An epidemic risk judgment method and system based on age structure

Abstract

A kind of epidemic risk based on age structure is judged method and system, module includes: epidemic transmission model construction module: for according to vaccination rate, vaccination benefit, infection rate, latent period, the reduction coefficient of the probability of being symptomatic, discovery period, discovery period extension rate, establish differential dynamic equation set, to construct epidemic transmission model.Contact frequency between each age group construction module: consider the influence of age structure on transmission, construct the contact frequency between each age group under different environmental settings, and add it to epidemic transmission model.Basic reproduction number calculation module: the basic reproduction number R0 is calculated using next generation matrix method respectively.Epidemic risk judgment model sensitivity analysis module: sensitivity analysis is carried out on epidemic risk judgment model, and the influence of vaccination rate, the reduction coefficient of the probability of being symptomatic, discovery period extension rate on the whole transmission process is studied.The present application helps to analyze the influence of multiple factors and age structure on epidemic transmission risk.

Description

Technical Field

[0001] This invention belongs to the field of disease transmission, specifically relating to a method for assessing epidemic risk based on age structure. Background Technology

[0002] In the prior art, the patent with authorization announcement number CN112786210B, entitled "A Method and System for Tracking the Spread of an Epidemic, Based on Spatiotemporal Big Data and Artificial Intelligence Technology," combines real-time data mining technology with knowledge graph technology to construct a spatiotemporal relationship graph of people. It applies infectious disease models to dynamic personnel relationship graphs with local community structures and integrates them with epidemiological surveys to achieve individual infection risk assessment and modeling prediction, facilitating the early detection of potential high-risk infected individuals and improving epidemic prevention and control management capabilities.

[0003] While this technology can identify high-risk potential carriers, it still has some problems:

[0004] 1. Individual risk factors for disease can be affected by vaccination:

[0005] While vaccination reduces the probability of infection during the pandemic, it also reduces the likelihood of people developing symptoms after infection, which means there are more potential risks.

[0006] 2. Weak or absent symptoms can prolong the time it takes to detect asymptomatic infections:

[0007] Asymptomatic carriers, who do not exhibit obvious symptoms, can only be detected through nucleic acid testing. This process further prolongs the virus transmission cycle, increasing the risk of transmission.

[0008] Mathematical models are crucial tools for evaluating the spread of epidemics and assessing risks. In recent years, researchers have proposed numerous models to study the dynamic processes of viral outbreaks. However, simple SIR and SEIR models are overly simplistic in their population classification and assume homogeneity, failing to consider the impact of heterogeneous populations on epidemic transmission. This is primarily reflected in the following aspects:

[0009] 1. For vulnerable populations, vaccination has been implemented in the actual prevention and control of the epidemic. This measure has resulted in different infection rates between vaccinated and unvaccinated populations. Therefore, it is necessary to consider vaccinated and unvaccinated populations separately.

[0010] 2. Whether an infected person exhibits symptoms directly impacts their risk of spreading the virus. Based on practical experience, asymptomatic carriers do not display obvious symptoms and require specific testing methods for detection. Therefore, asymptomatic and symptomatic carriers need to be considered separately.

[0011] 3. Common models assume a homogeneous population, with each individual carrying the same transmission risk. However, in reality, people of different ages have varying frequencies of exposure, and their transmission risks differ accordingly. Therefore, the impact of age structure on transmission risk needs to be considered.

[0012] In conclusion, conventional transmission models have revealed many problems and shortcomings in the process of assessing epidemic risks, and it is necessary to develop more accurate and effective methods for assessing epidemic risks. Summary of the Invention

[0013] To address the aforementioned issues, this invention provides a method and system for assessing epidemic risk based on age structure.

[0014] The technical solution of this invention is: a method for assessing epidemic risk based on age structure, comprising:

[0015] Step S1: Based on vaccination rate, vaccination effectiveness, infection rate, incubation period, reduction coefficient of symptomatic probability, detection period, and detection period extension rate, establish a set of differential dynamic equations to construct an epidemic transmission model;

[0016] Step S2: Consider the impact of age structure on transmission, construct the contact frequency between each age group, and incorporate it into the epidemic transmission model;

[0017] Step S3: Calculate the basic reproduction number of the epidemic transmission model;

[0018] Step S4: Conduct a sensitivity analysis on the epidemic risk assessment model to study the impact of vaccination rate, the reduction coefficient of the probability of symptom on the whole transmission process, and the extension rate of the detection period.

[0019] An epidemic risk assessment system based on age structure includes the following modules:

[0020] The epidemic transmission model construction module is used to establish a set of differential dynamic equations based on vaccination rate, vaccination effectiveness, infection rate, incubation period, reduction coefficient of symptomatic probability, detection period, and detection period extension rate, in order to construct an epidemic transmission model.

[0021] Contact frequency construction module between age groups: Considering the impact of age structure on transmission, the contact frequency between age groups is constructed under different environmental settings and incorporated into the epidemic transmission model;

[0022] The basic reproduction number calculation module calculates the basic reproduction number R0 using the next-generation matrix method.

[0023] Sensitivity analysis module of the epidemic risk assessment model: Conduct sensitivity analysis on the epidemic risk assessment model to study the impact of vaccination rate, the reduction coefficient of the probability of symptom on the whole transmission process, and the extension rate of the detection period.

[0024] When using this invention, the input is: the initial values ​​of the number of people in various states of the population and the values ​​of various parameters obtained from the census and big data; the output is: the change of population density in various states of the population over time.

[0025] In this invention, the experimental data processing part is based on spatiotemporal big data, using macro and micro data published on the National Population Census website, and conducting surveys on the family, health and economic status of different sample groups. Then, an adaptive algorithm is used to synthesize four environmental settings: family, school, workplace and others.

[0026] Compared with the prior art, the present invention has the following advantages:

[0027] Based on epidemiological transmission theory, this invention proposes an epidemic risk assessment method based on age structure, taking into account factors such as the vaccination rate of susceptible individuals, the reduction in the probability of symptom onset due to vaccination, the time of discovery of asymptomatic infected individuals, and the influence of population structure on the epidemic transmission process. The invention also simulates and analyzes the impact of vaccination rate, the reduction coefficient of the probability of symptom onset, the extension rate of the discovery period, and age structure on the risk of epidemic transmission. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating the epidemic risk assessment method based on age structure, as exemplified by the present invention.

[0029] Figure 2 This is a schematic diagram illustrating the state transitions of various population groups in the method of this invention.

[0030] Figure 3 This is a flowchart of step S2 in the epidemic risk assessment method of this invention;

[0031] Figure 4 This is a schematic diagram illustrating the calculation of contact frequency between different age groups in different environments, as an example of the present invention.

[0032] Figure 5 This is a flowchart illustrating the calculation of the basic reproduction number R0 in an epidemic transmission model, as described in this invention.

[0033] Figure 6 This is a flowchart of step S4 in the epidemic risk assessment method of this invention;

[0034] Figure 7 This is a schematic diagram of the epidemic risk assessment system based on age structure according to the present invention. Detailed Implementation

[0035] This invention provides a risk assessment method based on age structure. It uses an epidemic transmission model to simulate and analyze the impact of vaccination rate, the reduction coefficient of symptomatic probability, the extension rate of detection period, and age structure on the risk of epidemic transmission, demonstrating that strict control measures can effectively reduce the risk of epidemic.

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below through specific implementations and in conjunction with the accompanying drawings.

[0037] like Figure 1 As shown in the figure, the epidemic risk assessment method based on age structure provided by the embodiments of the present invention includes the following steps:

[0038] Step S1: Based on the vaccination rate, vaccination effectiveness, infection rate, incubation period, the reduction coefficient of the probability of symptom onset (the reduction in the probability of latent individuals becoming symptomatic infected individuals due to vaccination), detection period, and the rate of prolongation of the detection period, establish a set of differential dynamic equations to construct an epidemic transmission model.

[0039] Step S2: Considering the impact of age structure on transmission, construct the contact frequency between each age group under different environmental settings and incorporate it into the epidemic transmission model;

[0040] Step S3: Calculate the basic reproduction number R0 of the epidemic transmission model using the next-generation matrix method.

[0041] Step S4: Conduct a sensitivity analysis on the epidemic risk assessment model to study the impact of vaccination rate, the reduction coefficient of the probability of symptom on the whole transmission process, and the extension rate of the detection period.

[0042] In one embodiment, step S1 above, which involves establishing a system of differential dynamic equations based on vaccination rate, vaccination effectiveness, infection rate, incubation period, reduction coefficient of symptomatic probability, detection period, and detection period extension rate, specifically includes:

[0043]

[0044] Among them, S, Q represents the number of susceptible individuals, unvaccinated latent individuals, vaccinated latent individuals, unvaccinated asymptomatic infected individuals, vaccinated asymptomatic infected individuals, unvaccinated symptomatic infected individuals, vaccinated symptomatic infected individuals, and those in isolation / recovered individuals, respectively. Let represent the total number of people in the population, p represent the probability of not being vaccinated, w represent the infection rate decay coefficient, β represent the infection rate, and q represent the probability that a latent individual will become an asymptomatic carrier. represents the incubation period, and l represents the coefficient for reducing the probability of having symptoms. This represents the discovery period / recovery period, and k represents the discovery period extension rate.

[0045] In this example, the rules for the spread of the epidemic are defined as follows:

[0046] (1) Considering the impact of vaccination on susceptible individuals, the infection rate of vaccinated susceptible individuals is defined as decreasing.

[0047] (2) Once a susceptible person who has been vaccinated becomes a latent person, the incubation period is defined as being prolonged.

[0048] (3) The impact of the detection period on the spread of the epidemic was taken into consideration. It was defined that after a latent person becomes an asymptomatic infected person, the time to be detected will be longer because the person fails to show obvious symptoms.

[0049] Figure 2 The diagram illustrates the state transitions of various population groups in the risk assessment method of this invention.

[0050] like Figure 3 As shown, step S2 in this example: Considering the impact of age structure on transmission, the contact frequency between each age group is constructed under different environmental settings and added to the epidemic transmission model. Specifically, this includes: Step S21: Constructing the contact frequency between each age group in a specific environment, specifically including:

[0051]

[0052] Where i and j represent the i-th and j-th age groups respectively, and H (Household) represents the family environment. N represents the number of people in the i-th age group who have been exposed to the family environment. i This represents the number of people in the i-th age group. This represents the size of the family to which individual k belongs. This indicates contact with people in the family environment who belong to age group j, δ ij This represents the Kronecker delta function.

[0053] Similarly, the frequency of contact between age groups in school, workplace, and other environments was calculated.

[0054] Step S22: Based on the weights under different environments, synthesize a total contact frequency, specifically including:

[0055]

[0056] Where H, S, W, and O represent Household, School, Workplace, and Others, respectively, and ω* This indicates the weight of the corresponding environment.

[0057] Step S23: Based on formula (1), incorporate the age structure into the epidemic transmission model, specifically including:

[0058]

[0059] Where i and j represent the i-th age group and the j-th age group, respectively.

[0060] Figure 4 The diagram illustrates the contact frequency between different age groups under different environments.

[0061] like Figure 5 As shown, step S3 in this example, calculating the basic reproduction number R0 of the epidemic transmission model using the next-generation matrix method, specifically includes:

[0062] Step S31: According to formula (1), assuming that S = N at the disease-free equilibrium, the disease-free equilibrium point can be denoted as...

[0063]

[0064] Step S32: Calculate the basic reproduction number R0 of the epidemic transmission model using the next-generation matrix method;

[0065] First, the epidemic transmission model can be represented by the following formula:

[0066]

[0067] in, Where T represents the propagation part and Σ represents the transition part;

[0068] Next, calculate the next-generation matrix K:

[0069]

[0070] The spectral radius of K can be obtained as the fundamental reproduction number R0:

[0071]

[0072] like Figure 6 As shown, step S4 in this example involves conducting a sensitivity analysis on the epidemic risk assessment model to study the impact of vaccination rate, the reduction coefficient of symptomatic probability, and the rate of extended detection period on the entire transmission process. Specifically, this includes:

[0073] Step S41: Change the value of the vaccination rate p and simulate the change of the number of people in the infected state over time. Specifically, set the value of p to 0.1, 0.5 and 0.9 respectively.

[0074] Step S42: Determine the value of the reduction coefficient l for the probability of changing symptoms, and conduct simulation analysis on the change of the number of people in an infected state over time. Specifically, set the value of l to 0.2, 0.5, and 0.8.

[0075] Step S43: The value of the change detection period extension rate k is selected, and the number of infected persons changes over time is simulated and analyzed. Specifically, the value of k is set to 0.1, 0.3, and 0.6.

[0076] The verification experiment of the epidemic risk assessment method in this embodiment is described below:

[0077] The total number of people in each state in step S1 is the Shanghai population figure published in the China Statistical Yearbook by China Statistics Press (2010). The initial infected person is defined as an unvaccinated symptomatic infected person, and the number is set to one ten-thousandth of the total population. The parameters w, q, σ, and γ in the model are all from relevant references.

[0078] In step S2, the distribution of people in the four environments is obtained from census data, and the contact frequency between different age groups in different environments is calculated in step S21.

[0079] In step S4, the number of infected individuals over time is obtained by varying the unvaccinated proportion p, verifying that increased vaccination rates can reduce the peak and total number of infected individuals. The number of unvaccinated asymptomatic individuals, vaccinated asymptomatic individuals, unvaccinated symptomatic individuals, and vaccinated symptomatic individuals over time is obtained by varying the symptomatic probability reduction coefficient l resulting from vaccination, verifying that vaccination reduces the probability of latent individuals becoming symptomatic, leading to an increase in asymptomatic infections and thus increasing the risk of further spread of the epidemic. The number of infected individuals over time is obtained by varying the detection period extension rate k, verifying that asymptomatic individuals, due to weak or absent symptoms, cannot be detected in time, leading to isolation measures and further prolonging the transmission cycle and increasing the risk of infection.

[0080] This embodiment determines the risk of epidemic transmission by analyzing changes in the number of people with infected status.

[0081] The experimental data processing part of this invention is based on spatiotemporal big data. It uses macro and micro data published on the National Population Census website and investigates the family, health and economic status of different sample groups. Then, an adaptive algorithm is used to synthesize four environmental settings: family, school, workplace and others.

[0082] refer to Figure 7 The system for implementing the age-based epidemic risk assessment method of this embodiment includes:

[0083] The epidemic transmission model construction module is used to establish a set of differential dynamic equations based on vaccination rate, vaccination effectiveness, infection rate, incubation period, reduction coefficient of symptomatic probability, detection period, and detection period extension rate, in order to construct an epidemic transmission model.

[0084] Contact frequency construction module between age groups: Considering the impact of age structure on transmission, the contact frequency between age groups is constructed under different environmental settings and incorporated into the epidemic transmission model;

[0085] The basic reproduction number calculation module calculates the basic reproduction number R0 using the next-generation matrix method.

[0086] Sensitivity analysis module of the epidemic risk assessment model: Conduct sensitivity analysis on the epidemic risk assessment model to study the impact of vaccination rate, the reduction coefficient of the probability of symptom on the whole transmission process, and the extension rate of the detection period.

[0087] Each module can be implemented in the computer system as a program.

[0088] Based on epidemiological transmission theory, this invention takes into account the impact of vaccination rates on susceptible individuals, the prolonged incubation period caused by vaccination, the timing of asymptomatic infection detection, and population structure on the transmission process of an epidemic. It proposes an epidemic risk assessment method based on age structure and simulates the impact of vaccination rates, the reduction coefficient of the probability of symptom on the detection period, and age structure on the risk of epidemic transmission. The results demonstrate that strict control measures can effectively reduce the risk of an epidemic.

[0089] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for assessing epidemic risk based on age structure, characterized in that, include: Step S1: Based on vaccination rate, vaccination effectiveness, infection rate, incubation period, reduction coefficient of symptomatic probability, detection period and detection period extension rate, establish a set of differential dynamic equations as an epidemic risk assessment model; The infection rate is defined as lower in susceptible individuals who are vaccinated; The probability of a vaccinated asymptomatic carrier becoming a symptomatic carrier is reduced. This is defined as a prolonged period of time for detection after a latent person becomes an asymptomatic carrier, as they fail to exhibit obvious symptoms. Step S2: Considering the impact of age structure on transmission, construct the contact frequency between each age group under different environmental settings, and incorporate it into the epidemic transmission model. The steps include: Step S21: Construct the contact frequency among different age groups in a specific environment; Step S22: Based on the weights in different environments, synthesize the total exposure frequency of each age group in different environments. Step S23: Based on the differential dynamics equations, incorporate the contact frequency factor into the epidemic transmission model; Step S3: Calculate the basic reproduction number of the epidemic risk assessment model. The steps include: Step S31: Calculate the disease-free equilibrium point based on the differential dynamic equations; Step S32: Calculate the basic reproduction number R0 of the epidemic transmission model incorporating age structure using the next-generation matrix method; Step S4: Conduct a sensitivity analysis on the epidemic risk assessment model to study the impact of vaccination rate, the reduction coefficient of symptomatic probability, and the rate of extended detection period on the entire transmission process. The steps include: Step S41: Change the value of the vaccination rate and simulate the change in the number of people in an infected state over time; Step S42: Change the value of the reduction coefficient of the probability of becoming symptomatic, and simulate and analyze the change of the number of people in the infected state over time. Step S43: Change the value of the discovery period extension rate and simulate and analyze the change in the number of infected persons over time; The differential dynamic equations in step S1 are as follows: (1) in: Indicates a susceptible person, This indicates unvaccinated asymptomatic carriers. This indicates latent individuals who have already been vaccinated. This refers to asymptomatic individuals who have not been vaccinated. This indicates asymptomatic individuals who have been vaccinated. This refers to symptomatic individuals who have not been vaccinated. This indicates symptomatic individuals who have already been vaccinated. This represents the total number of people in quarantine and those who have recovered. This represents the total number of people in the entire population. ; This indicates the probability of not being vaccinated. Indicates the intensity of the decline in infection rate. Indicates the infection rate. This indicates the probability that a latent individual will become an asymptomatic carrier. Indicates the incubation period. A reduction factor representing the probability of having symptoms. Indicates the discovery period / recovery period. Indicates the rate of extended discovery period; Step S21: Construct the contact frequencies between different age groups in a specific environment: Family environment Contact frequency between different age groups: (2) Where i and j represent the i-th age group and the j-th age group, respectively. Indicates family environment. N represents the number of people in the i-th age group who have been exposed to the family environment. i This represents the number of people in the i-th age group. This represents the size of the family to which individual η belongs. This refers to contact with people in the family environment who belong to age group j. This represents the Kronecker delta function; Following the method of formula (2), the contact frequency between each age group in the school environment S', workplace environment W, and other environments O was calculated respectively. ; Step S22: Based on the weights under different environments, synthesize a total contact frequency: (3) This indicates the weight of the corresponding environment; Step S23: Based on formula (1), incorporate the age structure into the epidemic transmission model: （4） Where i and j represent the i-th age group and the j-th age group, respectively.

2. The method for assessing epidemic risk based on age structure as described in claim 1, characterized in that, Step S31: According to formula (1), assuming that S=N at the disease-free equilibrium, the disease-free equilibrium point is denoted as... ； Step S32: Calculate the basic reproduction number R0 of the epidemic transmission model using the next-generation matrix method: First, the epidemic risk assessment model is expressed as a formula: , ,in: Dissemination section , Transfer part ; Next, calculate the next generation matrix K: ， The spectral radius of K is obtained as the basic reproduction number R0: 。 3. The method for assessing epidemic risk based on age structure as described in claim 2, characterized in that, Step S4 includes: Step S41: Change vaccination rate The value of is used to simulate and analyze the change in the number of infected persons over time; Step S42: Change the reduction factor of the probability of developing symptoms The value of is used to simulate and analyze the change in the number of infected persons over time; Step S43: Change the rate of extended discovery period The value of is used to simulate and analyze the change in the number of infected individuals over time.

4. An epidemic risk assessment system based on the epidemic risk assessment method according to any one of claims 1 to 3, characterized in that, An epidemic risk assessment system based on age structure, employing the aforementioned epidemic risk assessment method, includes the following modules: The epidemic transmission model construction module is used to establish a set of differential dynamic equations based on vaccination rate, vaccination effectiveness, infection rate, incubation period, reduction coefficient of symptomatic probability, detection period, and detection period extension rate, in order to construct an epidemic transmission model. Contact frequency construction module between age groups: Considering the impact of age structure on transmission, the contact frequency between age groups is constructed under different environmental settings and incorporated into the epidemic transmission model; The basic reproduction number calculation module calculates the basic reproduction number R0 using the next-generation matrix method. Sensitivity analysis module of the epidemic risk assessment model: Conduct sensitivity analysis on the epidemic risk assessment model to study the impact of vaccination rate, the reduction coefficient of the probability of symptom on the whole transmission process, and the extension rate of the detection period.

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