community is defined as being considered to be affected by the epidemic situation if the number of the infected persons in the community is more than or equal to 1, and the calculation is carried out in the statistical category.
Index 3: spatial spreading degree of epidemic on day d (10, 20,30,40 days in this example)
And respectively counting the spatial diffusion degree of the full-market epidemic situation on the day d for the simulation result of each community as the community for initially placing the seeds.
For the degree of spatial diffusion, the invention uses a concept similar to the second-order center distance, and takes the number of infected persons in each community as a weight to calculate the average value of the square distance from the center of each community to the infected center.
The position of the center of gravity of the infection is first calculated:
Figure BDA0003402630810000161
the degree of spatial diffusion is then calculated:
Figure BDA0003402630810000162
fig. 3, 4 and 5 show the specific results of the calculation of the 3 indexes at days 10,20,30 and 40 in this example.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: although the present invention has been described in detail with reference to the above embodiments, those skilled in the art will appreciate that various changes, modifications and equivalents can be made in the embodiments of the invention without departing from the scope of the invention as defined by the appended claims.

Claims (10)

1. The quantitative evaluation method for the spatiotemporal transmission risk of the infectious disease at the initial outbreak position is characterized by comprising the following steps:
simulating the space-time transmission condition of the infectious disease after outbreak at different positions by using an infectious disease space-time transmission model to obtain a simulation result;
and processing the simulation result into a space-time propagation risk quantitative evaluation index.
2. The quantitative evaluation method for the spatiotemporal infectious disease transmission risk at the initial outbreak position according to claim 1, wherein the construction process of the spatiotemporal infectious disease transmission model is specifically as follows:
firstly, defining a basic evaluation unit, and then processing the mobile phone positioning data into a plurality of types of data based on the basic evaluation unit, wherein the plurality of types of data based on the basic evaluation unit comprise: the number of resident population of each basic evaluation unit, the number of daily out population of each basic evaluation unit and the population flow among the basic evaluation units;
and constructing an infectious disease space-time transmission model based on susceptibility-latent-infection-removal according to several types of data based on a basic evaluation unit.
3. The quantitative evaluation method for the spatiotemporal infectious disease transmission risk at the initial outbreak position according to claim 2, wherein the model construction of the spatiotemporal infectious disease transmission based on susceptibility-stealth-infection-removal is specifically as follows:
dividing the resident population in each basic evaluation unit into susceptible population, latent population, infected population and removed population, wherein the infected population comprises dominant infectors and latent infectors;
based on pathogenesis and transmission mechanism, a space-time transmission model of infectious diseases which are susceptible, latent, infected and removed is constructed as follows:
Figure FDA0003402630800000011
Figure FDA0003402630800000012
Figure FDA0003402630800000021
Figure FDA0003402630800000022
Figure FDA0003402630800000023
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003402630800000024
Nlthe number of resident population of the basic evaluation unit l;
Si(t)、Li(t)、
Figure FDA0003402630800000025
and Ri(t) the number of susceptible, occult, dominant infected, occult infected and removed persons within the basic evaluation unit i on day t, respectively,
Figure FDA0003402630800000026
and
Figure FDA0003402630800000027
respectively, the basic evaluation unit on day tThe number of dominant and recessive infectors within l;
beta is the effective infection rate of a dominant infected person;
delta is the conversion rate from the latent period to the infectious period, and the value is the reciprocal of the latent period;
γ1the removal rate of the dominant infected person is the reciprocal of the infection period of the dominant infected person;
γ0the removal rate of a recessive infected person is the reciprocal of the infection period of the recessive infected person;
epsilon represents the ratio of the effective infection rate of recessive to dominant infected persons;
σ is the proportion of dominant infected persons;
hijindicates the number of persons from basic evaluation units i to j, h, throughout the dayljIndicates the number of persons from basic evaluation units l to j, h, all dayijThe device is composed of two parts: when i ≠ j, hijFor the number of persons from basic assessment unit i to j all day, when i ═ j, hijThe number of persons who did not leave the basic evaluation unit all day, on the basis of which h is calculatedijEach row of the matrix is normalized to ensure
Figure FDA0003402630800000028
∑lhljNlRepresenting the population number in the basic evaluation unit j when the population is mixed;
Figure FDA0003402630800000029
representing the number of infected persons in the basic evaluation unit j when mixed;
only beta is an unknown parameter in the model, and the beta estimation method is as follows:
1) taking different values of beta, operating a space-time transmission model of the infectious disease, and obtaining a corresponding daily newly-increased case quantity curve of the whole market;
2) estimating R0 from each daily new case curve using exponential growth, via R0 toolkit in R language, to obtain pairs of (β, R0) values;
3) and fitting the relation between the beta and the R0 to obtain the effective infection rate beta corresponding to the basic regeneration number R0 of the infectious disease.
4. The quantitative assessment method for the spatiotemporal transmission risk of infectious diseases caused by the initial outbreak position according to claim 1, wherein the simulation of the spatiotemporal transmission situation of infectious diseases after the outbreak at different positions by using the infectious disease spatiotemporal transmission model comprises the following specific processes:
setting the number of seeds initially placed in a single basic evaluation unit;
for a certain basic evaluation unit, if the total population of the basic evaluation unit is smaller than the seed number, directly setting the seed number placed in the basic evaluation unit as the total population of the basic evaluation unit, otherwise, setting the seed number placed in the basic evaluation unit as the seed number, then performing propagation simulation, and recording the propagation condition of each day; and traversing all basic evaluation units in the infectious disease space-time transmission model, counting all simulation results, and obtaining the disease transmission condition of each basic evaluation unit as an initial outbreak position.
5. The quantitative assessment method for spatiotemporal transmission risk of infectious diseases at initial outbreak location according to claim 1, wherein the quantitative assessment index for spatiotemporal transmission risk specifically comprises:
index 1: the total infected population in the city on day d;
respectively counting the total number of infected persons in the whole market on the d day according to the simulation result of each basic evaluation unit as the basic evaluation unit for initially placing the seeds;
index 2: on day d, epidemic situation and the number of basic evaluation units are counted;
respectively counting the number of the whole-market epidemic situation and the number of the basic evaluation units on the d day for the simulation result of each basic evaluation unit as the basic evaluation unit for initially placing the seeds, and if the number of infected persons in the basic evaluation unit is more than or equal to 1, determining that the basic evaluation unit is affected by the epidemic situation and counting the number of the infected persons in the statistical range;
index 3: the spatial diffusion degree of epidemic situation on day d;
and respectively counting the spatial diffusion degree of the full-market epidemic situation on the d day according to the simulation result of each basic evaluation unit as the basic evaluation unit for initially placing the seeds.
6. The method of claim 5, wherein the calculation of the spatial spread degree is as follows:
the position of the center of gravity of the infection is first calculated:
Figure FDA0003402630800000041
the degree of spatial diffusion is then calculated:
Figure FDA0003402630800000042
in the formula, N is the number of basic evaluation units.
7. The quantitative evaluation system for the spatiotemporal spread risk of the infectious disease at the initial outbreak position is characterized by comprising a simulation module and an evaluation module, wherein:
a simulation module: the method is used for simulating the space-time transmission condition of the infectious disease after the infectious disease is outbreak at different positions by utilizing the infectious disease space-time transmission model to obtain a simulation result;
an evaluation module: and the method is used for processing the simulation result into a space-time propagation risk quantitative evaluation index.
8. The system for quantitatively evaluating the spatiotemporal transmission risk of infectious disease caused by an initial outbreak position according to claim 7, wherein the process of constructing the spatiotemporal transmission model of infectious disease is specifically as follows:
firstly, defining a basic evaluation unit, and then processing the mobile phone positioning data into a plurality of types of data based on the basic evaluation unit, wherein the plurality of types of data based on the basic evaluation unit comprise: the number of resident population of each basic evaluation unit, the number of daily out population of each basic evaluation unit and the population flow among the basic evaluation units;
constructing an infectious disease space-time propagation model based on susceptibility-occult-infection-removal according to a plurality of types of data based on a basic evaluation unit, wherein the infectious disease space-time propagation model based on susceptibility-occult-infection-removal is specifically constructed as follows:
dividing the resident population in each basic evaluation unit into susceptible population, latent population, infected population and removed population, wherein the infected population comprises dominant infectors and latent infectors;
based on pathogenesis and transmission mechanism, a space-time transmission model of infectious diseases which are susceptible, latent, infected and removed is constructed as follows:
Figure FDA0003402630800000051
Figure FDA0003402630800000052
Figure FDA0003402630800000053
Figure FDA0003402630800000054
Figure FDA0003402630800000055
wherein the content of the first and second substances,
Figure FDA0003402630800000056
Nlthe number of resident population of the basic evaluation unit l;
Si(t)、Li(t)、
Figure FDA0003402630800000057
and Ri(t) the number of susceptible, occult, dominant infected, occult infected and removed persons within the basic evaluation unit i on day t, respectively,
Figure FDA0003402630800000058
and
Figure FDA0003402630800000059
the number of dominant and recessive infectors within the basal assessment unit l on day t, respectively;
beta is the effective infection rate of a dominant infected person;
delta is the conversion rate from the latent period to the infectious period, and the value is the reciprocal of the latent period;
γ1the removal rate of the dominant infected person is the reciprocal of the infection period of the dominant infected person;
γ0the removal rate of a recessive infected person is the reciprocal of the infection period of the recessive infected person;
epsilon represents the ratio of the effective infection rate of recessive to dominant infected persons;
σ is the proportion of dominant infected persons;
hijindicates the number of persons from basic evaluation units i to j, h, throughout the dayljIndicates the number of persons from basic evaluation units l to j, h, throughout the dayijThe device is composed of two parts: when i ≠ j, hijFor the number of persons from basic assessment unit i to j all day, when i ═ j, hijThe number of persons who did not leave the basic evaluation unit all day, on the basis of which h is calculatedijEach row of the matrix is normalized to ensure
Figure FDA0003402630800000061
∑lhljNlRepresenting the population number in the basic evaluation unit j when the population is mixed;
Figure FDA0003402630800000062
representing the number of infected persons in the basic evaluation unit j when mixed;
only beta is an unknown parameter in the model, and the beta estimation method is as follows:
1) taking different values of beta, operating a space-time transmission model of the infectious disease, and obtaining a corresponding daily newly-increased case quantity curve of the whole market;
2) estimating R0 from each daily new case curve using exponential growth, via R0 toolkit in R language, to obtain pairs of (β, R0) values;
3) and fitting the relation between the beta and the R0 to obtain the effective infection rate beta corresponding to the basic regeneration number R0 of the infectious disease.
9. The quantitative evaluation system for spatiotemporal transmission of infectious disease at initial outbreak location according to claim 7, wherein the simulation of the spatiotemporal transmission of infectious disease after outbreak at different locations by the spatiotemporal transmission model of infectious disease comprises the following steps:
setting the number of seeds initially placed in a single basic evaluation unit;
for a certain basic evaluation unit, if the total population of the basic evaluation unit is smaller than the seed number, directly setting the seed number placed in the basic evaluation unit as the total population of the basic evaluation unit, otherwise, setting the seed number placed in the basic evaluation unit as the seed number, then performing propagation simulation, and recording the propagation condition of each day; and traversing all basic evaluation units in the infectious disease space-time transmission model, counting all simulation results, and obtaining the disease transmission condition of each basic evaluation unit as an initial outbreak position.
10. The quantitative evaluation system for spatiotemporal propagation risk of infectious diseases at initial outbreak location according to claim 7, wherein the quantitative evaluation index for spatiotemporal propagation risk specifically comprises:
index 1: the total infected population in the city on day d;
respectively counting the total number of infected persons in the whole market on the d day according to the simulation result of each basic evaluation unit as the basic evaluation unit for initially placing the seeds;
index 2: epidemic situation and number of basic evaluation units on day d;
respectively counting the number of the total market epidemic situation and the number of the basic evaluation units on the d day for the simulation result of each basic evaluation unit as the basic evaluation unit for initially placing the seeds, and if the number of infected people in the basic evaluation unit is more than or equal to 1, determining that the basic evaluation unit is affected by the epidemic situation and counting the number of the infected people in the statistical range;
index 3: the spatial diffusion degree of epidemic situation on day d;
respectively counting the spatial diffusion degree of the full-market epidemic situation on the d day for the simulation result of each basic evaluation unit as the basic evaluation unit for initially placing the seeds; the calculation process of the spatial diffusion degree is as follows:
the position of the center of gravity of the infection is first calculated:
Figure FDA0003402630800000071
the degree of spatial diffusion is then calculated:
Figure FDA0003402630800000072
in the formula, N is the basic evaluation unit number.
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