Early epidemic infection risk quantification method based on regional flow

Abstract

The invention belongs to the technical field of epidemic infection risk assessment, and provides an early epidemic infection risk quantification method based on regional flow. The method comprises the following steps of: 1) constructing a dynamic mobile traffic perception graph by using human mobility data to obtain the degree of association between a flow mode of each region constructed by a dynamic flow and other regions; 2) calculating an epidemic infection risk value caused by flow in the county area based on a spatial interaction function model SIF; 3) quantifying the influence of inter-county flow based on the inflow and outflow quantity of the county, and generating a county-level dynamic mobile flow perception graph to dynamically quantify the cross-county propagation risk; and 4) calculating an infection risk value of the studied county by integrating inter-county risk quantification and intra-county risk quantification. According to the method disclosed by the invention, the mobility in the region and cross-region is comprehensively considered, and the early epidemic infection risk of the region can be quickly and accurately quantified.

Description

Technical Field

[0001] The present invention belongs to the technical field of epidemic infection risk assessment, and in particular relates to an early epidemic infection risk quantification method based on regional flow. Background Art

[0002] Infectious diseases, such as the one caused by COVID-19, pose a serious threat to global public health and the economy. Such viruses can spread rapidly in cities through daily human activities and social interactions. In the face of such early epidemic infection prevention and control, it is crucial to accurately and effectively assess the disease risk level in each region.

[0003] Existing early epidemic infection risk prediction and assessment methods include using confirmed infection cases and death data, using proxy compartment models and other means to model the spread of infectious diseases. Such models can predict the virus concentration in a specific time and area, thereby assessing the risk level. However, they usually require a deep understanding of the disease and are therefore not suitable for emerging disease infections. Another type of method inputs data such as infection cases, deaths and cures into deep learning models to predict epidemic trends, population infection rates, and medical resource requirements. Considering that mechanistic data such as contact type, frequency and transmission probability are usually difficult to obtain, recent studies have begun to use human mobility data. For example, some researchers used human mobility data to identify potential transmission of Zika virus in Singapore and conducted a rational analysis (Rajarethinam J, Ong J, Lim SH, et al. Using human movement data to identify potential areas of Zika transmission: case study of the largest Zika cluster in Singapore [J]. International journal of environmental research and public health, 2019, 16 (5): 808.). Other researchers have found that the inherent spatial structure of urban mobility has an impact on the progression of the epidemic (Aguilar J, Bassolas A, Ghoshal G, et al. Impact of urban structure on infectious diseases prereading [J]. Scientific reports, 2022, 12 (1): 3816.). In Namibia, researchers used spatially explicit mobility risk networks to calculate annual HIV infection risks and identified high-risk areas for HIV transmission. However, there are two problems with such methods. First, these models are often static because they focus primarily on modeling and predicting the behavior of one type of virus, so they may not adapt well when the epidemic shifts to a new or different stage of transmission. Second, these models rely on large amounts of training data, which is often difficult to obtain in the early stages of an epidemic.

[0004] Therefore, how to effectively and accurately identify risk areas in the early stages of an epidemic remains an important and unresolved challenge. Summary of the invention

[0005] In view of this, the present invention proposes a new method for quantifying the infection risk of early epidemics based on regional mobility, which is specifically aimed at the early outbreak of epidemics. The method of the present invention pays special attention to two core factors: internal regional infection factors and cross-regional infection factors. The former is based on the observation that infectious diseases are mainly transmitted through interpersonal contact, so the infection risk of a region is closely related to the interpersonal interaction rate. The latter is inspired by some studies that have found that the mobility of people between regions can reveal the level of infection risk, and areas with higher mobility are often more susceptible to infectious diseases. In order to effectively adapt to the rapid changes of the virus and effectively intervene in the early stages of the epidemic, the method of the present invention allows the infection parameters in the model to be adjusted in real time to adapt to the changes of the virus. In addition, regardless of the size of the region, the method of the present invention can effectively identify high-risk areas, which fully demonstrates its wide applicability. Especially in the early outbreak stage when case data is limited and the virus transmission mechanism is unclear, the method of the present invention can quickly and accurately quantify the infection risk of the region and predict the future spread trend of the disease.

[0006] The present invention provides a method for quantifying early epidemic infection risk based on regional flow, which is characterized by comprising:

[0007] Step 1: Use human mobility data to construct a dynamic mobile traffic perception map to obtain a weight matrix W that records the degree of association between the flow pattern of each area constructed by the dynamic flow and other areas DFAG , wherein the human mobility data is an origin-end matrix (OD matrix) of human mobility;

[0008] Step 2: Calculate the epidemic infection risk value caused by the flow within the county based on the spatial interaction function model SIF, where the infection risk value caused by the flow within the county i in time period t is calculated using the following formula:

[0009]

[0010] Among them, Z ii represents the number of individuals who stay in county i during time period t, and Z ba and Z ab They represent the number of individuals that migrated from area a to area b and from area b to area a in time period t, respectively;

[0011] Step 3: Quantify the impact of inter-county mobility based on the inflow and outflow numbers of counties, and generate a county-level dynamic mobile traffic perception map to dynamically quantify the risk of cross-county transmission, where the cross-county mobility risk value of county i in time period t is obtained by the following formula:

[0012]

[0013] Among them, WDFAG (i, j) is the weight matrix of the degree of association between the flow pattern of county i and county j constructed by the dynamic flow, Z ji represents the number of people who moved from county j to county i during time period t, while Z ij represents the number of people who migrated from county i to county j during time period t;

[0014] Step 4: Calculate the infection risk value of the studied county by integrating the inter-county risk quantification with the intra-county risk quantification. Normalize each risk value by dividing it by the maximum value of all counties and time periods. Then weight the inter-county and intra-regional risk values ​​by their respective weights to obtain the risk value of county i. As shown in the following formula:

[0015] Furthermore, in step 1, assuming that there are N regions, for each region i, the daily inflow data Z from it to all other regions is d The vector regarded as the dth day Right now Where d∈[1,D], the daily flow pattern information of each area is obtained by calculating the size of the flow vector, that is, the daily inflow data pattern from area i to all other areas j in the time interval D:

[0016]

[0017] In this equation, P n represents the probability distribution obtained from the vector sequence, which indicates the proportion of people flowing from area i to area j on day d;

[0018] Then the dot product similarity between the crowd flow vectors is used as the cost function,

[0019]

[0020] Incorporating the above formula into the calculation of Wasserstein distance, we obtain a metric called dynamic flow-aware distance, which is used to measure the flow difference between regions; calculate the flow-aware distance between region i and region j on day d:

[0021]

[0022] The weight matrix W is obtained by applying the formula to calculate the Wasserstein distance for the OD matrix of each small census area: DFAG , where W DFAG [i,j]=d DFAG ∈[0,1], the weight matrix records the degree of correlation between the flow pattern of each area constructed by the dynamic flow and other areas.

[0023] Furthermore, in step 2, using SIF t To represent the SIF at time t, its mathematical expression is as follows:

[0024]

[0025] Among them, D ab represents the basic connectivity between or within regions; λ represents the scaling parameter; γ is a parameter used to determine the weight of the tail of the function; P t It represents the proportion of the number of people flowing within the small-scale census area to the total inflow and outflow of the area during time period t.

[0026] Furthermore, the early epidemic infection risk quantification method of the present invention also includes a risk superposition module for quantifying the impact of historical risk values ​​on regional risk values, wherein when calculating time t, the risk value from historical time 0 to time t-1 is included in the calculation, as shown in the following formula:

[0027]

[0028] in, It represents the superposition of risk values ​​of county i from historical time 0 to t-1, and β represents the transmission probability of virus infection, which is adjusted according to the diverse and dynamic virus situation.

[0029] Compared with the prior art, the present invention has the following advantages:

[0030] 1. This invention proposes a new method that can effectively quantify the infection risk level in a given geographical area without having in-depth knowledge of the details of the infectious disease or virus transmission.

[0031] 2. The method of the present invention integrates analysis at multiple geographic granularities and comprehensively considers the liquidity within and across regions to accurately quantify the risk level.

[0032] 3. The inventors evaluated the method of the present invention based on actual COVID-19 data in four US states. The results showed that the method of the present invention showed excellent results in both short-term, medium-term and long-term risk quantification schemes. The risk quantification method of the present invention showed high performance in all time categories and overall accuracy. DETAILED DESCRIPTION

[0033] The present invention will be further described below with reference to specific embodiments, but the present invention is not limited thereto.

[0034] In order to more clearly describe the present invention, the following definitions are provided.

[0035] Definition - Census Community and County: The regions involved in the present invention are mainly divided into two types: small census areas and county census areas. The difference between small census areas and counties is that they have different levels of geographic granularity. Small census areas are smaller areas with a population range of about 3,000 to 5,000 people, while counties are larger areas based on counties. In the present invention, "small census areas" are used as a geographical unit one level smaller than "counties".

[0036] Definition 2: Region location graph: These regions are modeled as a directed graph Where V represents the set of small census areas, E represents the set of edges, and W represents the edge weights of the graph. The weight of each edge is not calculated based solely on the geographical distance between different areas. Instead, it is determined by considering the geographical distance and the frequency of interaction between areas. This will be discussed in the model structure and algorithm design.

[0037] Definition 3: Areas with pandemic infection risk: During a certain period [t f ,t p ], the risk of infection of an infectious disease R d =[t p ,t f ] is defined as the number of new cases N in a region d d The sum of (t), where the calculation method is If at some future time t f , the number of new cases in region d is relatively high, and d can be designated as the region with the highest number of new cases in period [t p ,t f ] The specific method of determining high-risk counties will be elaborated in detail below. It should be noted here that N d (t) quantification and period [t p ,t f ] settings may vary depending on various factors such as actual conditions and epidemic forecasts, which will be discussed below.

[0038] The goal of the present invention is to extract historical flow data from each county. Start with input into the infection risk quantification model In order to predict the infection risk value of each county at a given time point, that is, the infectious disease vulnerability of each county, the spatiotemporal risk area can be quantified.

[0039] Specifically, suppose we expect to predict the pandemic risk value of a disease in county n at time T+t, denoted as R n (T+t), we can get the following expression:

[0040]

[0041] Unlike methods that rely on historical infection data, the regional flow-based early epidemic infection risk quantification method of the present invention can quickly and accurately quantify regional virus infection risks and predict future trends in disease transmission. The entire method consists of four main modules: (1) Dynamic mobile traffic perception map: It uses a data-driven approach to discover differences in flow patterns between different regions and measure the spatial heterogeneity of risk transmission. (2) Intra-district factor modeling: Based on a social interaction model, it measures the epidemic transmission risk caused by intra-county mobility and uses this information to estimate the probability of virus transmission. (3) Inter-district factor modeling: Considering the interaction between counties, it measures the extent to which epidemic transmission is affected by distance. (4) Intra-district-interval comprehensive risk quantification: By integrating intra-district factor modeling and interval factor modeling, the infection risk values ​​of all small-scale census areas in the study county are calculated.

[0042] Next, the early epidemic infection risk quantification method based on regional flow of the present invention will be described in detail.

[0043] Construction of dynamic mobile traffic-aware graph

[0044] In this section, we discuss how to use human mobility data to construct epidemic risk weight maps. We propose a data-driven approach called Dynamic Flow-Aware Graph (DFAG), which uses the origin-destination (OD) matrix of human mobility to determine the spatial correlation between regions. We construct epidemic risk weight maps from mobility data to capture the trend of epidemic spread and identify high-risk areas.

[0045] Specifically, by analyzing the daily origin-destination (OD) data flows between regions, the Wasserstein distance is used to capture the similarity of the probability distribution of small-scale census tract movements, which represents the dynamic spatial dependence between small-scale census tracts. This method of measuring the similarity of human flow patterns can better understand the trend of virus transmission. For example, if two regions have a large number of people moving to high-risk areas, then this movement pattern may increase their likelihood of contracting the virus.

[0046] Assume there are N regions, for each region i, we can calculate the daily inflow data Z from it to all other regions. d The vector regarded as the dth day Right now where d∈[1,D]. The daily flow pattern information of each area is obtained by calculating the size of the flow vector, that is, the daily inflow data pattern from area i to all other areas j in the time interval D.

[0047]

[0048] In this equation, P n Represents the probability distribution obtained from the vector sequence, which indicates the proportion of people flowing from area i to area j on the dth day.

[0049] Then we need to get the conversion cost of each probability mass. We use the dot product similarity between the flow vectors as the cost function.

[0050]

[0051] Incorporating the above formula into the calculation of Wasserstein distance, we can get a metric called dynamic flow-aware distance, which is used to measure the flow difference between regions. Then we can calculate the flow-aware distance between region i and region j on day d.

[0052]

[0053] By applying the formula to calculate the Wasserstein distance for the OD matrix of each small census area, a weight matrix W can be obtained. DFAG , where W DFAG [i,j]=d DFAG ∈[0,1]. This matrix records the degree of correlation between the flow pattern of each area constructed by the dynamic flow and other areas, that is, the degree of correlation between residents with the same flow pattern and other areas.

[0054] Internal modeling of counties based on social interaction model

[0055] Intra-regional mobility plays an important role in the spread of infectious diseases. Especially within counties composed of multiple small census tracts, this inter-regional interaction can be used to vividly describe the flow within the region, thereby parsing out one of the main drivers of virus transmission. To quantify this effect, a dynamic mobility flow-aware map (DFAG) was generated at the small census tract level using the above formula. However, it is also important to note that infectious disease outbreaks may occur at a finer geographic scale. Obtaining such fine-grained data may be difficult due to privacy and other issues. Therefore, we turned to other measurement methods to assess risk at a finer geographic level.

[0056] In the present invention, the spatial interaction function model (SIF) is used, which is a model based on small census areas, to describe the probability of any two small census areas in a county being connected (i.e., in contact) at a given distance. t To represent the SIF at time t, its mathematical expression is as follows.

[0057]

[0058] Among them, D ab represents the basic connectivity between or within regions, and can be interpreted as the probability of face-to-face contact between or within two regions. λ represents a scaling parameter that defines the phenomenological distance unit of the probability decay, and γ is a parameter that determines the weight of the tail of the function (higher values ​​indicate less long-range connections, etc.).

[0059] Taking the small-scale census area as the smallest spatial analysis unit, the spatial interaction function model is used to evaluate the infection risk associated with internal mobility in the small-scale census area. Here, SIF stands for the regional internal infection model, and P t It represents the proportion of the number of people moving within the small-scale census area in time period t to the total number of people flowing in and out of the area. The model parameters are fixed at $λ2=0.035 and γ2=6. Finally, the infection risk value generated by the internal flow of county i in time period t is calculated using the following formula:

[0060]

[0061] Among them, Z ii represents the number of individuals who stay in county i during time period t, and Z ba and Z ab They represent the number of individuals migrating from area a to area b and from area b to area a during time period t.

[0062] Modeling interactions between counties

[0063] The spread of infectious diseases is influenced by a complex interaction of multiple factors, such as lifestyle, economic conditions, and transportation, which are transmitted across different geographical regions. Therefore, in addition to the possibility of infection caused by intra-regional mobility, the cross-county population mobility pattern also constitutes a key mechanism for disease transmission. The goal here is to effectively capture this mobility pattern to reveal the inherent mechanism of disease transmission and provide a basis for prevention and control strategies.

[0064] In the cross-county infection risk quantification map, the focus is on the infection risk caused by cross-county migration at the county level. This infection risk is mainly related to the risk propagation correlation of inflows and outflows between counties. The number of inflows and outflows in each county is used to quantify the impact of inter-county flows, and a county-level dynamic mobile flow-aware map (DFAG) is generated using the previous formula to dynamically quantify the risk propagation correlation.

[0065] In this figure, the cross-county mobility risk of county i in time period t can be obtained by the following formula:

[0066]

[0067] Among them, W DFAG (i, j) is the weight matrix of the degree of association between the flow pattern of county i and county j constructed by the dynamic flow, Z ji represents the number of people who moved from county j to county i during time period t, while Z ij Represents the number of people who moved from county i to county j during time period t.

[0068] Integration of inter-county risk quantification and intra-county risk quantification

[0069] As described above, a quantitative model is used to evaluate the risk values ​​from inter-county and intra-county flows to measure the risk values ​​of counties. Then, assuming that the risks generated by these two flows are equivalent in disease transmission, they are weighted and summed. This is consistent with the mechanism of disease transmission, that is, the probability of disease transmission does not change due to different modes and scales of movement. First, each risk value is normalized by dividing it by the maximum value of all counties and time periods, and then the inter-county and intra-regional risk values ​​are weighted by their respective weights to obtain the risk value of county i at time t Finally, by summing the two weighted risk values, the risk value of county i is obtained, as shown in the following formula:

[0070]

[0071] In addition, the inventors referred to the transmission mechanism of the disease and found that most diseases have an incubation period. During this period, although the patient is asymptomatic, they are contagious. Therefore, the risks generated in the past region may persist in the future risk value. This impact is affected by the virus itself. In order to simulate the actual epidemic situation spread through flow, the inventors designed a risk superposition module to quantify the impact of historical risk values ​​on regional risk values. Specifically, when calculating time t, the risk value from historical time 0 to time t-1 also needs to be included in the calculation, as shown in the following formula:

[0072]

[0073] in, It represents the superposition of risk values ​​of county i from historical time 0 to t-1, and β represents the probability of spread of virus infection, which can be adjusted according to the diverse and dynamic virus situation.

[0074] Through the quantitative method of the present invention, a continuous and dynamic epidemic spread risk value R within the study area is obtained. i .

[0075] The above is only a preferred embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of various equivalent modifications or substitutions within the technical scope disclosed by the present invention, and these modifications or substitutions should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for quantifying early epidemic infection risk based on regional mobility, characterized in that: include: Step 1: Use human mobility data to construct a dynamic mobile traffic perception map to obtain a weight matrix W that records the degree of association between the flow pattern of each area constructed by the dynamic flow and other areas DFAG , wherein the human mobility data is a start-end matrix of human mobility; Step 2: Calculate the epidemic infection risk value caused by the flow within the county based on the spatial interaction function model SIF, where the infection risk value caused by the flow within the county i in time period t is calculated using the following formula: Among them, Z ii represents the number of individuals who stay in county i during time period t, and Z ba and Z ab They represent the number of individuals that migrated from area a to area b and from area b to area a in time period t, respectively; Step 3: Quantify the impact of inter-county mobility based on the inflow and outflow numbers of counties, and generate a county-level dynamic mobile traffic perception map to dynamically quantify the risk of cross-county transmission, where the cross-county mobility risk value of county i in time period t is obtained by the following formula: Among them, W DFAG (i, j) is the weight matrix of the degree of association between the flow pattern of county i and county j constructed by dynamic flow, Z ji represents the number of people who moved from county j to county i during time period t, while Z ij represents the number of people who migrated from county i to county j during time period t; Step 4: Calculate the infection risk value of the studied county by integrating the inter-county risk quantification with the intra-county risk quantification. Normalize each risk value by dividing it by the maximum value of all counties and time periods. Then weight the inter-county and intra-regional risk values ​​by their respective weights to obtain the risk value of county i. As shown in the following formula:

2. The method for quantifying the risk of early epidemic infection according to claim 1, characterized in that: In step 1, assuming there are N regions, for each region i, the daily inflow data Z from it to all other regions is d The vector regarded as the dth day Right now Where d∈[1,D], the daily flow pattern information of each area is obtained by calculating the size of the flow vector, that is, the daily inflow data pattern from area i to all other areas j in the time interval D: In this equation, P n represents the probability distribution obtained from the vector sequence, which indicates the proportion of people flowing from area i to area j on day d; Then the dot product similarity between the flow vectors is used as the cost function, Incorporating the above formula into the calculation of Wasserstein distance, we obtain a metric called dynamic flow-aware distance, which is used to measure the flow difference between regions; calculate the flow-aware distance between region i and region j on day d: The weight matrix W is obtained by applying the formula to calculate the Wasserstein distance for the origin-destination matrix of each small census area: DFAG , where W DFAG [i,j]=d DFAG ∈[0,1], the weight matrix records the degree of correlation between the flow pattern of each area constructed by the dynamic flow and other areas.

3. The method for quantifying the risk of early epidemic infection according to claim 1, characterized in that: In step 2, use SIF t To represent the SIF at time t, its mathematical expression is as follows: Among them, D ab represents the basic connectivity between or within regions; λ represents the scaling parameter; γ is a parameter used to determine the weight of the tail of the function; P t It represents the proportion of the number of people flowing within the small-scale census area to the total inflow and outflow of the area during time period t.

4. The method for quantifying the risk of early epidemic infection according to claim 1, characterized in that: It also includes a risk superposition module, which is used to quantify the impact of historical risk values ​​on regional risk values. When calculating time t, the risk value from historical time 0 to time t-1 is included in the calculation, as shown in the following formula: in, It represents the superposition of risk values ​​of county i from historical time 0 to t-1, and β represents the transmission probability of virus infection, which is adjusted according to the diverse and dynamic virus situation.

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