A parameter estimation method, apparatus, and electronic equipment for a fractional-order infectious disease model.

Abstract

This invention discloses a parameter estimation method, apparatus, and electronic device for a fractional-order infectious disease model. Specifically, it includes: for the fractional-order infectious disease model, treating system parameters and the fractional order as independent unknown variables, transforming the parameter estimation problem into an optimization problem; based on real data of the infectious disease transmission process, using an improved particle swarm optimization algorithm to find the minimum value of the objective function, thereby determining the optimal results for the system parameters and the fractional order, and obtaining a more suitable infectious disease model to describe the transmission process. This invention's infectious disease model based on fractional-order calculus can well fit the dynamic transmission process of infectious diseases, and the improved particle swarm optimization algorithm can provide an effective tool for parameter estimation of nonlinear fractional-order systems, greatly improving the accuracy of parameter estimation for fractional-order infectious disease models.

Description

Technical Field

[0001] This invention relates to the field of system modeling and parameter identification, and in particular to a parameter estimation method, apparatus and electronic device for a fractional-order infectious disease model. Background Technology

[0002] The spread of the pandemic has had severe consequences for human health and the global economy. Research on the dynamics of infectious diseases has attracted widespread attention and has become an interdisciplinary field spanning mathematics, epidemiology, computational physics, ecology, evolutionary biology, immunology, sociology, and public health. Therefore, modeling infectious diseases and studying their transmission characteristics is of significant practical importance for understanding and suppressing disease outbreaks.

[0003] Currently, a common method for studying infectious disease dynamics is to establish integer-order models, among which the SI and SIR models have been widely used. However, integer-order models typically neglect the memory and nonlocal properties of disease transmission, thus having certain limitations. Among commonly used parameter estimation methods, the Particle Swarm Optimization (PSO) algorithm has been used to solve many different optimization problems due to its simplicity and ease of implementation. However, existing techniques still suffer from drawbacks such as neglecting memory characteristics and the nonlocal nature of disease spread, difficulty in balancing local exploration and global search, and a tendency to get trapped in local optima.

[0004] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention

[0005] This invention aims to solve the technical problems of existing technologies that often ignore memory characteristics and the non-local nature of disease spread, make it difficult to achieve a balance between local exploration and global search, and are prone to getting trapped in local optima.

[0006] The technical solution adopted in this invention is as follows: a parameter estimation method, device, and electronic device for a fractional-order infectious disease model are provided.

[0007] According to a first aspect of the present invention, a parameter estimation method for a fractional-order infectious disease model includes the following steps:

[0008] S1: Establish a fractional-order infectious disease model and a corresponding estimation system model;

[0009] S2: The system parameters and fractional order of the fractional infectious disease model are estimated as independent unknown parameters, transforming the parameter identification problem of the fractional infectious disease model into an optimization problem.

[0010] S3: Construct an improved particle swarm optimization algorithm to find the minimum value of the objective function, thereby determining the optimal results for system parameters and fractional order.

[0011] Furthermore, the establishment of the fractional-order infectious disease model described in step S1 includes:

[0012] S1.1: Obtain infectious disease data within a time period T, including the daily number of new infections, the cumulative number of confirmed cases, the number of recoveries and deaths, and preprocess the infectious disease data;

[0013] S1.2: Based on the transmission characteristics of infectious diseases and the characteristics of the dataset, the population is divided into four categories: S, E, I and R. Among them, S and E represent susceptible populations and exposed individuals, respectively, I represents infected individuals, and R represents the number of recovered or deceased individuals.

[0014] S1.3: Based on the above population classification and preprocessed infectious disease data, the following fractional-order infectious disease model is established:

[0015]

[0016]

[0017]

[0018]

[0019] Where q∈(0,1] represents the fractional order. Let α1 represent the q-th order Caputo fractional derivative, N = S + E + I + R represent the total number of people affected by the infectious disease; α2 represent the probability that a healthy person becomes an exposed person through contact with an exposed person in the incubation period; σ represents the probability of diagnosis; and γ represents the probability of recovery or death.

[0020] The above fractional-order infectious disease model can be represented in the following vector form: Where X(t)=(S(t), E(t), I(t), R(t)) T t∈[0,T] represents the system state, X0=(S0,E0,I0,R0) T The initial conditions for the system are θ = (α1, α2, σ, γ). T This represents the unknown parameters of the system.

[0021] Furthermore, the establishment of the corresponding estimation system model as described in S1 includes:

[0022] The estimated system model established based on the fractional-order infectious disease model is as follows:

[0023]

[0024]

[0025]

[0026]

[0027] The above estimation system model is expressed as: in t∈[0,T] represents the estimated state vector of the system. Let θ be an estimate.

[0028] Furthermore, step S2, which transforms the parameter identification problem of the fractional-order infectious disease model into an optimization problem, includes:

[0029] S2.1: Establish the objective function;

[0030] S2.2: Set the objective function sampling termination time t for the optimization problem n And step size h.

[0031] Furthermore, the expression for the objective function is as follows:

[0032]

[0033] Where Ω represents the search space range, ||·|| E This represents the Euclidean norm.

[0034] Furthermore, the construction of the improved particle swarm optimization algorithm described in step S3 includes:

[0035] S3.1: Initialize the parameters of the particle swarm optimization algorithm, including setting the population size N. p The number of iterations N, and the upper and lower bounds of the search space x max，j and x min，j The learning factor in the speed update formula is c1 = c2;

[0036] S3.2: Set the initial velocity v for particle swarm optimization. i，j =(v i，1 v i，2 , ..., v i，D ) = 0, where D represents the dimension of the search space, and the particle's position is initialized according to the following rules:

[0037] x i，j =x min，j +(x max，j -x min，j )*ε

[0038] Where x min，j x max，j Let represent the lower and upper bounds of the search space, respectively, and let ε represent a random number uniformly distributed in the interval [0, 1].

[0039] S3.3: Introduce a generalized back-learning method when initializing particle positions, and find the position x according to the following rules. i，j Reverse candidate solution

[0040]

[0041] in This represents the minimum and maximum values ​​of the j-th dimension in the current population during the k-th iteration; if a particle exceeds the boundary during the backward learning of the generalization, i.e. The following rules are used to restrict particles:

[0042]

[0043] S3.4: Determine the fitness function of the particle swarm optimization algorithm based on the objective function:

[0044]

[0045] in

[0046]

[0047] In the formula X k (·,q,θ) and Let ||·|| represent the true state vector and the estimated state vector of the system when the sampling time is k, respectively. E The Euclidean norm is represented, and the numerical solution of the system is estimated using the predictor-corrector method.

[0048] S3.5: Calculate the fitness value of each particle and its reverse candidate solution based on the fitness function, and retain the top N with the smallest fitness values. p For each particle, the historical best position pbest and the global best position gbest are determined according to the greedy principle.

[0049] S3.6: Introduces Lévy flight to update particle velocity and position;

[0050] S3.7: Apply boundary constraints:

[0051]

[0052] S3.8: Introduce generalized reverse learning, evaluate candidate solutions and their reverse solutions based on the particle's fitness value, and retain the top N. pEach particle is processed, and its pbest and gbest values ​​are updated according to a greedy principle.

[0053] S3.9: Determine whether the iteration termination condition is met. If it is met, output the optimal position gbest and end the iteration; otherwise, return to step S3.6.

[0054] S3.10: After the iteration is completed, the output optimal position vector gbest is the value of the parameters q and θ to be identified.

[0055] Furthermore, step S3.6, which introduces Lévy flight to update the velocity and position of the particles, includes:

[0056] Lévy flight is introduced to dynamically update the inertial weights and random functions, which help particles escape local optima by occasionally generating large values;

[0057] ω~L(x,α,β), rand1~L(x,α,β), rand2~L(x,α,β)

[0058] L(x, α, β) represents the Lévy flight distribution function; the above formula means modifying ω, rand1, and rand2 to be random numbers that satisfy the Lévy flight distribution function;

[0059] The update formulas for the velocity and position of particle i in the j-th dimension during the k-th iteration are as follows:

[0060]

[0061] In the formula This represents the particle's velocity at the (k+1)th iteration; Let be the current velocity of particle i; Let be the position of the individual extreme point of particle i in the j-dimensional space during the k-th iteration. ω represents the position of the global extreme point in the j-dimensional space during the k-th iteration; ω is the inertia weight used to control the particle velocity; rand1 and rand2 represent random functions; c1 and c2 are acceleration coefficients, which adjust the maximum step size of the particle flying in the pbest and gbest directions, respectively. Let i represent the current position of particle i and the position of particle i at iteration k+1, respectively.

[0062] According to a second aspect of the present invention, a parameter estimation device for a fractional-order infectious disease model includes the following units:

[0063] The model building unit is used to build fractional-order infectious disease models and corresponding estimation system models.

[0064] The problem transformation unit is used to estimate the system parameters and fractional order of the fractional infectious disease model as independent unknown parameters, transforming the parameter identification problem of the fractional infectious disease model into an optimization problem.

[0065] The parameter identification unit is used to construct an improved particle swarm optimization algorithm. The improved particle swarm optimization algorithm is used to find the minimum value of the objective function, thereby determining the optimal results of the system parameters and fractional order.

[0066] According to a third aspect of the present invention, an electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the fractional-order infectious disease model parameter estimation method.

[0067] According to a fourth aspect of the invention, a storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the fractional-order infectious disease model parameter estimation method.

[0068] The technical solution provided by this invention has the following beneficial effects:

[0069] (1) Using fractional calculus for modeling better reflects the actual situation and can more accurately describe the memory and nonlocality characteristics of the system.

[0070] (2) A parameter estimation method for fractional-order infectious disease models based on an improved particle swarm optimization algorithm solves the problem that traditional particle swarm optimization algorithms are prone to getting trapped in local minima. In the improved particle swarm optimization algorithm, when a particle gets trapped in a local optimum, the occasionally larger step size generated during flight can help the particle escape the local optimum, making the identification results closer to the true values ​​and having good accuracy. The generalized back learning method can help increase population diversity and accelerate the convergence speed. Attached Figure Description

[0071] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0072] Figure 1 This is a flowchart illustrating the overall process of parameter estimation for a fractional-order infectious disease model in an embodiment of the present invention.

[0073] Figure 2 This is a diagram showing the variable structure of the fractional-order SEIR infectious disease model in this embodiment of the invention.

[0074] Figure 3 This is a flowchart of the improved particle swarm optimization algorithm in an embodiment of the present invention;

[0075] Figure 4 This is a numerical simulation diagram of the fractional-order SEIR infectious disease model in an embodiment of the present invention;

[0076] Figure 5 This is a curve showing the fitting of the model results to the real data in the implementation of this invention;

[0077] Figure 6 The diagram shows the evolution of the objective function of the improved particle swarm optimization algorithm and the traditional particle swarm optimization algorithm in the embodiments of the present invention.

[0078] Figure 7 This is a schematic diagram of the overall structure of a parameter estimation device for a fractional-order infectious disease model according to an embodiment of the present invention. Detailed Implementation

[0079] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0080] This invention takes an outbreak as an example, establishes a fractional-order SEIR infectious disease model, and identifies the parameters of the fractional-order SEIR infectious disease model by introducing a particle swarm optimization algorithm improved by flight and generalization back learning. The overall process framework is as follows: Figure 1 As shown. To further illustrate the technical solution provided by the present invention, the specific steps of the embodiment are as follows:

[0081] S1: Establish a fractional-order SEIR infectious disease model and a corresponding estimation system model;

[0082] Specifically, it includes:

[0083] S1.1: Obtain epidemic data over a period of time, including daily new infections, cumulative confirmed cases, recoveries and deaths, and preprocess the data.

[0084] S1.2: Based on the characteristics of epidemic transmission and dataset features, the population is divided into four categories: S, E, I, and R. S and E represent susceptible individuals and exposed individuals, respectively; I represents infected individuals; and R represents the number of recovered or deceased individuals.

[0085] S1.3: Based on the above population classification, the following fractional-order SEIR infectious disease model is established:

[0086]

[0087]

[0088]

[0089]

[0090] Where q∈(0,1] represents the fractional order. Let α1 represent the q-th order Caputo fractional derivative, N = S + E + I + R represent the total number of people affected by the infectious disease; α1 represents the constant infection rate, α2 represents the probability that a healthy person becomes exposed through contact with an exposed person in the incubation period, σ represents the probability of diagnosis, and γ represents the probability of recovery or death; the variable structure relationship is as follows: Figure 2 As shown.

[0091] The above fractional-order infectious disease model can be represented in the following form: Where X(t)=(S(t), E(t), I(t), R(t)) T t∈[0,T] represents the system state, X0=(S0,E0,I0,R0) T The initial conditions for the system are θ = (α1, α2, σ, γ). T This represents the unknown parameters of the system. The acquired data is preprocessed to obtain the system state vector X(t) and the initial state vector X0. The numerical simulation results of the actual data are as follows: Figure 4 As shown.

[0092] S1.4: The estimated system model established based on the above system model is as follows:

[0093]

[0094]

[0095]

[0096]

[0097] The above system is represented as in and The optimal values ​​of the system parameters to be identified are obtained through an improved particle swarm optimization algorithm.

[0098] S2: The system parameters θ = (α1, α2, σ, γ) of the fractional-order infectious disease model. T The fractional order q is estimated as an independent unknown parameter, transforming the parameter identification problem of the fractional infectious disease model into an optimization problem.

[0099] The implementation process of S2 is as follows:

[0100] S2.1: Establish the objective function:

[0101]

[0102] Where Ω=[0.8,1]×[0.01,5]×[0.01,5]×[0.01,1]×[0.01,2] represents the search space range, ||·|| E Denotes the Euclidean norm;

[0103] S2.2: Set the objective function sampling termination time t for the optimization problem n =5, step size h=0.1.

[0104] It should be noted that the search space range, sampling termination time, and step size mentioned above are preferred data in this embodiment. In other embodiments, they can be adjusted according to actual needs.

[0105] S3: Construct an improved particle swarm optimization algorithm, and use the improved particle swarm optimization algorithm to find the minimum value of the objective function, thereby determining the optimal results of system parameters and fractional order.

[0106] like Figure 3 As shown, the specific implementation steps of step S3 are as follows:

[0107] S3.1: Initialize the parameters of the particle swarm optimization algorithm, including setting the population size N. p The number of iterations N, and the upper and lower bounds of the search space x max，j and x min，j The learning factor in the speed update formula is c1 = c2;

[0108] Preferably, the population size N is set. p =50, iteration count N=100, upper and lower bounds of the search space x max，j = (1, 5, 5, 1, 2) and x min，j = (0.8, 0.01, 0.01, 0.01, 0.01), where the learning factors c1 = c2 = 2 in the speed update formula. In other embodiments, the above data can be adjusted according to actual needs.

[0109] S3.2: Set the initial velocity v for particle swarm optimization. i，j =(v i，1 v i，2 , ..., v i，D ) = 0, where D represents the dimension of the search space, and the particle's position is initialized according to the following rules:

[0110] x i，j =x min，j +(x max，j -x min，j )*ε

[0111] Where x min，j x max，jLet represent the lower and upper bounds of the search space, respectively, and let ε represent a random number uniformly distributed in the interval [0, 1].

[0112] S3.3: Introduce a generalized back-learning method when initializing particle positions, and find the position x according to the following rules. i，j Reverse candidate solution

[0113]

[0114] in This represents the minimum and maximum values ​​of the j-th dimension in the current population during the k-th iteration; if a particle exceeds the boundary during the backward learning of the generalization, i.e. The following rules are used to restrict particles:

[0115]

[0116] S3.4: Determine the fitness function of the particle swarm optimization algorithm based on the objective function:

[0117]

[0118] in

[0119]

[0120] In the formula X k (·,q,θ) and Let ||·|| represent the true state vector and the estimated state vector of the system when the sampling time is k, respectively. E The Euclidean norm is represented by the value of the numerical solution of the system. The numerical solution of the system is estimated by the prediction and correction method, which is a commonly used method for solving numerical solutions of fractional-order systems.

[0121] S3.5: Calculate the fitness value of each particle and its reverse candidate solution based on the fitness function, and retain the top N with the smallest fitness values. p For each particle, the historical best position pbest and the global best position gbest are determined according to the greedy principle.

[0122] S3.6: Introducing Lévy flight to update particle velocity and position:

[0123] Smaller inertia weights lead to poorer population diversity, while larger inertia weights can increase computation time. This embodiment introduces Lévy flight to dynamically update the inertia weights and the random function, and uses the Lévy distribution to achieve long-distance jump search, which utilizes the search space more effectively than traditional algorithms to achieve the goal of obtaining the global optimum.

[0124] Lévy flight is a class of non-Gaussian stochastic processes whose step size satisfies the following Lévy distribution function L(x, α, β):

[0125]

[0126] Where α represents the location parameter and β represents the scale parameter of the degree of distribution dispersion.

[0127] Calculate Lévy flight using computer-generated symmetric stable random variables:

[0128] If α ≠ 1, then calculate:

[0129]

[0130] in V is a random variable uniformly distributed over an interval, and W is an independent exponential random variable with a mean of 1.

[0131] If α = 1, then:

[0132]

[0133] Modifying ω, rand1, and rand2 to satisfy Lévy flight random vectors allows particles to occasionally generate large velocities, increasing population diversity and helping particles escape local optima.

[0134] ω~L(x,α,β), rand1~L(x,α,β), rand2~L(x,α,β)

[0135] L(x, α, β) represents the Lévy flight distribution function; the above formula means modifying ω, rand1, and rand2 to be random numbers that satisfy the Lévy flight distribution function.

[0136] The update formulas for the velocity and position of particle i in the j-th dimension during the k-th iteration are as follows:

[0137]

[0138] In the formula This represents the particle's velocity at the (k+1)th iteration; Let be the current velocity of particle i; Let be the position of the individual extreme point of particle i in the j-dimensional space during the k-th iteration. ω represents the position of the global extreme point in the j-dimensional space during the k-th iteration; ω is the inertia weight used to control the particle velocity; rand1 and rand2 represent random functions; c1 and c2 are acceleration coefficients, which adjust the maximum step size of the particle flying in the pbest and gbest directions, respectively. Let i represent the current position of particle i and the position of particle i at iteration k+1, respectively.

[0139] S3.7: Apply boundary constraints:

[0140]

[0141] S3.8: Introduce generalized reverse learning, evaluate candidate solutions and their reverse solutions based on the particle's fitness value, and retain the top N. p Each particle is processed, and its pbest and gbest values ​​are updated according to a greedy principle.

[0142] S3.9: Determine whether the iteration termination condition is met. If it is met, output the optimal position gbest and end the iteration; otherwise, return to step S3.6.

[0143] S3.10: After the iteration, the output optimal position vector gbest is the value of the parameters q and θ to be identified, and finally a more suitable infectious disease model for describing the transmission process is obtained.

[0144] In this embodiment, the fitting curve of the number of infections between the simulation results and the real data is as follows: Figure 5 As shown, circles represent the actual number of infected individuals, and solid lines represent the simulation results obtained by substituting the numerical values ​​of the identification parameters. In this embodiment, parameter identification was performed on the aforementioned epidemic data using both the traditional particle swarm optimization algorithm and the improved particle swarm optimization algorithm proposed in this embodiment. The evolution process of the objective function for both algorithms is as follows: Figure 6 As shown in Figure 6, the improved particle swarm optimization algorithm has better accuracy than the traditional algorithm.

[0145] The key technical point of this invention is:

[0146] 1. Lévy flight and promotion of reverse learning combined with particle swarm optimization algorithm to produce an overall framework for improving particle swarm optimization algorithm.

[0147] 2. How to use the improved particle swarm optimization algorithm to solve the parameter estimation problem of fractional-order infectious disease models, form a system, and lay the foundation for subsequent dynamic analysis and control research of fractional-order systems.

[0148] The results of the embodiments of this invention show that the fractional-order infectious disease model established by this invention can more accurately simulate the spread of an epidemic, providing an important foundation for formulating epidemic control measures. Furthermore, the improved particle swarm optimization algorithm proposed in this invention effectively increases the global search capability of particles, largely solving the defect of classical particle swarm optimization algorithms that easily lead to local errors in the search strategy. The parameter estimation method for the fractional-order infectious disease model based on the improved particle swarm optimization algorithm shows significant improvements in both prediction speed and effectiveness compared to existing methods.

[0149] It should be noted that the parameter estimation method for a fractional-order infectious disease model provided by this invention is not only applicable to the parameter estimation of the above-mentioned fractional-order SEIR model, but also applicable to the parameter estimation of any type of fractional-order infectious disease model, and its implementation steps are similar to the above method.

[0150] The following describes a parameter estimation device for a fractional-order infectious disease model provided by the present invention. The parameter estimation device for a fractional-order infectious disease model described below can be referred to in correspondence with the parameter estimation method for a fractional-order infectious disease model described above.

[0151] like Figure 7 As shown, this embodiment of the invention provides a parameter estimation device for a fractional-order infectious disease model, comprising the following units:

[0152] Model building unit 1 is used to build a fractional-order infectious disease model and the corresponding estimation system model;

[0153] Problem transformation unit 2 is used to estimate the system parameters and fractional order of the fractional infectious disease model as independent unknown parameters, and transform the parameter identification problem of the fractional infectious disease model into an optimization problem.

[0154] The parameter identification unit 3 is used to construct an improved particle swarm optimization algorithm. The improved particle swarm optimization algorithm is used to find the minimum value of the objective function, thereby determining the optimal results of the system parameters and fractional order.

[0155] On the other hand, embodiments of the present invention also provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the fractional-order infectious disease model parameter estimation method.

[0156] In another aspect, embodiments of the present invention provide a storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the fractional-order infectious disease model parameter estimation method.

[0157] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0158] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments. In the unit claims listing several devices, several of these devices may be embodied by the same hardware item. The use of the terms first, second, and third, etc., does not indicate any order and can be interpreted as identifiers.

[0159] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A parameter estimation method for a fractional-order infectious disease model, characterized in that, Includes the following steps: S1: Establish a fractional-order infectious disease model and a corresponding estimation system model; Step S1, which involves establishing a fractional-order infectious disease model, includes: S1.1: Obtain infectious disease data within a time period [0,T], including the daily number of new infections, the cumulative number of confirmed cases, the number of recoveries and deaths, and preprocess the infectious disease data; S1.2: Based on the transmission and data characteristics of infectious diseases, the population is divided into four categories: S, E, I, and R. Among them, S and E represent susceptible populations and exposed individuals, respectively, I represents infected individuals, and R represents the number of recovered or deceased individuals. Step S1, establishing the corresponding estimation system model, includes: The estimated system model established based on the fractional-order infectious disease model is as follows: The above estimation system model is expressed as: in This represents the estimated state vector of the system. It is an estimator of θ; Where q∈(0,1] represents the fractional order. Let α1 represent the q-th order Caputo fractional derivative, N = S + E + I + R represent the total number of people affected by the infectious disease, α2 represent the probability that a healthy person becomes an exposed person through contact with an exposed person in the incubation period, σ represent the probability of diagnosis, and γ represent the probability of recovery or death. S2: The system parameters and fractional order of the fractional infectious disease model are estimated as independent unknown parameters, transforming the parameter identification problem of the fractional infectious disease model into an optimization problem. S3: Construct an improved particle swarm optimization algorithm to find the minimum value of the objective function, thereby determining the optimal results for system parameters and fractional order.

2. The parameter estimation method for the fractional-order infectious disease model according to claim 1, characterized in that, Step S1, which involves establishing a fractional-order infectious disease model, further includes: S1.3: Based on the above population classification and preprocessed infectious disease data, the following fractional-order infectious disease model is established: The above fractional-order SEIR infectious disease model can be represented in the following vector form: Where X(t)=(S(t),E(t),I(t),R(t)) T t∈[0,T] represents the system state, X0=(S0,E0,I0,R0) T Let θ = (α1, α2, σ, γ) be the initial condition for the system. T This represents the unknown parameters of the system.

3. The parameter estimation method for the fractional-order infectious disease model according to claim 2, characterized in that, Step S2, which transforms the parameter identification problem of the fractional-order infectious disease model into an optimization problem, includes: S2.1: Establish the objective function; S2.2: Set the objective function sampling termination time t for the optimization problem n And step size h.

4. The parameter estimation method for the fractional-order infectious disease model according to claim 3, characterized in that, The expression for the objective function is as follows: Where Ω represents the search space range, ||·|| E This represents the Euclidean norm.

5. The parameter estimation method for the fractional-order infectious disease model according to claim 4, characterized in that, Step S3, which involves constructing the improved particle swarm optimization algorithm, includes: S3.1: Initialize the parameters of the particle swarm optimization algorithm, including setting the population size N. p The number of iterations N, and the upper and lower bounds of the search space x max,j and x min,j The learning factor in the speed update formula is c1 = c2; S3.2: Set the initial velocity v for particle swarm optimization. i,j =(v i,1 ,v i,2 ,…,v i,D ) = 0, where D represents the dimension of the search space, and the particle's position is initialized according to the following rules: x i,j =x miu,j +(x max,j -x min,j )*ε Where x min,j x max,j Let represent the lower and upper bounds of the search space, respectively, and let ε represent a random number uniformly distributed in the interval [0,1]. S3.3: Introduce a generalized back-learning method when initializing particle positions, and find the position x according to the following rules. i,j Reverse candidate solution in This represents the minimum and maximum values ​​of the j-th dimension in the current population during the k-th iteration; if a particle exceeds the boundary during the backward learning of the generalization, i.e. The following rules are used to restrict particles: S3.4: Determine the fitness function of the particle swarm optimization algorithm based on the objective function: in In the formula X k (·,q,θ) and Let ||·|| represent the true state vector and the estimated state vector of the system when the sampling time is k, respectively. E The Euclidean norm is represented, and the numerical solution of the system is estimated using the predictor-corrector method. S3.5: Calculate the fitness value of each particle and its reverse candidate solution based on the fitness function, and retain the top N with the smallest fitness values. p For each particle, the historical best position pbest and the global best position gbest are determined according to the greedy principle. S3.6: Introduces Lévy flight to update particle velocity and position; S3.7: Apply boundary constraints: S3.8: Introduce generalized reverse learning, evaluate candidate solutions and their reverse solutions based on the particle's fitness value, and retain the top N. p Each particle is processed, and its pbest and gbest values ​​are updated according to a greedy principle. S3.9: Determine whether the iteration termination condition is met. If it is met, output the optimal position gbest and end the iteration; otherwise, return to step S3.

6. S3.10: After the iteration is completed, the optimal position gbest output is the value of the parameters q and θ to be identified.

6. The parameter estimation method for the fractional-order infectious disease model according to claim 5, characterized in that, Step S3.6, which introduces Lévy flight to update the velocity and position of the particles, includes: Lévy flight is introduced to dynamically update inertial weights and a random function, helping particles escape local optima: ω~L(x,α,β), rand1~L(x,α,β), rand2~L(x,α,β) L(x,α,β) represents the distribution function of Lévy flight, and its calculation formula is: Where α represents the location parameter and β represents the scale parameter of the distribution dispersion; the above formula means modifying ω, rand1 and rand2 to be random numbers that satisfy the Lévy flight distribution function; The update formulas for the velocity and position of particle i in the j-th dimension during the k-th iteration are as follows: In the formula This represents the particle's velocity at the (k+1)th iteration; Let be the current velocity of particle i; Let be the position of the individual extreme point of particle i in the j-dimensional space during the k-th iteration. ω represents the position of the global extreme point in the j-dimensional space during the k-th iteration; ω is the inertia weight used to control the particle velocity; rand1 and rand2 represent random functions; c1 and c2 are acceleration coefficients, which adjust the maximum step size of the particle flying in the pbest and gbest directions, respectively. Let i represent the current position of particle i and the position of particle i at iteration k+1, respectively.

7. A parameter estimation device based on a fractional-order infectious disease model, characterized in that, Includes the following units: The model building unit is used to build fractional-order infectious disease models and corresponding estimation system models. The model building unit, which establishes a fractional-order infectious disease model, includes: S1.1: Obtain infectious disease data within a time period [0,T], including the daily number of new infections, the cumulative number of confirmed cases, the number of recoveries and deaths, and preprocess the infectious disease data; S1.2: Based on the transmission and data characteristics of infectious diseases, the population is divided into four categories: S, E, I, and R. Among them, S and E represent susceptible populations and exposed individuals, respectively, I represents infected individuals, and R represents the number of recovered or deceased individuals. The model building unit establishes the corresponding estimation system model, including: The estimated system model established based on the fractional-order infectious disease model is as follows: The above estimation system model is expressed as: in This represents the estimated state vector of the system. It is an estimator of θ; Where q∈(0,1] represents the fractional order. Let α1 represent the q-th order Caputo fractional derivative, N = S + E + I + R represent the total number of people affected by the infectious disease, α2 represent the probability that a healthy person becomes an exposed person through contact with an exposed person in the incubation period, σ represent the probability of diagnosis, and γ represent the probability of recovery or death. The problem transformation unit is used to estimate the system parameters and fractional order of the fractional infectious disease model as independent unknown parameters, transforming the parameter identification problem of the fractional infectious disease model into an optimization problem. The parameter identification unit is used to construct an improved particle swarm optimization algorithm. The improved particle swarm optimization algorithm is used to find the minimum value of the objective function, thereby determining the optimal results of the system parameters and fractional order.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the parameter estimation method for the fractional-order infectious disease model as described in any one of claims 1-6.

9. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the parameter estimation method for the fractional-order infectious disease model as described in any one of claims 1-6.

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