PINN-based natural epidemic disease transmission mechanism modeling method and system

Abstract

The invention provides a PINN-based natural epidemic disease transmission mechanism modeling method and system, which are used for mechanism deduction and space-time prediction of a natural epidemic disease transmission process. The method comprises the following steps: firstly, constructing a host population model and a host-population coupling propagation dynamics model; secondly, the dynamic equation set serves as a physical constraint to be embedded into the physical information neural network; and finally, through joint loss function optimization network learning, bidirectional driving of case data prediction and parameter inversion is realized. The method solves the problems that in the prior art, a host-crowd coupling mechanism is lacked, environmental factor modeling is insufficient, and data driving and mechanism modeling are separated, two-way driving of mechanism modeling and data learning is achieved, and space-time simulation precision, interpretability and model generalization ability are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of infectious disease transmission modeling and artificial intelligence, and specifically relates to a host-population coupling dynamics modeling method based on physical information neural network (PINN). Background Technology

[0002] Natural focal diseases typically originate from animal hosts and are influenced by multiple factors, including natural ecology, human activities, and host dynamics. Their transmission processes exhibit multi-level, highly nonlinear, and spatiotemporally heterogeneous characteristics. Traditional differential equation-based modeling methods (such as SIR / SEIR) rely heavily on prior knowledge and are highly sensitive to parameters, making it difficult to integrate dynamic environmental factors. While purely data-driven machine learning methods offer high prediction accuracy, the lack of physical constraints leads to poor generalization, weak interpretability, and difficulty in revealing transmission mechanisms.

[0003] Physics-Informed Neural Network (PINN) is a deep learning framework that embeds differential equations, boundary conditions, and physical constraints into the neural network training process. By guiding the network to approximate solutions to differential equations through physical residuals, PINN maintains high simulation accuracy even with limited observational data, combining mechanistic interpretability with data fitting capabilities. It has been successfully applied in fields such as fluid mechanics and materials science, but its application in infectious disease modeling is still limited, particularly lacking deep fusion methods for host-population coupling mechanisms. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, the purpose of this invention is to provide a modeling method for the transmission mechanism of natural focal diseases based on Physical Information Neural Networks (PINN). This invention aims to address the problems existing in current infectious disease transmission modeling methods, such as the lack of a host-population coupling mechanism, resulting in an inability to accurately describe cross-species transmission paths; neglect of the dynamic feedback regulation of environmental and human factors, leading to insufficient modeling of transmission driving factors; and the separation of data-driven and mechanism-based modeling, resulting in weak model generalization ability and difficulty in generalization. The modeling framework proposed in this invention introduces PINN to embed a multi-level host-population coupled transmission mechanism, achieving bidirectional driving of mechanism modeling and data learning, significantly improving the accuracy, interpretability, and generalization ability of spatiotemporal simulations.

[0005] The technical solution adopted in this invention is: a method for modeling the transmission mechanism of natural focal diseases based on PINN, comprising the following steps: S1, Construction of multi-source heterogeneous datasets; S2, based on the physiological characteristics of the host of the target natural focal disease, constructs the environmental response function of the host's birth rate and carrying capacity as key parameters to characterize its dynamic response to environmental factors. The form of the environmental response function is adjusted or reconstructed according to the epidemiological experiment. S3. Construct a host-population coupled SEI-SEIR propagation dynamics differential equation system, which characterizes the susceptibility within the host population. , infiltration ,Infect Individuals and populations are susceptible , infiltration ,Infect ,recover The dynamic evolutionary process of an individual; S4, with time variable Using the input, a PINN neural network is constructed, and the differential equation in step S3 is transformed into an automatic differential form and embedded into the loss function. The network parameters and the undetermined physical parameters are jointly optimized through backpropagation. S5 employs a GPU-based multi-process computing framework to output time-series curves of state variables, dynamic trends of propagation parameters, environmental response function graphs, and predicted case data, enabling regional modeling and visualization analysis of propagation mechanisms.

[0006] Furthermore, in step S1, epidemiological reporting data, demographic data, natural environment data, and socio-cultural driving factor data of the target area are collected and normalized, interpolated, and missing value imputation are performed to construct a unified spatiotemporal dataset. Among them, the epidemiological reporting data includes the number of new cases per week, the natural environment data includes temperature, precipitation, and vegetation index, and the socio-cultural driving factor data includes population density, traffic flow, and intensity of intervention measures.

[0007] Furthermore, the environmental regulation function in step S2 is not fixed to specific disease physiological data. The function can be expressed as a polynomial, Gaussian, Boltzmann function or a combination thereof. It can be quantitatively fitted and adjusted according to experimental research or epidemiological data of specific target diseases, and has adaptability and flexibility across diseases and regions.

[0008] Furthermore, in step S3, the propagation dynamics equation adopts a propagation dynamics model based on individual SEI-SEIR, and the specific calculation formula is as follows: (1) (2) (3) (4) (5) (6) (7) in, Total number of hosts; The total number of people, For the host's birth rate, For population carrying capacity; These represent the rate of change in the number of susceptible, latent, and infected hosts, respectively. These represent the rate of change in the number of susceptible, latent, infected, and recovered individuals, respectively. These are the infection rate of the host, the incubation period exit rate, and the mortality rate; These are the infection rate, incubation period transfer rate, and recovery rate of the population; , These are the birth rate and death rate of the population, respectively. This represents the rate of immune attenuation.

[0009] Furthermore, the PINN neural network described in step S4 includes one input layer, at least five hidden layers, and one output layer; the hidden layers use the Softplus activation function, and the output layer corresponds to seven state variables. , These are estimates of the host's susceptibility, latency, and infection status, respectively. These represent estimates of the susceptibility, latency, infection, and recovery status of the population.

[0010] Furthermore, in step S4, the composite loss function is defined as follows: (8) in, and These are the data loss weights, physical loss weights, and initial value loss weights, respectively. The data loss term represents the mean square error between the predicted number of cases and the actual observed number. The physical loss term characterizes the degree to which the neural network output satisfies the SEI-SEIR differential equation system, and is obtained by calculating the residuals of the differential equations. This is the initial value loss term, ensuring that the initial state of the SEI-SEIR differential equation system matches the actual observation data; By jointly optimizing the aforementioned loss terms, the backpropagation algorithm is used to simultaneously train the neural network parameters and the epidemiological and ecological dynamic parameters in the differential equation system.

[0011] Furthermore, the data loss term is specifically defined as: (9) in, express The number of new cases predicted in real time is based on the number of asymptomatic carriers. With conversion rate parameters Calculated; This represents the actual number of newly observed cases; MSE is the mean squared error calculation function. The physical loss term is defined as the sum of squares of the residuals of the differential equation: (10) The residual function is given by the following equation: (11) in, This represents the derivative of the state variable, which is calculated using PyTorch's automatic differentiation module. In the SEI-SEIR model, the first... The right-hand side function of a differential equation These correspond to equations (1)-(7) in the system of differential equations, respectively; For state variables; Indicates environmental driving factors; This represents a parameter vector, which includes epidemiological parameters and ecological dynamic parameters.

[0012] Furthermore, the initial value loss term is defined as: (12) in, This indicates the neural network at the initial time. For the The predicted values ​​of each state variable, Indicates the first The state variables at the initial time The actual observed value.

[0013] Furthermore, in step S5, the StepLR learning rate decay strategy is adopted during model training, and an early stopping mechanism is set when the validation set... Training is automatically terminated when the score does not improve for three consecutive training cycles or the total loss changes below a threshold; in addition, gradient clipping is used to prevent gradient explosion.

[0014] The present invention also provides a PINN-based modeling system for the transmission mechanism of natural focal diseases, comprising: a processor and a memory, wherein the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute a PINN-based modeling method for the transmission mechanism of natural focal diseases as described in the above technical solution.

[0015] The beneficial effects of this invention are as follows: (1) Integrating a dynamic environmental feedback mechanism, by constructing an environmental response function for key parameters such as host birth rate and carrying capacity, the system introduces the dynamic regulation capability of natural habitat and socio-cultural driving factors such as temperature, realistically simulating the impact of environmental variation on the propagation mechanism, and improving the spatiotemporal adaptability and prediction accuracy of the model. (2) A bidirectional driving modeling framework: effectively integrating dynamic mechanism modeling and data-driven methods, physical constraints are embedded in the neural network training process through automatic differentiation, realizing the unity of data fitting and physical consistency, solving the "black box" prediction problem, and significantly enhancing the interpretability and generalization ability of the model. (3) Automated multi-region modeling and visualization output, utilizing GPU parallel acceleration and multi-process scheduling mechanism, supporting large-scale region modeling and task scheduling. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method for modeling the transmission mechanism of natural focal diseases based on Physical Information Neural Network (PINN) according to the present invention.

[0017] Figure 2 A schematic diagram of the SEI-SEIR transmission mechanism of natural focal diseases involving host-human coupling.

[0018] Figure 3 This is a schematic diagram of the PINN model architecture.

[0019] Figure 4 This is the dynamic response curve of the environmental regulation function as a function of temperature in a specific instance.

[0020] Figure 5 This is a prediction of the evolution of state variables over time in a host-population coupled SEI-SEIR model for a specific instance.

[0021] Figure 6 This is a comparison chart of the predicted PINN values ​​and actual observed data for new infection cases in a specific population. Detailed Implementation

[0022] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The following examples are used to illustrate the technical methods of the present invention, but do not constitute a limitation on the scope of protection of the present invention.

[0023] like Figure 1 As shown, this invention provides a method for modeling the transmission mechanism of natural focal diseases based on PINN, specifically including the following steps: S1: Construct a multi-source heterogeneous input dataset, collect epidemiological reporting data (such as the number of new cases per week), demographic data, natural environmental data (such as temperature, precipitation, and vegetation index), and socio-cultural driving factor data (such as population density, traffic flow, and intensity of intervention measures) of the target area, and construct a unified spatiotemporal dataset.

[0024] S2: An environmental regulation function is introduced to dynamically characterize the response characteristics of key biological parameters (such as host fertility rate, population carrying capacity, etc.) to environmental factors, so as to reflect the real-time impact of environmental changes on host population dynamics and disease transmission processes.

[0025] S3: Construct a host-population coupled SEI-SEIR propagation dynamics equation system. This system characterizes the susceptibility within the host population ( ), infiltration ( ),Infect( Individuals, and susceptible individuals within a population. ), infiltration ( ),Infect( ),recover( The dynamic evolutionary process of an individual.

[0026] S4: Construct a Physical Information Neural Network (PINN) model and embed differential physical constraints. The dynamic equations constructed in step S3 are embedded into the loss function in an automatic differential form to achieve network learning guided by physical mechanisms.

[0027] S5: Construct a parallel modeling and interpretable output module. Supports parallel modeling of multiple regions / cities, automatically dividing computational tasks; after training, outputs prediction results and time series of key parameters, realizing interpretability of the propagation mechanism and regional comparative analysis.

[0028] Preferably, the input variables are standardized in step S1, including normalization, interpolation, and missing value imputation.

[0029] Preferably, the environmental regulation function in step S2 is not fixed to specific disease physiological data. The function can be expressed as a polynomial, Gaussian, Boltzmann function or a combination thereof. It can be quantitatively fitted and adjusted according to experimental research or epidemiological data of specific target diseases, and has adaptability and flexibility across diseases and regions.

[0030] Preferably, the coupled disease transmission dynamics system of host (V) and population (H) in step S3 is as follows: (1) (2) (3) (4) (5) (6) (7) in, Total number of hosts; The total number of people; These represent the rate of change in the number of susceptible, latent, and infected hosts, respectively. These represent the rate of change in the number of susceptible, latent, infected, and recovered individuals, respectively. These are the infection rate of the host, the incubation period exit rate, and the mortality rate; These are the infection rate, incubation period transfer rate, and recovery rate of the population; , These are the birth rate and death rate of the population (which may include natural death rate and other emigration rates). For immune attenuation rate, only enable in non-lifetime immune disease models. SEI - SEIR Epidemiological Model Framework Reference Figure 2 .

[0031] Preferably, in step S4, the time-based construction is performed. The neural network model as input Its output is an estimated vector of host and population state variables:

[0032] in, These are estimates of the host's susceptibility, latency, and infection status, respectively. These represent estimates of the susceptibility, latency, infection, and recovery status of the population, respectively. The network structure is as follows: Figure 3 As shown, it includes an input layer, multiple hidden layers, and an output layer. The output layer uses non-negative activation functions such as Softplus to ensure the non-negativity of all state estimates, which is consistent with the characteristics of biological populations.

[0033] Preferably, in step S4, a composite loss function is constructed using a physical information neural network framework, and the residual of the differential equation is calculated using automatic differentiation technology. Specifically, this includes the following steps: First, define the composite loss function as follows: (8) in, and These are the data loss weights, physical loss weights, and initial value loss weights, respectively. The data loss term represents the mean square error between the predicted number of cases and the actual observed number. The physical loss term characterizes the degree to which the neural network output satisfies the SEI-SEIR differential equation system, and is obtained by calculating the residuals of the differential equations. This is the initial value loss term, ensuring that the initial state of the SEI-SEIR differential equation system matches the actual observation data.

[0034] The data loss term is specifically defined as follows: (9) in, express The number of new cases predicted in real time is based on the number of asymptomatic carriers. With conversion rate parameters Calculated; This represents the actual number of newly observed cases; MSE is the mean squared error calculation function.

[0035] The physical loss term is defined as the sum of squares of the residuals of the differential equation: (10) The residual function is given by the following equation: (11) in, This represents the derivative of the state variable, which is calculated using PyTorch's automatic differentiation module. In the SEI-SEIR model, the first... The right-hand side function of a differential equation These correspond to the differential equation systems (equations (1)-(7)); For state variables; Environmental driving factors are represented by inputting external monitoring data into the model; This represents a parameter vector containing epidemiological parameters and ecodynamic parameters, where the epidemiological parameters include: Infection rate, incubation period transfer rate, mortality rate; Infection rate, incubation period transfer rate, and recovery rate in the population; , Population birth rate and death rate; Immune attenuation rate; Ecodynamic parameters include: , The parameters it contains and Because different diseases correspond to different hosts, the specific expressions also differ; the initial value loss term is defined as: (12) in, This indicates the neural network at the initial time. For the The predicted values ​​of each state variable, Indicates the first The state variables at the initial time The actual observed value.

[0036] By jointly optimizing the aforementioned loss terms, the backpropagation algorithm is used to simultaneously train the neural network parameters and the epidemiological and ecological dynamic parameters in the differential equation system.

[0037] As a preferred approach, to ensure the scalability and efficiency of large-scale region modeling in step S5, a GPU-based parallel modeling framework is constructed, employing the following scheduling strategies: (1) Learning rate control: A standard learning rate scheduling strategy is adopted, with the learning rate decreasing by 5% every 5000 training steps to gradually reduce the learning rate, which is conducive to stable convergence; (2) Early stopping mechanism: Training is terminated when the score does not improve for three consecutive training cycles or the total loss changes below the threshold; (3) Gradient clipping: The maximum norm of the gradient is set to 1.0 to prevent gradient explosion; (4) Multi-region parallelism: Based on the Python standard multiprocessing module, independent random seeds are allocated according to the hash value of the geographical region, and the task is dynamically sliced ​​and scheduled. A single GPU batch can process up to 8 regions; (5) Memory optimization: Memory resources are dynamically recycled by synchronizing CUDA kernel operations and periodically clearing the cache to ensure stable training operation.

[0038] Preferably, in step S5, after the model training is completed, the prediction results and analysis data are output to achieve interpretability analysis of the propagation mechanism and regional comparison.

[0039] To verify the effectiveness of the proposed method for modeling the transmission of zoonotic diseases and to demonstrate its operational procedures and modeling advantages in practical applications, this embodiment uses dengue fever monitoring data from 27 states in a certain country between 2010 and 2024 as the research object. A host (mosquito vector)-human coupled SEI-SEIR transmission model is constructed, combined with an environmental temperature regulation function, and the Physical Information Neural Network (PINN) method is used to achieve multi-region modeling, parameter inversion, and transmission mechanism analysis. The specific implementation process is as follows: Step 1: Data Collection and Preprocessing. Obtain the following data from public databases: Table 1 Data sources for the dengue fever host-population coupling model

[0040] All data were time-aligned according to a uniform epidemiological week, and a three-dimensional tensor input dataset of "space × time" was constructed using state-level administrative units as the spatial scale. The time variable was normalized to the [0, 1] interval to improve the model's convergence stability.

[0041] Step 2: Environmental Response Function Design. Based on experimental fitting data and the physiological characteristics of the main dengue vector (Aedes aegypti mosquito) provided in the references, the following temperature driving function is defined: Table 2 Temperature-driven functions related to the physiological characteristics of Aedes aegypti

[0042] The host birth rate is obtained by multiplying several temperature-sensitive parameters:

[0043] Population carrying capacity is constructed using a Gaussian exponential decay function, based on the Boltzmann formula and the physiological optimum temperature.

[0044] In the formula, The physiologically optimal temperature Boltzmann constant represents the maximum possible number of mosquitoes in a population. ,activation energy .

[0045] Step 3: Based on the temperature-driven function defined in Step 2, and combining ecological mechanisms and epidemic transmission characteristics, establish a coupled transmission model between the host and the human population. The parameters of host transmission rate, host incubation period emigration rate, and human transmission rate are defined as follows:

[0046]

[0047]

[0048] Differential equations (1)-(7) are used to describe the transition relationships of each state variable, including susceptible S, latent E, infected I, and recovered R, and the dynamic evolution path is calculated by combining the total number of hosts and the total population.

[0049] Step 4: Construction and Training of the Physical Information Neural Network. A deep, fully connected neural network model is built using PyTorch. The input layer is time. The hidden layer contains 5 fully connected layers, each with 32 neurons, and the activation function is Softplus (guaranteed non-negative); the output layer has 7 state variables. .

[0050] During model training, the above dynamic equations are converted into residual terms as physical constraints, and the time derivative is calculated through automatic differentiation. The weight hyperparameters in the loss function (8) are... Set them to 1000, 1, and 10 respectively.

[0051] population incubation period transfer rate Recovery rate Immune attenuation rate Initial number of hosts Joint optimization is achieved through backpropagation.

[0052] Step S5: To improve training efficiency and multi-region modeling capabilities, this example uses multiprocessing to initiate a multi-process parallel mechanism.

[0053] In order to improve the model convergence efficiency and prevent overfitting during the model training process, the following training scheduling strategy and early stopping mechanism are set up in this example.

[0054] The training optimizer uses the Adam algorithm with an initial learning rate of 0.001. To ensure convergence capability in the later stages of model training, a StepLR learning rate scheduler is configured, automatically decaying the learning rate by 5% after every 5000 training steps. This strategy improves convergence speed in the early stages of training and then slowly converges to the optimal value in the later stages.

[0055] To avoid overfitting and resource waste, an early stopping mechanism is set as the training termination condition. Model training will automatically terminate when any of the following conditions are met: (1) Validation set performance stagnation: In multiple consecutive evaluation cycles, the model's performance on the validation set stagnates. (1) No significant improvement in score; (2) Slow decrease in loss function: In recent training cycles, the decrease in total loss function is less than the set threshold. (3) Parameter convergence is stable: the range of change of learnable parameters in consecutive training rounds is very small, indicating that the model has reached a stable state.

[0056] After the model training is completed, the functional response relationship between the output propagation parameters and environmental factors is determined. Figure 4 ); Evolution trajectory of state variables ( Figure 5 ), depicting the dynamics of dissemination. Figure 6 This is a comparison chart of observed and predicted dengue fever cases in 27 states according to an embodiment of the present invention. Each sub-chart shows the comparison results for one state, where the gray area represents the actual observed cases, the black curve represents the model-predicted cases, and the sub-chart title indicates the region name and the coefficient of determination. Value. (Through) Figure 6 It can be seen that the model has high prediction accuracy, covering more than 90% of regions. A value greater than 0.85 indicates accurate propagation dynamics reconstruction, and the model prediction curve highly overlaps with the observed data.

[0057] On the other hand, embodiments of the present invention also provide a PINN-based modeling system for the transmission mechanism of natural focal diseases, comprising: a processor and a memory, wherein the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute a PINN-based modeling method for the transmission mechanism of natural focal diseases as described in the above technical solution.

[0058] It should be understood that any parts not described in detail in this specification belong to the prior art.

[0059] It should be understood that the above description of the preferred embodiments is quite detailed, but it should not be considered as a limitation on the scope of protection of this invention. Those skilled in the art, under the guidance of this invention, can make substitutions or modifications without departing from the scope of protection of the claims of this invention, and all such substitutions or modifications fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for modeling the transmission mechanism of natural focal diseases based on PINN, characterized in that, Includes the following steps: S1, Construction of multi-source heterogeneous datasets; S2, based on the physiological characteristics of the host of the target natural focal disease, constructs the environmental response function of the host's birth rate and carrying capacity as key parameters to characterize its dynamic response to environmental factors. The form of the environmental response function is adjusted or reconstructed according to the epidemiological experiment. S3. Construct a host-population coupled SEI-SEIR propagation dynamics differential equation system, which characterizes the susceptibility within the host population. , infiltration ,Infect Individuals and populations are susceptible , infiltration ,Infect ,recover The dynamic evolutionary process of an individual; S4, with time variable Using the input, a PINN neural network is constructed, and the differential equation in step S3 is transformed into an automatic differential form and embedded into the loss function. The network parameters and related physical parameters are jointly optimized through backpropagation. S5 employs a GPU-based multi-process computing framework to output time-series curves of state variables, dynamic trends of propagation parameters, environmental response function graphs, and predicted case data, enabling regional modeling and visualization analysis of propagation mechanisms.

2. The method for modeling the transmission mechanism of natural focal diseases based on PINN according to claim 1, characterized in that: In step S1, epidemiological reporting data, demographic data, natural environment data, and socio-cultural driving factor data of the target area are collected and normalized, interpolated, and missing value imputation are performed to construct a unified spatiotemporal dataset. Among them, the epidemiological reporting data includes the number of new cases per week, the natural environment data includes temperature, precipitation, and vegetation index, and the socio-cultural driving factor data includes population density, traffic flow, and intensity of intervention measures.

3. The method for modeling the transmission mechanism of natural focal diseases based on PINN according to claim 1, characterized in that: In step S2, the environmental regulation function is not fixed to specific disease physiological data. The function can be expressed as a polynomial, Gaussian, Boltzmann function or a combination thereof. It can be quantitatively fitted and adjusted according to experimental research or epidemiological data of specific target diseases, and has adaptability and flexibility across diseases and regions.

4. A method for modeling the transmission mechanism of natural focal diseases based on PINN according to claim 1, characterized in that: In step S3, the propagation dynamics equation adopts a propagation dynamics model based on individual SEI-SEIR, and the specific calculation formula is as follows: （1） （2） （3） （4） （5） （6） （7） in, Total number of hosts; The total number of people, For the host's birth rate, For population carrying capacity; These represent the rate of change in the number of susceptible, latent, and infected hosts, respectively. These represent the rate of change in the number of susceptible, latent, infected, and recovered individuals, respectively. These are the infection rate of the host, the incubation period exit rate, and the mortality rate; These are the infection rate, incubation period transfer rate, and recovery rate of the population; , These are the birth rate and death rate of the population, respectively. This represents the rate of immune attenuation.

5. The method for modeling the transmission mechanism of natural focal diseases based on PINN according to claim 1, characterized in that: The PINN neural network described in step S4 includes one input layer, at least five hidden layers, and one output layer; the hidden layers use the Softplus activation function, and the output layer corresponds to seven state variables. , These are estimates of the host's susceptibility, latency, and infection status, respectively. These represent estimates of the susceptibility, latency, infection, and recovery status of the population.

6. A method for modeling the transmission mechanism of natural focal diseases based on PINN according to claim 4, characterized in that: Step S4 defines the composite loss function as follows: （8） in, and These are the data loss weights, physical loss weights, and initial value loss weights, respectively. The data loss term represents the mean square error between the predicted number of cases and the actual observed number. The physical loss term characterizes the degree to which the neural network output satisfies the SEI-SEIR differential equation system, and is obtained by calculating the residuals of the differential equations. This is the initial value loss term, ensuring that the initial state of the SEI-SEIR differential equation system matches the actual observation data; By jointly optimizing the aforementioned loss terms, the backpropagation algorithm is used to simultaneously train the neural network parameters and the epidemiological and ecological dynamic parameters in the differential equation system.

7. A method for modeling the transmission mechanism of natural focal diseases based on PINN according to claim 6, characterized in that: The data loss term is specifically defined as follows: （9） in, express The number of new cases predicted in real time is based on the number of asymptomatic carriers. With conversion rate parameters Calculated; This represents the actual number of newly observed cases; MSE is the mean squared error calculation function. The physical loss term is defined as the sum of squares of the residuals of the differential equation: （10） The residual function is given by the following equation: （11） in, This represents the derivative of the state variable, which is calculated using PyTorch's automatic differentiation module. In the SEI-SEIR model, the first... The right-hand side function of a differential equation These correspond to equations (1)-(7) in the system of differential equations, respectively; For state variables; Indicates environmental driving factors; This represents a parameter vector, which includes epidemiological parameters and ecological dynamic parameters.

8. A method for modeling the transmission mechanism of natural focal diseases based on PINN according to claim 6, characterized in that: The initial value loss term is defined as: （12） in, This indicates the neural network at the initial time. For the first The predicted values ​​of each state variable, Indicates the first The state variables at the initial time The actual observed value.

9. The method for modeling the transmission mechanism of natural focal diseases based on PINN according to claim 1, characterized in that: In step S5, the StepLR learning rate decay strategy is used during model training, and an early stopping mechanism is set. When the validation set... Training is automatically terminated when the score does not improve for three consecutive training cycles or the total loss changes below a threshold; in addition, gradient clipping is used to prevent gradient explosion.

10. A modeling system for the transmission mechanism of natural focal diseases based on PINN, characterized in that, include: A processor and a memory, wherein the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute the PINN-based method for modeling the transmission mechanism of natural focal diseases as described in any one of claims 1-9.

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