A method for digital contact tracing of supergraph transmitted disease spread

Abstract

This invention discloses a digital contact tracing method for infectious disease transmission on a hypergraph. It constructs an infectious disease transmission model with contact tracing on a hypergraph; maps the hypergraph to a factor graph, where hypervertices correspond to general nodes and hyperedges correspond to factor nodes, and constructs a redundant distribution generating function for general nodes and factor nodes; maps the scale of the infectious disease to the size of the giant connected components of the edge percolation on the factor graph, and predicts the transmission range and outbreak threshold of the infectious disease through percolation theory; finally, it randomly simulates the spread of an epidemic based on transmission parameters such as the infectious disease transmission rate, the average cardinality of hyperedges, and the carrier rate of individual contact tracing applications, predicting the performance of the contact tracing strategy. This invention extends the transmission scenario from one-to-one point-to-point interaction to higher-order interaction with collective behavior, enriching individual interaction modes and more closely resembling real-world transmission scenarios, thus facilitating a more accurate analysis of the impact of contact tracing on infectious disease transmission.

Description

Technical Field

[0001] This invention relates to the field of digital contact tracing technology, specifically a method for digital contact tracing of infectious disease transmission on a hypermap. Background Technology

[0002] Urbanization has brought about new lifestyles, such as subways, cinemas, and parties, making it easier for people to gather together. These gatherings are one of the main reasons for the emergence of super-spreading events. Against this backdrop, digital contact tracing technology, as a fundamental non-pharmaceutical intervention, has become one of the means of controlling new infections and outbreaks. How to better utilize digital contact tracing to prevent infectious diseases has become an important research area.

[0003] In this research direction, Kojaku et al. discussed the factors that determine the effectiveness of contact tracing, and they found that "backward" tracing is more effective than "forward" tracing.

[0004] Reyna-Lara et al. proposed a compartmentalized model that combines infection dynamics with contact tracing and case isolation. They developed an analytical expression for the effective basic reproduction number of cases, revealing the role of contact tracers in mitigating and suppressing infectious diseases. Their results indicate that applying contact tracing to asymptomatic individuals can suppress outbreaks. Furthermore, network structure has been shown to be a crucial factor influencing the effectiveness of contact tracing (DCT).

[0005] Kryven et al. investigated how combining contact tracing and isolation processes in a configuration model affects the final scale of an infectious disease. The results showed that the effectiveness of such a tracing process largely depends on the network structure.

[0006] However, existing research, based on individual contact networks and utilizing digital contact tracing technology to locate individuals and analyze the spread of the epidemic, is crucial for controlling infection. In current research, interactions between individuals are often described as one-to-one pairwise interactions. However, mounting empirical evidence suggests that higher-order interactions occur widely in most groups. In many cases, simply reducing higher-order interactions to pairwise interactions introduces errors. Therefore, how to utilize digital contact tracing technology for epidemic prevention and control in scenarios involving higher-order interactions requires further research. Summary of the Invention

[0007] To address the aforementioned problems, the present invention aims to provide a digital contact tracing method for infectious disease transmission on a hypergraph. By constructing a hypergraph-based digital contact tracing model and utilizing percolation theory, the impact of contact tracing on the spread and outbreak threshold of infectious diseases is analyzed, thereby predicting the performance of contact tracing strategies. The technical solution is as follows:

[0008] A method for digital contact tracing of infectious disease transmission on a hypermap includes the following steps:

[0009] S1. Construct an infectious disease transmission model with contact tracing on a hypergraph;

[0010] S2. Map the hypergraph to a factor graph, where hyper points correspond to general nodes and hyper edges correspond to factor nodes. Construct the redundancy distribution generation function for general nodes and factor nodes.

[0011] S3. Map the scale of infectious diseases to the size of the giant connected components of the percolation on the research factor graph, and predict the spread range and outbreak threshold of infectious diseases through percolation theory.

[0012] Furthermore, step S1 specifically includes the following steps:

[0013] S11. Define individuals in a physical contact network as having three states: susceptible state S, infected state I, and recovered state R. During virus transmission, when an individual in susceptible state S comes into contact with an individual in infected state I, the individual in susceptible state S is infected with probability p, while the individual in infected state I changes to recovered state R with probability μ = 1 and no longer participates in the transmission process.

[0014] S12. Construct a hypergraph network including superpoints and hyperedges, and define the digital contact tracing pattern on the hypergraph. The probability that an individual in the system carries a tracking application is T. It is stipulated that on the hypergraph, if there is a superpoint in a certain hyperedge that does not carry a tracking application, then the infectious disease has a probability p that it can spread through the hyperedge. The hyperedge is defined as a traceable hyperedge. A hyperedge in which all superpoints carry tracking applications is defined as an untraceable hyperedge.

[0015] S13. Use the SIR virus propagation model to evoke the spread of infectious diseases in a hypergraph network.

[0016] S2 specifically includes the following steps:

[0017] S21. The hyperdegree distribution P(k) in a hypergraph represents the degree distribution of general nodes in the factor graph, and the cardinality distribution of hyperedges. Depth distribution of factor nodes; average degree of superpoints <k>and super-edge average base <m>These represent the average degree of general nodes and factor nodes in the factor graph, respectively.

[0018] S22. Give the general node degree distribution P(k) and the factor node degree distribution. The generating functions H(x) and F(k) are:

[0019]

[0020]

[0021] Where x is the independent variable of the function; k and m represent the degree of the general node and the degree of the factor node, respectively; the average degree of the general node and the factor node in the factor graph is obtained by averaging the degrees of all general nodes and factor nodes in the network. <k>and <m>;

[0022] Then the redundant distribution generation function of general nodes and factor nodes and They are represented as:

[0023]

[0024]

[0025] Here, H′(1) and F′(1) represent the values ​​of the derivative functions of the generating functions H(x) and F(x) at x = 1, respectively.

[0026] Furthermore, step S3 specifically includes the following steps:

[0027] S31. Define four probabilities and derive the corresponding equations based on edge percolation theory:

[0028] Define the probability that a factor node is reached along an edge in the factor graph, the corresponding hyperedge of which is connected to the giant connected component, and all other nodes of which carry the tracking application.

[0029]

[0030] Define the probability S of reaching a node along an edge of a factor graph, where the corresponding superpoint carries the tracking application and is connected to a giant connected component. T :

[0031]

[0032] Define the probability that a factor node is reached along an edge in the factor graph, the corresponding hyperedge of which is connected to a giant connected component, and at least one of its other nodes does not carry a tracking application.

[0033]

[0034] Define S as the probability that a node is reached along an edge of a factor graph, the corresponding supernode of that node does not carry a tracking application, and is connected to a giant connected component. N ;

[0035]

[0036] S32. Determine the spread of the infectious disease: that is, the proportion of infected individuals to the total number of individuals in the hypergraph network. This value corresponds to the size S of the giant connected component in the seepage; mathematically, it is expressed as the probability that a randomly selected general node is connected to the giant connected component through at least one hyperedge, written as:

[0037]

[0038] S33. Calculate the threshold p for an infectious disease outbreak. c First, define the system of equations as follows:

[0039]

[0040] Taking the partial derivatives of the above system of equations, the Jacobian matrix J is calculated as follows:

[0041]

[0042] in,

[0043]

[0044]

[0045] Decipher the mundane x * Substituting (0, 0, 0, 0) into the Jacobian matrix J, we get:

[0046]

[0047] in,

[0048]

[0049]

[0050]

[0051]

[0052] matrix J * If the eigenvalues ​​are defined as Λ1, Λ2, Λ3, and Λ4, then the largest eigenvalue of the Jacobian matrix is:

[0053] Λ max =max{Λ1,Λ2,Λ3,Λ4}=0

[0054] At this point, the threshold for an infectious disease outbreak is: p c =Func( <k> ， <m>Func(·) represents a function with three independent variables: <k> ， <m>The function formed by T.

[0055] Furthermore, when calculating the threshold for an infectious disease outbreak, due to the super-degree distribution P(k) and the hyper-edge cardinality distribution... If all follow a Poisson distribution, then:

[0056]

[0057]

[0058] Then the system of equations (1) is simplified to

[0059]

[0060] Under this condition, the trivial solution x * Substituting (0, 0, 0, 0) into the Jacobian matrix, we get:

[0061]

[0062] Let Jacobi matrix J * The maximum eigenvalue is zero, i.e., Λmax = 0, then the threshold for an infectious disease outbreak is obtained.

[0063] Furthermore, after step S3, the process includes: randomly simulating the spread of an epidemic based on transmission parameters such as the infectious disease transmission rate, the average number of superedges, and the individual contact tracing application's carrying rate, to predict the performance of the contact tracing strategy; specifically, after obtaining the infectious disease transmission range and outbreak threshold, considering the impact of transmission factors in the hypergraph network on the spread of the infectious disease in conjunction with transmission dynamics, the transmission factors include the tracking application carrying rate T, the infectious disease transmission rate p, and the average number of superedges. <k>Super-edge average base <m>Subsequently, based on the infectious disease transmission rate p, the super-marginal average base... <m>And the individual contact tracing application carries the T random simulation of the spread of an epidemic to predict the performance of contact tracing strategies.

[0064] The beneficial effects of this invention are:

[0065] 1) This invention utilizes a hypergraph model to explore the impact of contact tracing on the spread of infectious diseases in high-order interaction scenarios. By mapping the hypergraph to a factor graph, the edge percolation theory is used to characterize the SIR (Susceptible Infective Removed) transmission process of infectious diseases on the hypergraph, predicting the spread range and outbreak threshold of infectious diseases.

[0066] 2) This invention also analyzes various transmission influencing factors of hypergraphs with contact tracing mechanisms, comprehensively analyzes virus transmission in hypergraphs, and can better reflect the real transmission situation compared with traditional simple networks, providing an important reference for controlling the scale of virus transmission.

[0067] 3) This invention expands the transmission scenario from one-to-one point-to-point interaction to higher-order interaction with collective behavior, enriches the individual interaction mode, is closer to the real-world transmission scenario, and is conducive to more accurate analysis of the impact of contact tracing on the spread of infectious diseases.

[0068] 4) This invention also provides a reference for other related issues in the same field. It can be used as a basis for further development and can be applied to the study of the effectiveness of contact tracing on hypergraphs in the same field, which has a very broad application prospect. Attached Figure Description

[0069] Figure 1 This is a flowchart of the digital contact tracing method for the spread of infectious diseases on a supergraph according to the present invention.

[0070] Figure 2 This is a diagram illustrating the virus transmission process.

[0071] Figure 3 This diagram illustrates the evolution of infectious disease transmission processes on a hypergraph network.

[0072] Figure 4 This is a schematic diagram of mapping a hypergraph to a factor graph.

[0073] Figure 5 This diagram illustrates how the spread range S of an infectious disease increases with the increase of the infectious disease transmission rate p.

[0074] Figure 6 This diagram illustrates how the scale of the epidemic changes as the carrier rate T of the tracking application changes.

[0075] Figure 7 The base of the hyperedge average <m>The impact of changes on the scale of transmission. Detailed Implementation

[0076] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0077] The flowchart of the digital contact tracing method for infectious disease transmission on a supergraph in this invention is as follows: Figure 1 As shown, the specific process is as follows:

[0078] S1. Construct an infectious disease transmission model with contact tracing on a hypergraph.

[0079] S11. Define individuals in a physical contact network as having three states: susceptible state (healthy state) S, infected state I, and recovered state R. For example... Figure 2 As shown, during the transmission of the virus, when an individual in a susceptible state comes into contact with an individual in an infected state, the individual in a susceptible state is infected with probability p, while the individual in an infected state transitions to a recovered state with probability μ = 1 and no longer participates in the transmission process.

[0080] Figure 2 This represents the individual state transition process based on the SIR model. Circles composed of black and white represent infected state hyperpoints without the app. Circles composed of black and diagonal lines represent infected state hyperpoints with the app. Similarly, dark gray and white (diagonal lines) represent recovered state hyperpoints (without) the app. Light gray and white (diagonal lines) represent susceptible state hyperpoints (without) the app. Light gray rectangles represent traceable hyperedges.

[0081] S12. Construct a hypergraph network, including hypervertices and hyperedges. Define a digital contact tracing pattern on the hypergraph, where the probability of an individual carrying a tracking application is T. Stipulate that if a hypervertice in a hyperedge does not carry a tracking application, then an infectious disease has a probability p that it can spread through that hyperedge. Define a hyperedge where all hypervertices carry a tracking application as an "untraceable hyperedge"; define a hyperedge as "traceable hyperedge" if at least one hypervertice in it does not carry a tracking application.

[0082] S13, such as Figure 3 As shown, the SIR virus propagation model is used to evoke the spread of infectious diseases in a hypergraph network.

[0083] S2. Map the hypergraph to a factor graph, where hyperpoints correspond to general nodes and hyperedges correspond to factor nodes. Construct the redundancy distribution generation function for general nodes and factor nodes.

[0084] S21, such as Figure 4 As shown, the hypergraph is mapped to a factor graph, where hypervertices correspond to general nodes and hyperedges correspond to factor nodes. Correspondingly, the hyperdegree distribution P(k) in the hypergraph represents the degree distribution of general nodes in the factor graph. Hyperedge cardinality distribution. This represents the degree distribution of the factor nodes. (Definition) <k>and <m>These represent the average degree of general nodes and factor nodes in the factor graph, respectively.

[0085] S22. Given the distribution P(k), The generating functions H(x) and F(k) are:

[0086]

[0087]

[0088] Where x is the independent variable of the function; k and m represent the degree of the general node and the degree of the factor node, respectively; the average degree of the general node and the factor node in the factor graph is obtained by averaging the degrees of all general nodes and factor nodes in the network. <k>and <m>.

[0089] Then the redundant distribution generation function of general nodes and factor nodes and They are represented as:

[0090]

[0091]

[0092] Here, H′(1) and F′(1) represent the values ​​of the derivative functions of H(x) and F(x) at x = 1, respectively.

[0093] S3. Map the scale of infectious diseases to the size of the giant connected components of the percolation on the research factor graph. Predict the spread and outbreak threshold of infectious diseases using percolation theory.

[0094] S31. Define four probabilities and derive the corresponding equations based on edge percolation theory.

[0095] definition It is to reach a factor node (superedge) along an edge of the factor graph, that superedge is connected to the giant connected component and all its other nodes carry the probability of the tracking application.

[0096] Define S T It is the probability of reaching a node (superpoint) along an edge of the factor graph, that superpoint carries the tracking application and is connected to the giant connected component.

[0097] definition It is to reach a factor node (superedge) along an edge of the factor graph, that superedge is connected to the giant connected component and its other nodes have at least one probability that they do not carry the tracking application.

[0098] Define S N It is the probability of reaching a node (superpoint) along an edge of the factor graph, where the superpoint does not carry a tracking application and is connected to a giant connected component.

[0099] Based on the above definition and the theory of edge seepage, the following equation is obtained:

[0100]

[0101]

[0102]

[0103]

[0104] in, Let T be the generating function representing the redundancy distribution of the factor nodes. Let represent the generating function that describes the redundancy distribution of the factor nodes, and let TS be the independent variable of the generating function. T ; Let S be the generating function representing the redundancy distribution of the factor nodes, and let the independent variable of the generating function be 1-S. T -S N ; Let the generating function represent the redundancy distribution of a general node, and let the independent variable of the generating function be...

[0105] S32. The spread of infectious diseases: This refers to the proportion of infected individuals to the total number of individuals in a hypergraph network, corresponding to the size S of the giant connected component in the seepage. Mathematically, it is expressed as the probability that a randomly selected general node is connected to the giant connected component through at least one hyperedge, written as:

[0106]

[0107] in, Let represent the generating function for the degree distribution of a general node, and let the independent variable of the generating function be .

[0108] S33. To calculate the threshold p for an infectious disease outbreak. c First, define the system of equations as follows:

[0109]

[0110] Taking the partial derivatives of the above system of equations, the Jacobian matrix J is calculated as follows:

[0111]

[0112] in,

[0113]

[0114]

[0115]

[0116] Decipher the mundane x * Substituting (0, 0, 0, 0) into the Jacobian matrix J, we get:

[0117]

[0118] in,

[0119]

[0120]

[0121]

[0122]

[0123] matrix J * The eigenvalues ​​are defined as Λ1, Λ2, Λ3, and Λ4. Therefore, when the largest eigenvalue of the Jacobian matrix is...

[0124] Λ max =max{Λ1,Λ2,Λ3,Λ4}=0.

[0125] At this point, the infectious disease outbreak threshold p c =Func( <k> ， <m>Func(·) can be calculated from the independent variable T, where Func(·) represents the expression derived from the independent variable. <k> ， <m>The function formed by T.

[0126] Consider a special case, namely P(k). All follow a Poisson distribution, and we have:

[0127]

[0128]

[0129] The defined system of equations can then be simplified to:

[0130]

[0131] Under this condition, the fixed point x * Substituting (0, 0, 0, 0) into the Jacobian matrix, we get:

[0132]

[0133] Let Jacobi matrix J * If the maximum eigenvalue is zero, i.e., Λmax = 0, then the threshold for an infectious disease outbreak can be obtained.

[0134] S4. Based on transmission parameters such as infectious disease transmission rate, super-side average base, and individual contact tracing application carrying rate, randomly simulate the transmission process of an epidemic to predict the performance of contact tracing strategies.

[0135] After obtaining the spread range and outbreak threshold of the infectious disease, the influence of transmission factors in the hypergraph network on the spread of the infectious disease is considered in conjunction with transmission dynamics. These transmission factors include the carrier rate T of the tracking application, the transmission rate p of the infectious disease, and the average degree of the superpoint. <k>Super-edge average base <m>The study then examined the infectious disease transmission rate p and the supermarginal mean base. <m>The study also investigates the impact of the individual contact tracing application's carry rate T on the transmission process of infectious diseases in hypergraph networks, thereby predicting the performance of contact tracing strategies.

[0136] like Figure 5 As shown, the spread range S of an infectious disease increases with the increase of the infectious disease transmission rate p. Figure 5 As shown in (a), the higher the carrier rate T of the tracking application, the smaller the outbreak size and the higher the outbreak threshold, indicating that the carrier tracking application has an inhibitory effect on the spread of infectious diseases. Figure 5 As shown in (b), the outbreak size varies with the super-side average base. <m>The threshold increases with the increase of the super-edge average base, while the outbreak threshold increases with the increase of the super-edge average base. <m>The increase in the superedge average base decreases. The results show that increasing the superedge average base... <m>This will exacerbate and promote the spread of the epidemic.

[0137] like Figure 6 As shown, as the carrier rate T of the tracking application increases, the scale of the outbreak gradually decreases until it reaches zero. (Observation) Figure 6 (a) It was found that when the infectious disease transmission rate p changed from 0.5 to 0.2, the transmission range S decreased significantly. When the infectious disease transmission rate p changed from 0.8 to 0.5, the transmission range S decreased slightly. This result indicates that when the transmission rate is high, further expansion of the transmission rate has a relatively small impact on the spread of the epidemic. Figure 6 (b) indicates that the super-edge average base is expanded. <m>It will also promote the spread of the epidemic.

[0138] like Figure 7 As shown in (a)-(c), the hyperedge average base <m> An increase in the carrier rate (T) significantly increases the scale of transmission. When the carrier rate (T) of the tracking app is fixed, an increase in the transmission rate (p) of the infectious disease definitely promotes its spread. When the transmission rate (p) of the infectious disease is very small, changes in the carrier rate (T) of the tracking app do not affect the scope of transmission (S). This phenomenon is because the infectious disease has not yet broken out, and its transmission scale remains zero. When the transmission rate (p) of the infectious disease is large, an outbreak will occur, and an increase in the carrier rate (T) of the tracking app will reduce the scale of the outbreak to some extent.< / m> < / m> < / m> < / m> < / m> < / m> < / m> < / k> < / m> < / k> < / m> < / k> < / m> < / k> < / m> < / k> < / m> < / m> < / m> < / k> < / m> < / k> < / m> < / k> < / m> < / k> < / m> < / k>

Claims

1. A method for digital contact tracing of infectious disease transmission on a hypergraph, characterized in that, Includes the following steps: S1. Construct an infectious disease transmission model with contact tracing on a hypergraph; S2. Map the hypergraph to a factor graph, where hyper points correspond to general nodes and hyper edges correspond to factor nodes. Construct the redundancy distribution generation function for general nodes and factor nodes. S3. Map the scale of infectious diseases to the size of the giant connected components of the percolation on the research factor graph, and predict the spread range and outbreak threshold of infectious diseases through percolation theory. S1 specifically includes the following steps: S11. Define individuals in a physical contact network as having three states: susceptible state S, infected state I, and recovered state R. During virus transmission, when an individual in susceptible state S comes into contact with an individual in infected state I, the individual in susceptible state S will... Infected individuals, who are in state I of infection, have a probability of It transitions to the recovery state R and no longer participates in the propagation process; S12. Construct a hypergraph network including hypervertices and hyperedges, and define the digital contact tracking pattern on the hypergraph. The probability that each individual in the system carries a tracking application is given by... ; The rule states that on a hypergraph, if any vertex along a hyperedge does not carry a tracking application, then there is a probability that an infectious disease may occur. If a hyperedge can propagate through itself, it is defined as a traceable hyperedge; if all hyperpoints in a hyperedge carry a tracking application, then the hyperedge is defined as an untraceable hyperedge. S13. Use the SIR virus propagation model to evoke the spread of infectious diseases in a hypergraph network.

2. The method for digital contact tracing of infectious disease transmission on a hypermap according to claim 1, characterized in that, S2 specifically includes the following steps: S21. Hyperscale distribution in a hypergraph The degree distribution of general nodes in a factor graph, and the cardinality distribution of hyperedges. Represents the degree distribution of factor nodes; Exceeding average degree and super-edge average base These represent the average degree of general nodes and factor nodes in the factor graph, respectively. S22. Give a general node degree distribution. Factor node degree distribution Generating functions , : ； ； in, It is the independent variable of the function; and Let represent the degree of a general node and the degree of a factor node, respectively. The average degree of all general and factor nodes in the network is then calculated by averaging their degrees to obtain the average degree of general and factor nodes in the factor graph. and ; Then the redundant distribution generation function of general nodes and factor nodes and They are represented as: ； ； in, and They represent generating functions respectively. and The value of the derivative function of at x = 1.

3. The method for digital contact tracing of infectious disease transmission on a hypermap according to claim 2, characterized in that, S3 specifically includes the following steps: S31. Define four probabilities and derive the corresponding equations based on edge percolation theory: Define the probability that a factor node is reached along an edge in the factor graph, the corresponding hyperedge of which is connected to the giant connected component, and all other nodes of which carry the tracking application. : ； Define the probability that a node is reached along an edge of a factor graph, that the corresponding superpoint carries the tracking application, and that it is connected to a giant connected component. : ； Define the probability that a factor node is reached along an edge in the factor graph, the corresponding hyperedge of which is connected to a giant connected component, and at least one of its other nodes does not carry a tracking application. : ； Reaching a node along an edge of the factor graph, where the corresponding supernode does not carry a tracking application and has a probability of being connected to a giant connected component is... ; ； S32. Determine the spread of infectious diseases: that is, the proportion of infected individuals to the total number of individuals in the hypergraph network. This value corresponds to the size of the giant connected components in the seepage. Mathematically, the probability that a randomly selected general node is connected to a giant connected component through at least one hyperedge is expressed as: ； S33. Calculate the threshold for an infectious disease outbreak. First, define the system of equations as follows: ； Taking the partial derivatives of the above system of equations, the Jacobian matrix... The calculation is as follows: ； in, , , , ; Deciphering the ordinary Substituting the Jacobian matrix ,get: ； in, ； ； ； ； matrix The eigenvalues ​​are defined as , , and Then the largest eigenvalue of the Jacobian matrix is: ； At this point, the threshold for an infectious disease outbreak is: , (·) indicates that there are three independent variables: The function formed.

4. The method for digital contact tracing of infectious disease transmission on a hypermap according to claim 3, characterized in that, When calculating the threshold for an infectious disease outbreak, due to the super-distribution... Hypermarginal cardinality distribution If all follow a Poisson distribution, then: ； ； The system of equations then simplifies to: ； Under this condition, the trivial solution Substituting the Jacobian matrix, we get: ； Let Jacobi matrix The maximum eigenvalue is zero, i.e., Λmax = 0, which gives the threshold for an infectious disease outbreak.

5. The method for digital contact tracing of infectious disease transmission on a hypermap according to claim 2, characterized in that, Step S3 is followed by: randomly simulating the spread of an epidemic based on transmission parameters such as the infectious disease transmission rate, the average cardinality of hyperedges, and the individual contact tracing application's carry rate, to predict the performance of the contact tracing strategy; specifically, after obtaining the infectious disease transmission range and outbreak threshold, considering the impact of transmission factors in the hypergraph network on the spread of the infectious disease in conjunction with transmission dynamics, wherein the transmission factors include the carry rate of the contact tracing application. Infectious disease transmission rate Exceeding average degree Super-edge average base Subsequently, based on the rate of infectious disease transmission... Super-edge average base and individual contact tracing applications carry rate The spread of an epidemic is simulated randomly to predict the performance of contact tracing strategies.

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