CN113096821B - Epidemic dynamics prediction method based on dynamic characteristics of multi-bin model - Google Patents
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Abstract
A epidemic dynamics prediction method based on a multi-bin model dynamic characteristic belongs to the epidemic prevention field. In order to accurately describe the transmission chain of epidemic diseases and predict the development of epidemic situation, firstly, an epidemic dynamics model for thinning bin division is established, the transmission rule of epidemic disease diffusion is described, and whether diagnosis is confirmed, symptoms exist or not and differential infection patients who can be hospitalized or not are considered. Secondly, the time-varying regeneration number is calculated, and the dynamic characteristics of epidemic spread are characterized based on the time-varying regeneration number. And finally, estimating main parameters of a biological mathematical equation, fitting epidemic dynamics by using the dynamic model, and simulating and predicting diffusion trend. The invention can accurately describe the dynamic transmission characteristics of infectious diseases under the framework of the bin model, can further predict the transmission trend of the infectious diseases, provides theoretical basis for scientific epidemic prevention and accurate construction of sudden infectious diseases, and has important scientific significance.
Description
Technical Field
The invention belongs to the epidemic prevention field, and relates to an epidemic dynamics prediction method based on a multi-bin model dynamic characteristic.
Background
The epidemic situation of periodic outbreaks causes huge harm to life health, social economy and ecological systems in local areas and even worldwide, and a public treatment system of the economic society is continuously and repeatedly created. The major infectious diseases burst at an exponentially increasing rate in early stages with strong transmissibility and unknowns, and once epidemic prevention and control misses a window period, the severity of the spread situation is difficult to estimate. The serious difficulty of the epidemic situation diffusion control work is to accurately describe the virus propagation chain and predict the development of the epidemic situation. The method determines whether an emergency treatment mechanism is started or not and a reasonable response level according to accurate prediction of disease dynamics, and is the most important scientific foundation for public treatment system construction under major sudden public health events. Underestimation of epidemic effects can lead to extensive infection with untimely responses and missed window periods, and overestimation of propagation trends can lead to unreasonable resource allocation and large economic loss allocation. For an infectious disease model analyzed using a mathematical method, the closer the considered factors are to reality, the more accurate the analysis and prediction result is. Therefore, the method accurately describes the dynamic transmission characteristics of epidemic situation and the prediction work based on the refined bin dynamics model, and has important scientific significance.
Disclosure of Invention
In order to solve the technical problems, the bin model based on epidemic dynamics comprehensively considers the dynamics of the propagation dynamics characteristics and the refined bin design, and provides an epidemic prediction method based on the propagation dynamics dynamic space-time characteristics. Under the framework of a biological mathematic prediction model, a prediction early warning system applied to epidemic public treatment is built, scientific formulation of epidemic prevention strategies under limited resources is assisted, and the method has good practicability.
In order to achieve the above purpose, the invention adopts the following technical scheme:
an epidemic situation prediction method of dynamic characteristics of a multi-bin model. Firstly, establishing an SPMILHRD model for refining bin division to describe the spreading rule of epidemic disease, and processing the spreading rate of different populations according to whether diagnosis is confirmed and whether symptoms exist or not. Secondly, the time-varying regeneration number is calculated, and the dynamic characteristics of virus transmission are characterized based on the time-varying regeneration number. Finally, parameters of a bin model are calculated according to epidemic situation statistical data, and the bin model (dynamic model) is used for fitting epidemic situation dynamics and simulating and predicting diffusion trend. The calculation flow chart of the invention is shown in fig. 1, and specifically comprises the following steps:
step 1: and constructing a refined bin model for epidemic disease spread.
All populations were classified as susceptible (S bin), undiagnosed asymptomatic infected (P bin), undiagnosed asymptomatic infected (M bin), undiagnosed symptomatic infected (I bin), symptomatic infected (L bin), hospitalized severe infected (H bin), rehabilitated (R bin), removers (D bin), total population n=s+p+m+i+l+h+r+d. The interaction relation between the bins is shown in fig. 2, and the following SPMILHRD bin model is established:
wherein,the number of the population in the chambers of the susceptible person, the undiagnosed asymptomatic infected person, the undiagnosed symptomatic infected person, the hospitalized severe infected person, the rehabilitated person and the remover at time t are respectively shown. Beta represents the transmission rate of undiagnosed infected persons, and beta' represents the transmission rate of undiagnosed infected persons; μ represents the probability of being diagnosed for asymptomatic infected persons, η represents the probability of being diagnosed for symptomatic infected persons; b represents the probability of conversion to symptomatic by an asymptomatic infected person; h represents the probability of a symptomatic infected person being diagnosed with admission therapy; gamma, gamma' are respectively hospitalized with and asymptomatic with infectionProbability of recovery for the infected person; sigma is the death probability of inpatients.
Step 2: and calculating the time-varying regeneration number, and describing dynamic and dynamic characteristics of epidemic spread based on the time-varying regeneration number.
Time-varying regeneration number R t The dynamic characteristics of infectious diseases which can accurately describe the change with time are the most important classical indexes in an infectious disease prediction model, represent that when an individual infected by virus is introduced into a group susceptible to other people, the average number of secondary infections generated is a threshold value for judging whether the infectious disease is popular or not. The time-varying regeneration number is calculated as follows:
2.1 First determining the sequence interval mean and its distribution, obtained by calculating the clinical seizure interval time between the initial case and the secondary case of the case sample.
2.2 Calculating the relative probability p for a case by likelihood (ML) ij I.e. case i at time t i The case j is at time t j Probability of infection:
wherein w represents the distribution of sequence intervals; n is n i Representing the number of cases of onset within the time period; t is t j -t k Represents the average sequence interval; t is t i -t j Representing the sequence interval of case i and case j.
Effective regeneration number R of case j j The method is calculated as follows:
R j ＝∑ i p ij (3)
the time-varying regeneration number considering all cases at time t is:
based on the sequence interval and distribution obtained in step 2.1), and the real-time updated dynamic case statistics, R t Can be calculated by the equationAnd (5) calculating to obtain the product.
Step 3: parameters of the bin model are estimated and the number of bin populations is modeled.
Finally, estimating key parameters of a bin model, fitting epidemic dynamics by using the dynamic model, and simulating and predicting diffusion trend, and particularly:
the transmission rate β of the undetected infected person: based on the dynamic regeneration number R of the undetected infected person t The ratio of the period D of infection of the infected person to that of the infected person not detected is calculated, and the transmission rate beta' of the infected person detected is obtained by a similar method (based on the dynamic regeneration number R of the infected person detected t Calculation of the ratio to the period D of infection of the detected infected person). Where the period of infection D refers to the time span from having the ability to be infected to losing the ability to be infected by quarantine or cure.
The asymptomatic infected person is diagnosed with probability μ: the method for calculating the diagnosis probability eta of symptomatic infected patients is the same as that calculated by dividing the diagnosis proportion among asymptomatic infected patients by the average time from infection to diagnosis (calculated by dividing the diagnosis proportion among symptomatic infected patients by the average time from infection to diagnosis);
the asymptomatic infected person converts to a symptomatic probability b: dividing the asymptomatic proportion in the infected person by the average number of days from infection to onset;
probability h of the diagnosed symptomatic infected person getting hospitalized: obtained by dividing the proportion of hospitalization in symptomatic infected persons by the average number of days from onset to admission;
recovery probability γ of the inpatients: the recovery ratio of the asymptomatic infected person is divided by the average recovery time, and the recovery probabilities gamma ', gamma' of the asymptomatic infected person and the symptomatic infected person are calculated in the same way (gamma 'is obtained by dividing the recovery ratio of the asymptomatic infected person by the average recovery time, and gamma' is obtained by dividing the recovery ratio of the symptomatic infected person by the average recovery time);
probability of death of the inpatients sigma: the mortality ratio of hospitalized infected persons was divided by the average number of days from admission to death.
Compared with the prior art, the invention has the beneficial effects that: the invention refines the bin by considering different populations such as detection, symptoms, admission and the like, realizes the time heterogeneity treatment of epidemic disease propagation models according to epidemic situation development dynamics, provides scientific criteria for public treatment of epidemic situation, and has important significance for scientific epidemic prevention of influenza. The method disclosed by the invention has strong operability and feasibility and is convenient for practical application.
Drawings
FIG. 1 is a flow chart of the calculation of the present invention.
FIG. 2 is a diagram of a bin model configuration of the invention.
FIG. 3 shows the dynamic regeneration number variation according to an example of the present invention.
Fig. 4 is a simulation of infection population variation for an example of the present invention.
Detailed Description
The invention is further illustrated with reference to specific examples.
Consider a pneumonia (covd-19) epidemic caused by the first wave of the novel coronavirus in spanish 2020. A new crown epidemic situation prediction method based on the dynamic characteristics of a multi-bin model is characterized in that a refined bin model considering whether detection exists, whether symptoms exist or not and whether hospital admission exists or not is firstly established, then a variable regeneration number is calculated, and finally epidemic situation diffusion conditions are fitted. The method comprises the following steps:
step 1: and constructing a refined bin model for epidemic disease spread.
An SPMILHRD bin model is created that describes the propagation of new coronaviruses as follows.
Wherein, each bin population feature: s: susceptibility, non-infection; p: infection, undetected, asymptomatic; m: infection, detection, no symptoms; i: infection, undetected, symptomatic; l: infection, detection, symptomatic; h: infection, hospitalization, severe symptoms, isolation; r: rehabilitation or healing; d: death. Wherein,each representing a change in the number of populations in the corresponding bin at time t. Beta represents the transmission rate of undiagnosed infected persons, and beta' represents the transmission rate of undiagnosed infected persons; μ represents the probability of being diagnosed for asymptomatic infected persons, η represents the probability of being diagnosed for symptomatic infected persons; b represents the probability of conversion to symptomatic by an asymptomatic infected person; h represents the probability of a symptomatic infected person being diagnosed with admission therapy; gamma, gamma', gamma "are the recovery probabilities of hospitalized infected persons, asymptomatic infected persons, symptomatic infected persons, respectively; sigma is the death probability of inpatients.
Step 2: and calculating the time-varying regeneration number, and describing dynamic and dynamic characteristics of epidemic spread based on the time-varying regeneration number.
Statistical analysis was performed on the first wave new crown epidemic case in spanish 2020, and the average sequence interval was 4.60 days with a standard deviation of 5.55 by calculating the clinical seizure interval time between the initial case and the secondary case of the case sample. Time-varying regeneration number R t Depending on the dynamic case statistics updated in real time, and calculated by the EpiEstim software package, in particular:
the likelihood Method (ML) is used for calculating the relative probability p of the case pair ij I.e. case i at time t i The case j is at time t j Probability of infection:
wherein w represents the distribution of sequence intervals; n is n i Representing the number of cases of onset within the time period; t is t j -t k Represents the average sequence interval; t is t i -t j Representing the sequence interval of case i and case j.
Effective regeneration number R of case j j The method is calculated as follows:
R j ＝∑ i p ij (7)
the time-varying regeneration number considering all cases at time t is:
obtain the regeneration number R of the time-varying regeneration from 20 days in the year 2 of 2020 to 08 days in the year 8 of 2020 t The calculated result of (2) is shown in FIG. 3, wherein the dotted line represents the time-varying regeneration number R t The solid line represents the number of new infectors per day. It can be observed that the spanish government takes measures of blocking, requiring social distance and the like to obviously control epidemic situation, the time-varying regeneration number is lower than 1 from the end of 4 months, but the time-varying regeneration number is more than 1 in 22 days of 6 months, and the second wave epidemic situation is entered.
Step 3: model parameters are estimated and the number of bin populations is modeled.
Based on statistical data of spanish new crown epidemic situation, the transmission rate beta of undiagnosed infected persons is based on time-varying regeneration number R t And infection period d=4.6, wherein the time-varying number of regenerations of the diagnosed infected person is about 1/50 of that of the undiagnosed infected person, and wherein the contact transmission probability of the undiagnosed infected person to the susceptible person is generally higher than that of the diagnosed infected person; the asymptomatic infected person has a diagnosis probability μ of 0.171, and symptomatic infected person has a diagnosis probability η of 0.371, with the symptomatic infected person being screened and diagnosed at a higher rate; the probability of conversion of asymptomatic infected persons to symptomatic b is 0.125; the probability h of hospitalization for symptomatic infected is 0.036; recovery probabilities gamma, gamma' of hospitalized infected persons, asymptomatic infected persons and symptomatic infected persons are respectively 0.07, 0.017 and 0.007; the death probability sigma of the hospitalized severe infected person is 0.0181.
Setting the total population n=4673 ten thousand, the initial values P (0) =3, m (0) =1, i (0) =3, l (0) =1, h (0) =0, r (0) =0, d (0) =0, then simulating the changes of each bin of the new crown epidemic situation from 22 nd month in spanish 2020 to 8 th month in 2020 as shown in fig. 4, and finding that the multi-bin new crown prediction model considering the time-varying regeneration number can better fit the actual situation of epidemic spread.
The examples described above represent only embodiments of the invention and are not to be understood as limiting the scope of the patent of the invention, it being pointed out that several variants and modifications may be made by those skilled in the art without departing from the concept of the invention, which fall within the scope of protection of the invention.
Claims (1)
1. The epidemic dynamics prediction method based on the dynamic characteristics of the multi-bin model is characterized in that firstly, an SPMILHRD model for refining bin division is established to describe the spreading rule of epidemic spread, and the spreading rates of different populations are processed according to whether diagnosis is confirmed and whether symptom differentiation exists or not; secondly, calculating a time-varying regeneration number, and describing dynamic characteristics of virus transmission based on the time-varying regeneration number; finally, calculating parameters of a bin model according to epidemic situation statistical data, fitting epidemic situation dynamics by using the bin model, and simulating and predicting diffusion trend; the method comprises the following steps:
step 1: constructing a refined bin model for epidemic disease diffusion;
all populations are classified into susceptible, undiagnosed asymptomatic, undiagnosed symptomatic, hospitalized severe, rehabilitated, and remover, wherein susceptible is S bin, undiagnosed asymptomatic is P bin, undiagnosed symptomatic is M bin, undiagnosed symptomatic is I bin, undiagnosed symptomatic is L bin, hospitalized severe is H bin, rehabilitated is R bin, and remover is D bin, total population n=s+p+m+i+l+h+r+d; based on the interaction relation among the bins, the following SPMILHRD bin model is established:
wherein,the change in population numbers in the cabins of susceptible persons, undiagnosed asymptomatic persons, undiagnosed symptomatic persons, hospitalized critically ill persons, rehabilitated persons, and remover, respectively, at time t; beta represents the transmission rate of undiagnosed infected persons, and beta' represents the transmission rate of undiagnosed infected persons; mu (mu)Represents the probability of being diagnosed for asymptomatic infected persons, η represents the probability of being diagnosed for symptomatic infected persons; b represents the probability of conversion to symptomatic by an asymptomatic infected person; h represents the probability of a symptomatic infected person being diagnosed with admission therapy; gamma, gamma', gamma "are the recovery probabilities of hospitalized infected persons, asymptomatic infected persons, symptomatic infected persons, respectively; sigma is the death probability of inpatients;
step 2: calculating a time-varying regeneration number, and describing dynamic characteristics of epidemic spread based on the time-varying regeneration number;
time-varying regeneration number R t The dynamic characteristics of infectious diseases which change with time can be accurately described, and the average number of secondary infections generated when an individual infected by viruses is introduced into a group susceptible to other people is a threshold value for judging the epidemic or not of the infectious diseases; the calculation steps are as follows:
2.1 Firstly, determining a sequence interval average value and distribution thereof, and obtaining the sequence interval average value by calculating the clinical attack interval time between an initial case and a secondary case of a case sample;
2.2 Calculating the relative probability p for the pair of cases by likelihood method ij I.e. case i at time t i The case j is at time t j Probability of infection:
wherein w represents the distribution of sequence intervals; n is n i Representing the number of cases of onset within the time period; t is t j -t k Represents the average sequence interval; t is t i -t j Representing the sequence interval of case i and case j;
effective regeneration number R of case j j The method is calculated as follows:
R j ＝∑ i p ij (3)
the time-varying regeneration number considering all cases at time t is:
step 3: estimating parameters of a bin model and simulating the population quantity of each bin;
estimating key parameters of a bin model, fitting epidemic dynamics by using the dynamic model, and simulating and predicting diffusion trend, wherein the method comprises the following steps of:
the transmission rate β of the undetected infected person: based on the dynamic regeneration number R of the undetected infected person t Calculating the ratio of the infectious period D of the non-detected infected person, and obtaining the transmission rate beta' of the detected infected person by a similar method; wherein, the infection period D refers to the time span from the infection ability of an infected person to the loss of the infection ability due to isolation or cure;
the asymptomatic infected person is diagnosed with probability μ: the method for calculating the diagnosis probability eta of symptomatic infected patients is the same as the method for calculating the diagnosis proportion of asymptomatic infected patients divided by the average time from infection to diagnosis;
the asymptomatic infected person converts to a symptomatic probability b: dividing the asymptomatic proportion in the infected person by the average number of days from infection to onset;
probability h of the diagnosed symptomatic infected person getting hospitalized: obtained by dividing the proportion of hospitalization in symptomatic infected persons by the average number of days from onset to admission;
recovery probability γ of the inpatients: the recovery ratio of the inpatients is divided by the average recovery time, and the recovery probability gamma ', gamma' of the asymptomatic infected persons and the symptomatic infected persons are calculated by the same method;
probability of death of the inpatients sigma: the mortality ratio of hospitalized infected persons was divided by the average number of days from admission to death.
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