A method for epidemic spread intervention based on bipartite graph

Abstract

The present invention discloses a method for intervening in epidemic spread based on a bipartite graph, comprising: first, given the initial information of the network, constructing a multi-population network on the bipartite graph; second, initializing the infection ratio of the node according to the multi-population network on the bipartite graph; then, setting the intervention parameters according to different intervention strategies; then, performing the SIS epidemic spread process according to the multi-population network structure on the bipartite graph; and finally, calculating the proportion of infected individuals in the network when the statistics are stable. The intervention strategy based on the network structure implemented by the present invention can better control the spread of the epidemic.

Description

Technical Field

[0001] The present invention relates to the technical field of epidemic spread on multi-population networks, and in particular to an intervention strategy method for a multi-population epidemic spread model based on a bipartite graph in which individuals periodically travel back and forth between residences and public places. Background Art

[0002] In the field of epidemic spread technology on multi-population networks, several factors that affect the spread of epidemics are usually studied in order to formulate intervention strategies to control the spread of epidemics. The factors that affect the spread of epidemics mainly include: infection rate, migration rate, contact rate, population density, network structure, etc. Studies have shown that the multi-population epidemic model in which individuals periodically travel back and forth between their residences and public places is more in line with the commuting patterns of real individuals, and the infection rates of different populations are also significantly different.

[0003] In existing technologies, research on intervention strategies for epidemic spread mainly considers intervention strategies on networks with a single type of node, while ignoring the individual's mobility behavior patterns between residences and public places. For the bipartite graph structure composed of residences and public places, the impact of individual mobility behavior caused by the heterogeneity of the connection structure of public places is often ignored. Therefore, research on intervention strategies based on bipartite graph multi-population epidemic models has become a technical problem that needs to be solved urgently. Summary of the invention

[0004] In view of the defects of the prior art, the purpose of the present invention is to provide an epidemic spread intervention method based on bipartite graphs and analyze the effectiveness of intervention measures in epidemic spread. The method implements differentiated intervention measures according to the structural attributes of public places and residential areas, thereby controlling the spread of epidemics and providing guidance for future response to sudden epidemics.

[0005] The concept of the present invention is:

[0006] The present invention first constructs a multi-population network on a bipartite graph in which individuals periodically travel between their residence and public places; then sets corresponding intervention parameters according to different intervention strategies to carry out the SIS epidemic propagation process; when the proportion of infected individuals in the network reaches a stable state, the propagation process ends; finally, the proportion of infected individuals in the network is counted to complete the intervention in the epidemic.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] A bipartite graph-based epidemic transmission intervention method is applied to a multi-population epidemic transmission model in which individuals periodically travel between their residence and public places on a bipartite graph. The operation steps are as follows:

[0009] Step S1: Given the initial information of the network, construct a multi-population network on the bipartite graph;

[0010] Step S2: Initialize the infection ratio ρ0 of the node according to the multi-population network on the bipartite graph;

[0011] Step S3: setting intervention parameters according to different intervention strategies;

[0012] Step S4: According to the multi-population network structure on the bipartite graph, the susceptible-infected-susceptible (SIS) epidemic transmission process is carried out;

[0013] Step S5: The proportion of infected individuals in the network is statistically stable, and the intervention ends.

[0014] Preferably, in step S1, given the initial information of the network, a multi-population network on a bipartite graph is constructed, and the specific method steps are as follows:

[0015] Step S1.1: Given the number of residential nodes N r and the number of nodes in public places N p , and the degree of public places follows a given power law distribution: P(k p ) = k p -γ (γ=2.1);

[0016] Step S1.2: Randomly connect the residential nodes according to the degree of the public places and randomly assign a weight to each edge until all the public place node edges meet the initially assigned connection degree;

[0017] Step S1.3: Set the individual migration rate p, recovery rate μ, and initial infection rates of residence and public places to β r , β p , and β p =mβ r ,m>0, where m represents the ratio of the initial infection rate in the residential area to the initial infection rate in the public places, and the initial population distribution in the residential area The initial population distribution is divided into: initial distribution of homogeneous population and heterogeneous initial population distribution in Node R represents the place of residence i The total weight of .

[0018] Preferably, in step S3, intervention parameters are set according to different intervention strategies, and the specific method steps are as follows:

[0019] Change of residence intervention factor c r , public place intervention factor c p and intervention priority factors Get different intervention strategies:

[0020] 1) No intervention: c r =1,c p =1,

[0021] 2) Uniform intervention in the place of residence: 0 <c r <1,c p =1,

[0022] 3) Uniform intervention in public places: c r =1,0 <c p <1,

[0023] 4) Uneven intervention in public places: c r =1,0 <c p <1, in

[0024] 5) Uniform interference in residential and public places: 0 <c r <1,0 <c p <1,

[0025] 6) Uniform intervention in residential areas and uneven intervention in public places: 0 <c r <1,0 <c p <1, The average degree of nodes in public places

[0026] Preferably, in step S4, the SIS epidemic propagation process is performed according to the multi-population network structure on the bipartite graph, and the specific method steps are as follows:

[0027] Step S4.1: Assuming that the network starts to spread at time t, then the residence R at time t+1 i , i=1,2,...,N r The proportion of infected individuals is equal to the number of infected individuals who have not recovered and the number of infected susceptible individuals at time t, that is,

[0028] Step S4.2: Individuals in the residential area migrate to public places with probability p. According to the transfer matrix Determine the target public place, where the transfer matrix Node R represents the place of residence i With public place node P j Edge weights, Node R represents the place of residence i The total weight of

[0029] Step S4.3: Place of residence R i There are four types of situations in which individuals are infected: the probability of being infected at the place of residence during the day; the probability of being infected in a public place during the day; the probability of not being infected in a public place during the day but being infected at the place of residence at night; the probability of not being infected at the place of residence during the day but being infected at night;

[0030] Place of residence i ,i=1,2,...,N r The probability of an individual being infected is calculated as follows:

[0031] in, The individual has not left the place of residence R i Probability of being infected during the day: The individual has not left the place of residence R i Probability of being infected at night: For individuals leaving their place of residence to reach a public place P j Probability of infection:

[0032] Step S4.4: When the place of residence R i , i=1,2,...,N r When the infected individuals in the population reach a balance state, the population of the settlement R i The rate of change of the proportion of infected individuals in the time is 0, that is,

[0033] Step S4.5: In steady state, the residence R i The expression of the proportion of infected individuals in is

[0034] Step S4.6: According to the place of residence R in step S4.2 i , i=1,2,...,N r The probability of an individual being infected Calculate the proportion of infected individuals in the network If we use the form of eigenvector to express it, we get a new expression: And when i = k, otherwise

[0035] Compared with the prior art, the present invention has the following obvious outstanding substantive features and significant advantages:

[0036] 1. The method of the present invention takes into account the heterogeneity of infection rates in different public places and implements intervention strategies that depend on the structural attributes of public places.

[0037] 2. The multi-population epidemic propagation model on the bipartite graph constructed by the method of the present invention, in which individuals periodically travel between their residence and public places, is more consistent with the real network. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The drawings herein are incorporated into the specification and constitute a part of the specification, showing embodiments consistent with the present application, and together with the specification, are used to explain the principles of the present application. In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. The drawings in the above description are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0039] Figure 1 It is a flow chart of the research on epidemic propagation model on multi-population network of the present invention.

[0040] Figure 2 Schematic diagram of the "Susceptible-Infected-Susceptible" (SIS) transmission model in an embodiment of the present invention. DETAILED DESCRIPTION

[0041] In order to enable those skilled in the art to better understand the technical solutions in the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0042] In order to better understand the present invention, the embodiments of the present invention are explained in detail below with reference to the accompanying drawings.

[0043] Embodiment 1

[0044] See also Figure 1 , a bipartite graph-based epidemic transmission intervention method, applied to multi-population networks on bipartite graphs, the operation steps are as follows:

[0045] Step S1: Given the initial information of the network, construct a multi-population network on the bipartite graph, specifically including:

[0046] Step S1.1: Given the number of residential nodes N r and the number of nodes in public places N P, and the degree of public places follows a given power law distribution: P(k p ) = k p -γ (γ=2.1);

[0047] Step S1.2: Randomly connect the residential nodes according to the degree of the public places and randomly assign a weight to each edge, ranging from 1 to 50, until all the public place node edges meet the initially assigned connectivity;

[0048] Step S1.3: Set the individual migration rate p, recovery rate μ, and initial infection rates of residence and public places to β r , β p , and β p =mβ r , m>0, where m represents the ratio of the initial infection rate in the place of residence and in public places, and the initial population distribution in the place of residence The initial population distribution is divided into: initial distribution of homogeneous population and heterogeneous initial population distribution in Node R represents the place of residence i The total weight of

[0049] Step S2: Initialize the infection ratio ρ0 of the node according to the multi-population network on the bipartite graph;

[0050] Step S3: Setting relevant intervention parameters without intervention, including:

[0051] Let the residential intervention factor c r =1, public place intervention factor c p =1, and intervention priority factor Then the representative did not make any intervention at this time;

[0052] Step S4: According to the multi-population network structure on the bipartite graph, the SIS epidemic propagation process is carried out, such as Figure 2 As shown; having:

[0053] Step S4.1: The network starts to spread at time t, then the residence R at time t+1 i The proportion of infected individuals is equal to the number of infected individuals who have not recovered and the number of infected susceptible individuals at time t, that is,

[0054] Step S4.2: Place of residence R i ,i=1,2,...,N r Individuals in the area migrate to the public place with a migration probability p, according to the transfer matrix Determine the target public place Pj , j = 1, 2, ..., N p , where the transfer matrix Node R represents the place of residence i With public place node P j The weight of the connected edge, Node R represents the place of residence i The total weight of

[0055] Step S4.3: Place of residence R i The situations in which individuals are infected can be divided into four types: the probability of being infected at the residence during the day; the probability of being infected in public places during the day; the probability of not being infected in public places during the day but being infected at the residence at night; the probability of not being infected at the residence during the day but being infected at night; the probability of being infected at the residence R i ,i=1,2,...,N r The probability of an individual being infected is calculated as follows: in The individual has not left the place of residence R i Probability of being infected during the day: The individual has not left the place of residence R i Probability of being infected at night: For individuals leaving their place of residence to reach a public place P j ,j=1,2,...,N p Probability of infection:

[0056] Step S4.4: When the place of residence R i ,i=1,2,...,N r When the infected individuals in the network reach a balanced state, the rate of change of the proportion of infected individuals in the network over time is 0, that is,

[0057] Step S4.5: In steady state, the residence R i ,i=1,2,...,N r The expression of the proportion of infected individuals in is

[0058] Step S4.6: According to the place of residence R in step S4.2 i ,i=1,2,...,N r The probability that an individual in Calculate the proportion of infected individuals in the network If we use the form of eigenvector to express it, we get a new expression: And when i = k, otherwise

[0059] Step S5: The proportion of infected individuals in the network is statistically stable, and the intervention ends.

[0060] The method of this embodiment studies the impact of population distribution on the spread of epidemics by comparing the spread of epidemics under different initial population distributions.

[0061] Embodiment 2

[0062] This embodiment is basically the same as the above embodiment, with the following special features:

[0063] Step S1: This step is the same as that in Embodiment 1;

[0064] Step S2: This step is the same as that in Embodiment 1;

[0065] Step S3: Setting relevant intervention parameters for uniform intervention of the residential area; specifically including:

[0066] Let the residential intervention factor be 0 <c r <1, public place intervention factor c p =1, and intervention priority factor This represents a uniform intervention in the place of residence.

[0067] Step S4: This step is the same as that in Embodiment 1;

[0068] Step S5: This step is the same as that in the first embodiment.

[0069] The method of this embodiment controls the spread of the epidemic by uniformly intervening in the residential area. Compared with no intervention, this intervention strategy effectively reduces the steady-state infection rate and increases the transmission threshold.

[0070] Embodiment 3

[0071] This embodiment is basically the same as the above embodiment, with the following special features:

[0072] Step S1: This step is the same as that in Embodiment 1;

[0073] Step S2: This step is the same as that in Embodiment 1;

[0074] Step S3: Setting relevant intervention parameters for uniform intervention in public places; specifically including:

[0075] Let the residential intervention factor c r=1, public place intervention factor 0 <c p <1 and intervention priority factor This then represents a uniform intervention in public places.

[0076] Step S4: This step is the same as that in Embodiment 1;

[0077] Step S5: This step is the same as that in the first embodiment.

[0078] The method of this embodiment controls the spread of the epidemic by uniformly intervening in public places, and compares the effects of no intervention and uniform intervention in residential areas.

[0079] Embodiment 4

[0080] This embodiment is basically the same as the above embodiment, with the following special features:

[0081] Step S1: This step is the same as that in Embodiment 1;

[0082] Step S2: This step is the same as that in Embodiment 1;

[0083] Step S3: Setting relevant intervention parameters for non-uniform intervention in public places; specifically including:

[0084] Let the residential intervention factor c r =1, public place intervention factor 0 <c p <1, intervention priority factor The average degree of nodes in public places This then represents uneven intervention in public places.

[0085] Step S4: This step is the same as that in Embodiment 1;

[0086] Step S5: This step is the same as that in the first embodiment.

[0087] The method of this embodiment controls the spread of the epidemic by performing non-uniform intervention on public places, and compares the effect of uniform intervention on residential areas and public places respectively without intervention.

[0088] Embodiment 5

[0089] This embodiment is basically the same as the above embodiment, with the following special features:

[0090] Step S1: This step is the same as that in Embodiment 1;

[0091] Step S2: This step is the same as that in Embodiment 1;

[0092] Step S3: Setting relevant intervention parameters for uniform intervention in residential areas and public places simultaneously; specifically including:

[0093] Let the residential intervention factor be 0 <c r <1, public place intervention factor 0 <c p <1, and intervention priority factor This means that there is a simultaneous and uniform intervention in residential areas and public places.

[0094] Step S4: This step is the same as that in Embodiment 1;

[0095] Step S5: This step is the same as that in the first embodiment.

[0096] The method of this embodiment controls the spread of the epidemic by uniformly intervening in residential areas and public places at the same time, and compares the effects of no intervention and uniform intervention in residential areas and public places respectively.

[0097] Embodiment 6

[0098] This embodiment is basically the same as the above embodiment, with the following special features:

[0099] Step S1: This step is the same as that in Embodiment 1;

[0100] Step S2: This step is the same as that in Embodiment 1;

[0101] Step S3: Setting relevant intervention parameters for uniform intervention in residential areas and non-uniform intervention in public places; specifically including:

[0102] Let the residential intervention factor be 0 <c r <1, public place intervention factor 0 <c p <1, and intervention priority factor The average degree of nodes in public places This means uniform intervention in residential areas and uneven intervention in public places.

[0103] Step S4: This step is the same as that in Embodiment 1;

[0104] Step S5: This step is the same as that in the first embodiment.

[0105] The method of this embodiment controls the spread of the epidemic by uniformly intervening in residential areas and non-uniformly intervening in public places, and compares the effects of uniformly intervening in residential areas and public places with no intervention.

[0106] The above describes the embodiments of the present invention in conjunction with the accompanying drawings, but the present invention is not limited to the above embodiments. Various changes can be made according to the purpose of the invention. Any changes, modifications, substitutions, combinations or simplifications made according to the spirit and principle of the technical solution of the present invention should be equivalent replacement methods. As long as they meet the purpose of the invention and do not deviate from the technical principles and inventive concepts of the present invention, they belong to the protection scope of the present invention.

Claims

1. A method for intervening in epidemic spread based on bipartite graph, characterized by: The multi-population epidemic propagation model applied to a bipartite graph where individuals periodically travel between their residence and public places is as follows: Step S1: Given the initial information of the network, construct a multi-population network on the bipartite graph; Step S2: Initialize the infection ratio ρ0 of the node according to the multi-population network on the bipartite graph; Step S3: setting intervention parameters according to different intervention strategies; Step S4: According to the multi-population network structure on the bipartite graph, the susceptible-infected-susceptible (SIS) epidemic transmission process is carried out; Step S5: Count the proportion of infected individuals in the network when it is stable, and the intervention ends; In step S3, intervention parameters are set according to different intervention strategies. The specific method steps are as follows: Change of residence intervention factor c r , public place intervention factor c p and intervention priority factors Get different intervention strategies: 1) No intervention: c r =1,c p =1, 2) Uniform intervention in the place of residence: 0 <c r <1,c p =1, 3) Uniform intervention in public places: c r =1,0 <c p <1, 4) Uneven intervention in public places: c r =1,0 <c p <1, in 5) Uniform interference in residential and public places: 0 <c r <1,0 <c p <1, 6) Uniform intervention in residential areas and uneven intervention in public places: 0 <c r <1,0 <c p <1, The average degree of nodes in public places In step S4, the SIS epidemic propagation process is carried out according to the multi-population network structure on the bipartite graph. The specific method steps are as follows: Step S4.1: Assuming that the network starts to spread at time t, then the residence R at time t+1 i ,i=1,2,...,N r The proportion of infected individuals is equal to the number of infected individuals who have not recovered and the number of infected susceptible individuals at time t, that is, Step S4.2: Individuals in the residential area migrate to public places with probability p. According to the transfer matrix Determine the target public place, where the transfer matrix i=1,2,...,N r ,j=1,2,...,N p ; Node R represents the place of residence i With public place node P j Edge weights, Node R represents the place of residence i The total weight of Step S4.3: Place of residence R i There are four types of situations in which individuals are infected: the probability of being infected at the place of residence during the day; the probability of being infected in a public place during the day; the probability of not being infected in a public place during the day but being infected at the place of residence at night; the probability of not being infected at the place of residence during the day but being infected at night; Place of residence i ,i=1,2,...,N r The probability of an individual being infected is calculated as follows: in, The individual has not left the place of residence R i Probability of being infected during the day: The individual has not left the place of residence R i Probability of being infected at night: For individuals leaving their place of residence to reach a public place P j Probability of infection: j=1,2,...,N p ; Step S4.4: When the place of residence R i ,i=1,2,...,N r When the infected individuals in the population reach a balance state, the population of the settlement R i The rate of change of the proportion of infected individuals in the time is 0, that is, Step S4.5: In steady state, the residence R i The expression of the proportion of infected individuals in is i=1,2,...,N r ; Step S4.6: According to the place of residence R in step S4.2 i ,i=1,2,...,N r The probability of an individual being infected Calculate the proportion of infected individuals in the network If we use the form of eigenvector to express it, we get a new expression: And when i = k, otherwise 2. The method for intervening in epidemic spread based on bipartite graph according to claim 1, characterized in that: In step S1, given the initial information of the network, a multi-population network on a bipartite graph is constructed, and the specific method steps are as follows: Step S1.1: Given the number of residential nodes N r and the number of nodes in public places N p , and the degree of public places follows a given power law distribution: P(k p ) = k p -γ (γ=2.1); Step S1.2: Randomly connect the residential nodes according to the degree of the public places and randomly assign a weight to each edge until all the public place node edges meet the initially assigned connection degree; Step S1.3: Set the individual migration rate p, recovery rate μ, and initial infection rates of residence and public places to β r ,β p , and β p =mβ r ,m>0, where m represents the ratio of the initial infection rate in the residential area to the initial infection rate in the public places, and the initial population distribution in the residential area The initial population distribution is divided into: initial distribution of homogeneous population and heterogeneous initial population distribution i=1,2,...,N r ,in Node R represents the place of residence i The total weight of .

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