CN115732098A - Infectious disease cross-city propagation prediction method and system based on improved SEIR model - Google Patents

Infectious disease cross-city propagation prediction method and system based on improved SEIR model Download PDF

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CN115732098A
CN115732098A CN202211527206.0A CN202211527206A CN115732098A CN 115732098 A CN115732098 A CN 115732098A CN 202211527206 A CN202211527206 A CN 202211527206A CN 115732098 A CN115732098 A CN 115732098A
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吴亚东
王桂娟
张巍瀚
邱雨
王中
王建松
郭皓
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Sichuan University of Science and Engineering
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Abstract

The invention relates to the technical field of infectious disease prediction, in particular to a Moving-SEIR infectious disease prediction model method and a system based on an improved SEIR model, wherein the method comprises the following steps: classifying the crowd according to the characteristics of the infectious diseases; taking population movement indexes of different areas as independent influence factors, and acquiring initial headcount in each area; the method comprises the steps of inputting existing data into a LightGBM model to track changes of infection rate and recovery rate; constructing a Moving-SEIR model according to the initial population, infection rate, recovery rate and mobility index of different people in each region; and (4) according to the constructed Moving-SEIR model, infectious disease prediction is carried out. The method considers the influence of the change of the population movement, infection rate and recovery rate of the cross-city on the spread of the infectious diseases, and effectively improves the prediction accuracy of the model.

Description

Infectious disease cross-city propagation prediction method and system based on improved SEIR model
Technical Field
The invention relates to the technical field of infectious disease prediction, in particular to an infectious disease cross-city propagation prediction method and system based on an improved SEIR model.
Background
The spreading form of infectious diseases is a brand new situation nowadays, and the prevalence of infectious diseases seriously threatens social activities and the life health of people, and becomes a great problem affecting global health and economy. The analysis and research of the process of the development process and the propagation trend of the infectious diseases by using a mathematical model become a common means for epidemic situation prevention and control, wherein the infectious disease propagation dynamic model can effectively track the growth characteristics of the population, the disease propagation rule and the like, and is widely applied to infectious disease tracking.
The SEIR (Infectious, recovered) model is used as a research hotspot of an Infectious disease transmission kinetic model, and the population is divided into four types of individuals: class S, susceptible (susceptable), represents a person who is not infected, but who is not immune, and may become infected upon contact with an infected person; class E (amplified), representing persons who have been Exposed to a patient with the infection but who are not infectious; class I, infectious (Infectious), represents an infected person, who has a certain infectivity; class R, recovered, represents people who recover from infection or die, and who are immune. The variation of the infectious diseases in the whole population is researched by analyzing the transfer relationship of the population in the three types of individuals.
The model is simple and clear to use and is used for modeling and analyzing various infectious diseases. However, the model does not take into account the changes in population mobility and infection and recovery rates, which cause the model to predict data that are greatly offset from the true situation. On one hand, different control measures are adopted in different provinces and cities in the country during the epidemic situation, and the measures limit population mobility and bring influence on disease propagation; on the other hand, the prior art needs to consider dynamic tracking of infection and recovery rates due to the impact of government control measures and vaccination with new corona vaccines on the infection and recovery rates of diseases. Meanwhile, with the development of artificial intelligence technology, the traditional infectious disease prediction model is difficult to adapt to the transmission characteristics of different diseases, and the defects of the prior art can be overcome by means of machine learning and the like.
Disclosure of Invention
The invention aims to provide an infectious disease cross-city propagation prediction method and system based on an improved SEIR model, and a Machine learning model Light Gradient hoisting Machine (LightGBM) framework is introduced to track the infectious disease rate and the recovery rate, so that the problem of low model prediction accuracy caused by the fact that the traditional model ignores the change of population cross-city flowing and the propagation rate is solved.
In order to achieve the purpose, the invention provides the following technical scheme:
an infectious disease cross-city transmission prediction method based on an improved SEIR model comprises the following steps:
step 1: classifying the crowd according to the characteristics of the infectious diseases;
and 2, step: taking population movement indexes of different areas as independent influence factors, and acquiring initial headcount in each area;
and step 3: the method comprises the steps of inputting existing data into a LightGBM model to track changes of infection rate and recovery rate;
and 4, step 4: constructing a dynamic model considering regional mobile Moving-SEIR infectious disease according to the initial population, infection rate, recovery rate and movement index of different populations in each region;
and 5: and (4) according to the constructed dynamic model of the infectious disease of Moving-SEIR, infectious disease prediction is carried out. Specifically, according to the constructed differential equation, the infectious disease prediction is carried out by adopting the following formula:
Figure BDA0003975286030000021
Figure BDA0003975286030000022
I[t+1]＝I[t]+σE[t]-γ(t)I[t]
R[t+1]＝R[t]+γ(t)I[t]
further, according to the characteristics of infectious diseases, the crowd is divided into: and the model building is more realistic, and helps researchers to comprehensively and accurately predict the spreading trend of infectious diseases and assist the formulation of prevention and control measures.
The machine learning method LightGBM is an efficient and open-source distributed Gradient framework based on a GBDT (Gradient Boosting Decision Tree) algorithm. When the feature dimension is high and the data size is large, the XGBoost algorithm needs to traverse all data to calculate information gain, resulting in a large time overhead. Aiming at the problem, the LightGBM framework provides two new methods, namely GOSS (Gradient-based One-Side Sampling based on binding) and EFB (Exclusive Feature binding), and accelerates the training process of the model by calculating the information gain of part of samples. The framework supports the strategies of feature parallelism, data parallelism and voting parallelism, improves the accuracy, reduces the time complexity, well solves the problem of processing mass data, and is widely applied to regression and classification prediction.
Preferably, in the step 3, the step of tracking the infection rate and recovery rate changes by using the existing data input LightGBM model includes the following steps:
step 3.1: screening the data characteristics based on the data characteristic correlation;
step 3.2: constructing a LightGBM-based prediction model by using the screened characteristics as input and the infection rate and the recovery rate as output;
step 3.3: acquiring an original data set, carrying out data normalization processing, and dividing the original data set into a training set and a test set;
step 3.4: based on the LightGBM model, performing model training by using a training set, and determining model parameters;
step 3.5: inputting LightGBM model parameters and a test set, and predicting infection rate and recovery rate;
step 3.6: and carrying out error assessment on the prediction result of the LightGBM model to obtain infection rate and recovery rate data.
Preferably, in the step 4, the method for constructing the dynamic model of Moving-SEIR infectious disease comprises the following steps:
step 4.1: according to the initial population, population movement index and population total number of different population types in the region, the following differential equation is adopted to calculate the change of the population number of different population types in each region in unit time:
Figure BDA0003975286030000041
Figure BDA0003975286030000042
Figure BDA0003975286030000043
Figure BDA0003975286030000044
wherein S (t) represents the number of susceptible persons at time t, E (t) represents the number of latent persons at time t, I (t) represents the number of infected persons at time t, R (t) represents the number of convalescent persons at time t, S in (t) the number of susceptible persons migrating to a certain area at time t, S out (t) the number of susceptible persons who have migrated out of a certain area at time t, E in (t) the number of latentiators migrating into a certain area at time t, E out (t) the number of latentiators moving out of a certain area at time t, β 1 Indicates the probability of contracting a disease after a susceptible person is contacted with an infected person, beta 2 Expressing the probability of infection after the susceptible person is contacted with the latent person, sigma expressing the probability of transforming the latent person into the infected person, and gamma expressing the probability of recovery of the infected person;
step 4.2: the number of moving susceptives and latentients is calculated by the following formula:
Figure BDA0003975286030000045
Figure BDA0003975286030000046
Figure BDA0003975286030000047
Figure BDA0003975286030000048
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003975286030000049
representing the probability of a latentiator migrating into a region;
on the other hand, another technical scheme adopted by the invention is that the infectious disease cross-city transmission prediction system based on the improved SEIR model comprises:
step 1: the crowd classification module is used for classifying crowds according to classes through the characteristics of the infectious diseases and acquiring parameters of an infectious disease dynamic model;
step 2: the model building module builds a dynamic model of the Moving-SEIR infectious disease through the built formula group;
and step 3: the infectious disease dynamics simulation module is used for visually simulating the infectious disease transmission dynamics of each region according to the constructed infectious disease dynamics model and the initial parameters;
and 4, step 4: and the infectious disease trend prediction module predicts and visualizes the future infectious disease spreading trend in a certain region by referring to the change of the number of people in different categories in the region.
Compared with the prior art, the invention has the beneficial effects that:
1. the infectious disease cross-city propagation prediction method and system based on the improved SEIR model provide a brand-new infectious disease cross-city propagation prediction method Moving-SEIR infectious disease dynamics model and system based on the improved SEIR model, and the model considers the synergistic influence of cross-city population movement, infection rate and recovery rate on infectious disease propagation.
2. According to the infectious disease cross-city propagation prediction method and system based on the improved SEIR model, a LightGBM machine learning method is used for tracking the change of infection rate and recovery rate along with time, a time-dependent continuous model is established, epidemic situations are tracked and predicted by combining a Moving-SEIR model and a LightGBM method, and city connectivity of different geographic positions and transmission rate along with time change are considered.
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FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a diagram illustrating state transition of the Moving-SEIR model according to an embodiment of the present invention;
fig. 3 is a schematic diagram of the system structure of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", and the like, indicate orientations or positional relationships based on those shown in the drawings, merely for convenience of description and simplicity of description, and do not indicate or imply that the device or element so referred to must have a particular orientation, be constructed in a particular orientation, and be operated, and thus, are not to be construed as limiting the present invention.
In the description of this patent, it is noted that unless otherwise specifically stated or limited, the terms "mounted," "connected," and "disposed" are to be construed broadly and can include, for example, fixedly connected, disposed, detachably connected, disposed, or integrally connected and disposed. The specific meaning of the above terms in this patent may be understood by one of ordinary skill in the art as appropriate.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically limited otherwise.
Referring to fig. 1-3, a technical solution provided by the present invention is:
as shown in fig. 1, the present embodiment provides a Moving-sei model for predicting the cross-city spread of infectious diseases based on an improved sei model, comprising the following steps:
step 1: the groups of people are classified according to the characteristics of infectious diseases. Specifically, in the present embodiment, the population categories are divided into susceptible persons S, latent persons E, infected persons I, recovering persons R, immigrated persons In, and immigrated persons Out according to the characteristics of the infectious diseases;
and 2, step: and taking the population movement indexes of different areas as independent influence factors to obtain the initial total number of people in each area. Specifically, according to the urban area division, the initial total number of people and population movement indexes of different areas are obtained, and the number of people moving in and out in the area is calculated;
and step 3: the LightGBM model is entered with existing data to track changes in infection rate and recovery rate. Specifically, at the early stage of epidemic disease transmission, the number of cases diagnosed is very low, and in order to analyze the initial stage of infectious disease outbreak, this embodiment assumes { S (t) ≈ N, t ≧ 0}, and the influence of the migratory population on the total number of local population is negligible, and there are:
Figure BDA0003975286030000071
simplifying to obtain:
I(t)＝e (kb-γ)I
after parameters of the formula are calculated through multiple times of fitting, fitting the infection rate and recovery by using a LightGBM model to obtain a predicted value;
and 4, step 4: constructing a dynamic model of the Moving-SEIR infectious disease according to the initial population, the infection rate, the recovery rate and the mobility index of different populations in each region;
specifically, according to the population movement number, the following formula is adopted to calculate the total population under dynamic balance in each area:
N[t]＝N[t-1]+In[t-1]-Out[t-1]
wherein N [ t ] represents the total number of people in the area at the current moment, and N [ t-1] represents the total number of people in the area at the last unit time.
According to the initial population of different categories, the total population under dynamic balance and the population movement number in each region, the conversion relationship of the population is as shown in the attached figure 2, and the change of the population of different categories in the region in unit time is calculated by adopting the following formula:
Figure BDA0003975286030000081
Figure BDA0003975286030000082
Figure BDA0003975286030000083
Figure BDA0003975286030000084
wherein S (t) represents the number of susceptible persons at time t, E (t) represents the number of latent persons at time t, I (t) represents the number of infected persons at time t, R (t) represents the number of convalescent persons at time t, S in (t) the number of susceptible persons migrating to a certain area at time t, S out (t) the number of susceptible persons who have migrated out of a certain area at time t, E in (t) the number of latentiators migrating into a certain area at time t, E out (t) the number of latentiators migrating out of a certain area at time t, beta 1 Indicates the probability of infection of a susceptible person after contact with an infected person, beta 2 Indicates the probability of infection after the susceptible person is exposed to the latent person, σ indicates the probability of the latent person transforming into the infected person, and γ indicates the probability of the infected person recovering.
Further, the number of moving susceptives and latentients is calculated by the following formula:
Figure BDA0003975286030000085
Figure BDA0003975286030000086
Figure BDA0003975286030000087
Figure BDA0003975286030000088
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003975286030000089
representing the probability of a latentiator migrating into a region;
and 5: and (4) according to the constructed dynamic model of the infectious disease of Moving-SEIR, infectious disease prediction is carried out. Specifically, in this embodiment, a piece of historical data { S (T), E (T), I (T), R (T), 0 ≦ T-1} is given, and the LightGBM framework is combined to predict the infection rate and the recovery rate, at this time:
Figure BDA0003975286030000091
Figure BDA0003975286030000092
Figure BDA0003975286030000093
Figure BDA0003975286030000094
Figure BDA0003975286030000095
Figure BDA0003975286030000096
wherein, S [ t ]]Representing the number of susceptible persons in the area at the current time, ST-1]Indicating the number of people susceptible to a particular event in the area, E [ t ]]Indicating the number of potential people in the area at the current time, E [ t-1]]Indicates the number of latentients in the area at a time unit, I [ t ]]Indicates the number of infected persons in the area at the current time, I [ t-1]]Indicates the number of infected persons at a unit time in the area, rt]Represents the number of people recovering the region at the current moment, R [ t-1]]Indicates the number of persons recovering at a unit time in the area, S in [t-1]Indicates the number of susceptible persons who have migrated into the area in the last unit time, S out [t-1]Indicates the number of susceptible persons who have migrated out of the area in the last unit time, E in [t-1]Indicating the number of latentients migrating into the area in the last unit of time, E out [t-1]Indicating the last unit time to move out of the areaThe number of latentious people,. Beta. 1 (t-1) represents the probability of contracting an infection after the susceptible person and the infected person have been in contact with each other in the previous unit time, beta 2 (t-1) represents the probability of contracting an infection after the susceptible person has been exposed to the latent person for the previous unit time, [ sigma ] represents the probability of the latent person being converted into an infected person, and [ gamma ] (t-1) represents the probability of the infected person recovering the previous unit time.
For the same reason, in
Figure BDA0003975286030000097
Under the condition of predicting
Figure BDA0003975286030000098
R (t) is as follows:
Figure BDA0003975286030000101
FIG. 3 is a system diagram of the prediction system for the cross-city spread of infectious diseases based on the improved SEIR model, which comprises:
step 1: the crowd classification module classifies crowds according to classes through the characteristics of the infectious diseases and acquires parameters of an infectious disease dynamic model;
step 2: the model building module builds a dynamic model of the Moving-SEIR infectious disease through the built formula group;
and 3, step 3: the infectious disease dynamics simulation module is used for visually simulating the infectious disease transmission dynamics of each region according to the constructed infectious disease dynamics model and the initial parameters;
and 4, step 4: and the infectious disease trend prediction module predicts and visualizes the future infectious disease transmission trend in the region by referring to the change of the number of people in different categories in the region.
The foregoing shows and describes the general principles, principal features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and the preferred embodiments of the present invention are described in the above embodiments and the description, and are not intended to limit the present invention. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (4)

1. An infectious disease cross-city transmission prediction method based on an improved SEIR model is characterized by comprising the following steps: the method comprises the following steps:
step 1: classifying the crowd according to the characteristics of the infectious diseases;
and 2, step: taking population movement indexes of different areas as independent influence factors, and acquiring initial total population in each area;
and step 3: using the existing data input LightGBM model to track the change of infection rate and recovery rate;
and 4, step 4: the method comprises the following steps of constructing a dynamic model of the Moving-SEIR infectious disease according to the initial population, the infection rate, the recovery rate and the mobility index of different populations in each region, wherein the dynamic model comprises the following steps:
step 4.1: according to the initial population, population movement index and population total number of different population types in the region, the following differential equation is adopted to calculate the change of the population number of different population types in each region in unit time:
Figure FDA0003975286020000011
Figure FDA0003975286020000012
Figure FDA0003975286020000013
Figure FDA0003975286020000014
wherein S (t) represents the number of susceptible persons at time t, E (t) represents the number of latent persons at time t, I (t) represents the number of infected persons at time t, R (t) represents the number of convalescent persons at time t, S in (t) the number of susceptible persons migrating to a certain area at time t, S out (t) the number of susceptible persons who have migrated out of a certain area at time t, E in (t) the number of latentiators migrating into a certain area at time t, E out (t) the number of latentiators migrating out of a certain area at time t, beta 1 Indicates the probability of contracting a disease after a susceptible person is contacted with an infected person, beta 2 The probability of infection of a susceptible person after the susceptible person is contacted with a latent person is shown, sigma is the probability of converting the latent person into an infected person, and gamma is the probability of recovery of the infected person;
step 4.2: the number of moving susceptives and latentients is calculated by the following formula:
Figure FDA0003975286020000021
Figure FDA0003975286020000022
Figure FDA0003975286020000023
Figure FDA0003975286020000024
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003975286020000025
representing the probability of the latency migrating into a certain area;
and 5: and (4) according to the constructed dynamic model of the infectious disease of Moving-SEIR, infectious disease prediction is carried out. Specifically, according to the constructed differential equation, the infectious disease prediction is carried out by adopting the following formula:
Figure FDA0003975286020000026
Figure FDA0003975286020000027
I[t+1]＝I[t]+σE[t]-γ(t)I[t]
R[t+1]＝R[t]+γ(t)I[t]。
2. the method of claim 1, wherein the method comprises the steps of: in the step 1, the population is divided into the following groups according to the characteristics of infectious diseases: susceptible, latent, infected, convalescent, migratory, and migratory.
3. The method of claim 1, wherein the method comprises the steps of: the step 3 of tracking the change of infection rate and recovery rate comprises the following steps:
step 3.1: screening the data characteristics based on the data characteristic correlation;
step 3.2: constructing a LightGBM-based prediction model by using the screened characteristics as input and the infection rate and the recovery rate as output;
step 3.3: acquiring an original data set, carrying out data normalization processing, and dividing the original data set into a training set and a test set;
step 3.4: based on the LightGBM model, performing model training by using a training set to determine model parameters;
step 3.5: inputting LightGBM model parameters and a test set, and predicting infection rate and recovery rate;
step 3.6: and carrying out error assessment on the prediction result of the LightGBM model to obtain infection rate and recovery rate data.
4. An improved SEIR model-based prediction system for cross-city spread of infectious diseases, comprising:
step 1: the crowd classification module classifies crowds according to classes through the characteristics of the infectious diseases and acquires parameters of an infectious disease dynamic model;
step 2: the model building module builds a dynamic model of the Moving-SEIR infectious disease through the built formula group;
and step 3: the infectious disease dynamics simulation module is used for visually simulating the infectious disease transmission dynamics of each region according to the constructed infectious disease dynamics model and the initial parameters;
and 4, step 4: and the infectious disease trend prediction module predicts and visualizes the future infectious disease transmission trend in the region by referring to the change of the number of people in different categories in the region.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117095832A (en) * 2023-10-19 2023-11-21 泰州蕾灵百奥生物科技有限公司 Modeling method and system for animal epidemic disease infection risk

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117095832A (en) * 2023-10-19 2023-11-21 泰州蕾灵百奥生物科技有限公司 Modeling method and system for animal epidemic disease infection risk
CN117095832B (en) * 2023-10-19 2023-12-19 泰州蕾灵百奥生物科技有限公司 Modeling method and system for animal epidemic disease infection risk

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