CN113450924B - Novel coronavirus propagation model establishing method and system - Google Patents

Abstract

The invention relates to a method and a system for establishing a novel coronavirus propagation model, wherein the method comprises the following steps: step S1: establishing a differential kinetic equation set according to the inoculation rate, the isolation period and the recovery rate to construct a new coronavirus transmission model; step S2: according to a differential kinetic equation set, acquiring a disease-free balance point and a disease balance point of a new coronavirus transmission model by utilizing kinetic modeling; and step S3: and (3) carrying out stability analysis on the new coronavirus transmission model, and determining conditions required for enabling the disease-free balance point and the disease balance point to achieve local stability by using the basic regeneration number. The invention provides a novel coronavirus propagation model, which simulates and analyzes the influence of an isolation period and a vaccination rate on a virus propagation process, proves that strict control measures have a better control effect on the propagation of new coronavirus, and verifies that the model has better fitting goodness by acquiring actual case data and fitting the model and the actual data.

Description

A method and system for establishing a novel coronavirus transmission model

technical field

The present invention relates to the field of virus transmission, in particular to a method and system for establishing a novel coronavirus transmission model.

Background technique

Mathematical models are important tools for examining the spread and control of different infectious diseases. Recently, researchers have proposed many models to study the dynamics of the new coronavirus, but the epidemic situation remains constantly changing, and more comprehensive studies on the spread of the new coronavirus are still needed.

Contents of the invention

In order to solve the above technical problems, the present invention provides a method and system for establishing a novel coronavirus transmission model.

The technical solution of the present invention is: a method for establishing a novel coronavirus transmission model, comprising:

Step S1: According to the vaccination rate, isolation period and recovery rate, establish a differential dynamic equation group to construct a new coronavirus transmission model;

Step S2: According to the differential dynamic equations, using dynamic modeling to obtain the disease-free equilibrium point and the diseased equilibrium point of the new coronavirus transmission model;

Step S3: Perform a stability analysis on the novel coronavirus transmission model, and use the basic reproduction number to determine the conditions required to make the disease-free equilibrium point and the diseased equilibrium point reach local stability.

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

The present invention is based on the theory of epidemic transmission, and considering that the isolation period and vaccination rate of susceptible groups can affect the virus transmission process, a new coronavirus transmission model is proposed, and the effect of isolation period and vaccination rate on the virus transmission process is simulated and analyzed. It proves that strict control measures have a good control effect on the spread of the new coronavirus, and by collecting actual case data and fitting the model with the actual data, it is verified that the model has a good goodness of fit.

Description of drawings

Fig. 1 is a flow chart of a method for establishing a novel coronavirus transmission model in an embodiment of the present invention;

Fig. 2 is a schematic diagram of the state transition of various groups of people in the model of the embodiment of the present invention;

Figure 3 is step S2 in a method for establishing a new coronavirus transmission model in an embodiment of the present invention: according to the differential dynamics equations, using dynamic modeling to obtain the disease-free equilibrium point and the diseased equilibrium point of the new coronavirus transmission model flow chart;

Figure 4 is step S3 in a method for establishing a novel coronavirus transmission model in an embodiment of the present invention: performing a stability analysis on the novel coronavirus transmission model, and using the basic reproduction number to determine that the disease-free equilibrium point and the diseased equilibrium point are locally stable A flowchart of the conditions required;

Fig. 5 is a curve diagram of the density of various groups of people at the disease-free equilibrium point of the new coronavirus transmission model in the embodiment of the present invention over time;

Fig. 6 is a curve diagram of the density of various groups of people at the sick balance point of the new coronavirus transmission model in the embodiment of the present invention over time;

Fig. 7 is the curve graph of the density of infected population changing with time under different isolation periods in the embodiment of the present invention;

Fig. 8 is a curve diagram of the immunized population changing over time under different vaccination rates in the embodiment of the present invention;

Fig. 9 is a structural block diagram of a system for establishing a novel coronavirus transmission model in an embodiment of the present invention.

Detailed ways

The present invention provides a method for establishing a new coronavirus transmission model, using the new coronavirus transmission model to simulate and analyze the impact of the isolation period and vaccination rate on the virus transmission process, and prove that strict control measures have a better effect on the spread of the new coronavirus Control effect.

In order to make the purpose, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below through specific implementation and in conjunction with the accompanying drawings.

Embodiment one

As shown in Figure 1, a method for establishing a novel coronavirus transmission model provided by an embodiment of the present invention includes the following steps:

Step S1: According to the vaccination rate, isolation period and recovery rate, establish a differential dynamic equation group to construct a new coronavirus transmission model;

Step S2: According to the differential dynamic equations, use dynamic modeling to obtain the disease-free equilibrium point and the diseased equilibrium point of the new coronavirus transmission model;

Step S3: Perform a stability analysis on the spread model of the new coronavirus, and use the basic reproduction number to determine the conditions required to make the disease-free equilibrium point and the diseased equilibrium point reach local stability.

In one embodiment, the above step S1: according to the inoculation rate, the isolation period and the recovery rate, establish a differential kinetic equation system, specifically including:

表示隔离期，β表示接种率，γ表示恢复率。Among them, S(t), I(t), and R(t) represent the density of susceptible, infected, and immune persons at time t, respectively, and μ represents the in-migration rate and out-migration rate of users,

Indicates the isolation period, β indicates the vaccination rate, and γ indicates the recovery rate.

In the embodiment of the present invention, the transmission rules for defining the new coronavirus are as follows:

(1) Considering the dynamic changes of the population, rather than spreading in a closed system;

(2) Divide the population into three categories, namely susceptible, infected and immune;

(3) Considering the impact of the isolation time of susceptible people on the spread of the new coronavirus, it is defined that in the process of converting a susceptible person into an infected person, the infection rate will decrease due to the increase in the isolation time;

(4) Considering the impact of the vaccination rate on the spread of the new coronavirus, it is defined that in the process of converting susceptible people into immunized people, due to the increase in vaccination rate, the number of immune populations will increase.

Fig. 2 shows a schematic diagram of state transition of various groups of people in the model of the embodiment of the present invention.

As shown in Figure 3, in one embodiment, the above step S2: according to the differential dynamics equations, using dynamic modeling to obtain the disease-free equilibrium point and the diseased equilibrium point of the new coronavirus transmission model, specifically including:

记为P₁＝(S₁，I₁，R₁)；Step S21: According to the formula (1), calculate the disease-free equilibrium point

Recorded as P ₁ =(S ₁ , I ₁ , R ₁ );

记为P₂＝(S₂，I₂，R₂)。Step S22: According to the formula (1), calculate the sick equilibrium point

Denote as P ₂ =(S ₂ , I ₂ , R ₂ ).

As shown in Figure 4, in one embodiment, the above step S3: perform stability analysis on the new coronavirus transmission model, and use the basic reproduction number to determine the conditions required to make the disease-free equilibrium point and the diseased equilibrium point reach local stability, Specifically include:

Step S31: Calculate the basic reproduction number R ₀ by using the reproduction matrix spectral radius method;

First, the novel coronavirus transmission model is recorded as the following formula:

in,

与矩阵ψ在P₁处的雅可比矩阵分别为：Second, the matrix

and the Jacobians of the matrix ψ at _P1 are:

in,

Then you can get,

The spectral radius of FV ^-1 can be obtained as the basic reproduction number R ₀ :

Step S32: Through the Routh-Hurwitz discriminant condition, and according to R ₀ and the disease-free equilibrium point P ₁ = (S ₁ , I ₁ , R ₁ ), it can be known that the disease-free equilibrium point needs to satisfy the condition R ₀ ≤ 1 to achieve local stability;

First, according to formula (1) and P ₁ , the Jacobian matrix can be obtained as:

make

The eigenvalues obtained are as follows:

λ ₁ =-μ-γ

λ ₂ =-μ

According to the Routh-Hurwitz discriminant condition, when R ₀ ≤ 1, the above three eigenvalues are all less than 0, that is, all eigenvalues have negative real parts, and the disease-free equilibrium point P ₁ is locally stable;

Step S33: Through the Routh-Hurwitz discriminant condition, and according to R ₀ and the diseased equilibrium point P ₂ = (S ₂ , I ₂ , R ₂ ), it can be known that the diseased equilibrium point needs to satisfy the condition R ₀ >1 to achieve local stability;

According to formula (1) and P ₂ , the Jacobian matrix can be obtained as:

make

The eigenvalues obtained are as follows:

λ ₁ =-μ-γ

According to the Routh-Hurwitz discriminant condition, when R ₀ >1, the above three eigenvalues are all less than 0, that is, all eigenvalues have negative real parts, and the sick equilibrium point P ₂ is locally stable.

Using the new coronavirus transmission model, the simulation analysis of the density of various populations at the disease-free equilibrium point changes over time, and the results are shown in Figure 5.

Using the new coronavirus transmission model, the simulation analysis of the changes of various groups of people at the sick balance point over time, the results are shown in Figure 6.

Using the new coronavirus transmission model, the simulation analysis of the density of infected people over time under different isolation periods is shown in Figure 7. Figure 7 shows the impact of changes in population isolation time on the number of people infected with the new coronavirus. As the time increases, the number of infections is decreasing, indicating that isolation has a great impact on the changes in the number of new coronavirus infections.

Using the new coronavirus transmission model, the simulation analysis under different vaccination rates, the density of infected population changes over time, the results are shown in Figure 8, Figure 8 shows the impact of changes in the vaccination rate on the number of people infected with the new coronavirus. It can be seen that the higher the vaccination rate, the greater the number of immunized people, and the number of infected people will also be reduced to a certain extent. It shows that the difference in vaccination rate will affect the changes in the number of people immune to the new crown virus. However, since the new crown vaccine will only become popular in January 2021, the collected data cannot reflect the impact of the vaccination rate on the spread of the new crown virus. However, through numerical simulation As a result, it can be concluded that as the vaccination rate increases, the number of immune populations can be effectively increased.

According to the actual data of the novel coronavirus epidemic situation in Beijing issued by the Beijing Municipal Health Commission, the novel coronavirus transmission model in the embodiment of the present invention is fitted with the actual data, and the relevant parameters in the model are estimated based on the collected actual data. The least square method was used for data fitting, and the goodness of fit of the new coronavirus transmission model in the embodiment of the present invention was verified.

The present invention is based on the theory of epidemic transmission, and considering that the isolation period and vaccination rate of susceptible groups can affect the virus transmission process, a new coronavirus transmission model is proposed, and the effect of isolation period and vaccination rate on the virus transmission process is simulated and analyzed. It proves that strict control measures have a good control effect on the spread of the new coronavirus, and by collecting actual case data and fitting the model with the actual data, it is verified that the model has a good goodness of fit.

Embodiment two

As shown in Figure 9, the embodiment of the present invention provides a novel coronavirus transmission model building system, including the following modules:

Constructing the new coronavirus transmission model module 41, which is used to establish a differential dynamic equation set according to the vaccination rate, isolation period and recovery rate, so as to build a new coronavirus transmission model;

Obtain the disease-free balance point and the disease-free balance point module 42, which is used to obtain the disease-free balance point and the disease-free balance point of the new coronavirus transmission model according to the differential dynamics equations, using dynamic modeling;

Determine the local equilibrium condition module 43 of the disease-free equilibrium point and the diseased equilibrium point, which is used to analyze the stability of the new coronavirus transmission model, and use the basic reproduction number to determine the local stability of the disease-free equilibrium point and the diseased equilibrium point. condition.

The above embodiments are provided only for the purpose of describing the present invention, not to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalent replacements and modifications made without departing from the spirit and principle of the present invention shall fall within the scope of the present invention.

Claims (3)

1. A method for establishing a novel coronavirus transmission model, comprising: Step S1: Based on the vaccination rate, isolation period and recovery rate, establish a differential dynamic equation system to construct a new coronavirus transmission model: According to the vaccination rate, isolation period and recovery rate, establish a differential dynamic equation system, including:

Among them, S(t), I(t), and R(t) represent the density of susceptible, infected, and immune persons at time t, respectively, and μ represents the in-migration rate and out-migration rate of users,

Indicates the isolation period, β indicates the vaccination rate, and γ indicates the recovery rate; Step S2: According to the differential dynamic equations, use dynamic modeling to obtain the disease-free equilibrium point and the diseased equilibrium point of the new coronavirus transmission model, specifically including: Step S21: Calculate the disease-free equilibrium point P ₁ =(S ₁ , I ₁ , R ₁ ) according to formula (1), where,

Step S22: According to the formula (1), calculate the sick equilibrium point P ₂ =(S ₂ , I ₂ , R ₂ ), where,

Step S3: Perform a stability analysis on the novel coronavirus transmission model, and use the basic reproduction number to determine the conditions required to make the disease-free equilibrium point and the diseased equilibrium point reach local stability. 2. The method for establishing a new coronavirus transmission model according to claim 1, characterized in that, the step S3: performing a stability analysis on the new coronavirus transmission model, using the basic reproduction number to determine the disease-free balance Point and the conditions required for local stability of the diseased equilibrium point, specifically include: Step S31: Calculate the basic reproduction number R ₀ by using the reproduction matrix spectral radius method; Step S32: Through the Routh-Hurwitz discriminant condition, and according to R ₀ and the disease-free equilibrium point P ₁ = (S ₁ , I ₁ , R ₁ ), it can be known that the disease-free equilibrium point needs to satisfy the condition R ₀ to achieve local stability ≤1; Step S33: According to the Routh-Hurwitz discriminant condition, and according to R ₀ and the diseased equilibrium point P ₂ =(S ₂ , I ₂ , R ₂ ), it can be known that the diseased equilibrium point needs to satisfy the condition R ₀ to achieve local stability >1. 3. A novel coronavirus transmission model building system, characterized in that it comprises the following modules: Construct the new crown virus transmission model module, which is used to establish a differential dynamic equation set according to the vaccination rate, isolation period and recovery rate to build a new crown virus transmission model: according to the vaccination rate, isolation period and recovery rate, establish a differential dynamic equation set, Specifically include:

Among them, S(t), I(t), and R(t) represent the density of susceptible, infected, and immune persons at time t, respectively, and μ represents the in-migration rate and out-migration rate of users,

Indicates the isolation period, β indicates the vaccination rate, and γ indicates the recovery rate; Obtaining a disease-free balance point and a disease-free balance point module, which is used to obtain the disease-free balance point and the sick balance point of the new coronavirus transmission model according to the differential dynamic equations, using dynamic modeling, specifically including: Step S21: Calculate the disease-free equilibrium point P ₁ =(S ₁ , I ₁ , R ₁ ) according to formula (1), where,

Step S22: According to the formula (1), calculate the sick equilibrium point P ₂ =(S ₂ , I ₂ , R ₂ ), where,

Determine the disease-free equilibrium point and the local equilibrium condition module of the disease-free equilibrium point, which is used to analyze the stability of the new coronavirus transmission model, and use the basic reproduction number to determine that the disease-free equilibrium point and the diseased equilibrium point reach Conditions required for local stability.

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