CN109192318A - The foundation and Laplace for describing the simplification SIS model of infectious disease transmission process are analyzed - Google Patents
The foundation and Laplace for describing the simplification SIS model of infectious disease transmission process are analyzed Download PDFInfo
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- 208000015181 infectious disease Diseases 0.000 title claims abstract description 51
- 208000035473 Communicable disease Diseases 0.000 title claims abstract description 42
- 238000000034 method Methods 0.000 title claims abstract description 40
- 230000005541 medical transmission Effects 0.000 title claims abstract description 30
- 230000008569 process Effects 0.000 title claims abstract description 29
- 230000006854 communication Effects 0.000 claims abstract description 7
- 230000007812 deficiency Effects 0.000 claims abstract description 4
- 230000007246 mechanism Effects 0.000 claims description 8
- 230000009466 transformation Effects 0.000 claims description 4
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- 201000010099 disease Diseases 0.000 description 6
- 208000037265 diseases, disorders, signs and symptoms Diseases 0.000 description 6
- 230000002265 prevention Effects 0.000 description 3
- 208000008128 pulmonary tuberculosis Diseases 0.000 description 3
- 230000014599 transmission of virus Effects 0.000 description 2
- 206010008631 Cholera Diseases 0.000 description 1
- 206010035148 Plague Diseases 0.000 description 1
- 241000700605 Viruses Species 0.000 description 1
- 241000607479 Yersinia pestis Species 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
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- 238000010200 validation analysis Methods 0.000 description 1
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Abstract
The present invention is the foundation and analysis of a kind of simplified SIS class infectious disease propagation model；The invention belongs to the crossing domains of complex network topologies dynamics, biomathematics and public cybersecurity；Present invention is generally directed to the classical deficiencies that analytic solutions are unable to get based on the SIS model of bilinearity infection rate, can describe to be simplified on the basis of SIS class infectious disease transmission crosses range request meeting；Simplified SIS model is intuitive, be easy to understand, analytic solutions can be obtained by Laplace transform method, can analyze infectious disease dynamic process and initial value on communication process influences, Steady-state Parameters value when can obtain infectious disease transmission feature and reach stable state.
Description
Technical field
The invention belongs to the crossing domains of complex network topologies dynamics, biomathematics and public cybersecurity, specially
The foundation and Laplace for describing the simplification SIS model of infectious disease transmission process are analyzed.
Background technique
Is originated from for the modeling of infectious disease transmission process, nineteen twenty-seven, Kermack and McKendrick were to Europe the 17th century
Plague is studied with cholera, is established the classical SIS model based on bilinearity infection rate, SIR model and is used till today.With
For SIS class infectious disease propagation model, mechanism is referring to attached drawing 2, shown in model citation form such as formula (1):
" compartment model " first has to it is confirmed that viral transmission process institute state that may be present, then according to state by net
Node in network is classified, and the differential equation of communication process is established further according to viral transmission mechanism, to describe virus from entering
The steady-state process of the original state of network to the end is invaded, we analyze available network node infection section by carrying out to model
Point peak value and to reach to peak value time and finally enter stable state time and enter stable state after various state nodes number
Amount.
" compartment model " this method modeled from macroscopic perspective right pop disease process is used till today
Because its is readily understood.Most at present " compartment model " or the basis based on classical " compartment model " and bilinearity infection rate
On, carry out condition relaxes and considers more situations such as: population migration, vertical transmission.But currently based on two-wire sexuality
There are two deficiencies with its improved model for the classics " compartment model " of dye rate:
1) analytic solutions are unable to get, equalization point can only be found out by the method for linearisation or prove the presence of equalization point, more
It can not influence of the analysis system initial value to infectious disease transmission；
2) influence of the topological structure to infectious disease transmission of transmitting carrier, subsequent improvement " compartment model " are not accounted for
Transmitting carrier topological structure factor is gradually being considered in modeling process.
Summary of the invention
The object of the present invention is to provide a kind of foundation of simplification SIS model for describing infectious disease transmission process and Laplace
Analysis.
The technical solution adopted by the present invention is that:
A kind of foundation and Laplace analysis of the simplification SIS model describing infectious disease transmission process, from SIS class infectious disease
The mechanism of transmission start with, be based on " warehouse modeling " thought, establish a SIS propagation model simplified, and based on the transformation side Laplace
Method analyzes the simplification SIS model established.
Simplify SIS model:
Simplification SIS infectious disease propagation model based on infectious disease transmission mechanism is intuitive, is easy to understand；
1) it can satisfy the basic demand of description SIS class infectious disease transmission process.
3, the foundation of the simplification SIS model of description infectious disease transmission process according to claim 1 and Laplace divide
Analysis, which is characterized in that analyzed based on Laplace transform method SIS model is simplified；
1) the SIS Epidemic Model simplified can use Laplace transformation and be analyzed, and obtain solution to model analysis solution；
It 2) being capable of influence of the analysis system initial value to SIS class infectious disease transmission；
3) state parameter that communication process reaches stable state can be obtained.
Simplify the foundation of SIS model；
For first deficiency of compartment model, under the premise of meeting the requirement of description infectious disease transmission process, from probability
Angle is started with, and carries out abbreviation to the classical SIS model based on bilinearity infection rate；The SIS model that abbreviation obtains is more intuitive, easy
Understand and can be analyzed by the method that Laplace is converted；The analytic solutions for analyzing available system, are obtained by analytic solutions
To infectious disease transmission dynamic characteristic, can analyze influence of the system initial value to infectious disease transmission process；Model abbreviation process is such as
Shown in lower:
This core concept for simplifying SIS model is to extract node from network node at random, certain shape probability of state etc.
Valence is in network with the ratio of the state node.
Simplify the Laplace analysis of SIS model；
The advantage analyzed in differential system is converted using Laplace, and the simplification SIS model established is analyzed, is obtained
To the analytic solutions of system (2) are as follows:
Analytically solution kind is easy to obtain the stable state of infectious disease and dynamic convergence process, and available system initial value s
(0), i (0) on communication process influences.
The invention has the advantages that the SIS model simplified is intuitive, is easy to understand, can be obtained by Laplace transform method
Analytic solutions can analyze infectious disease dynamic process and initial value and on communication process influence, can obtain infectious disease transmission feature and
Reach Steady-state Parameters value when stable state.
Detailed description of the invention
Fig. 1 is technical field logic relation picture.
Fig. 2 is SIS class infectious disease transmission mechanism figure.
Fig. 3 model validation simulation result.
Specific embodiment
The present invention is described in more detail by 1-3 with reference to the accompanying drawings of the specification.
1. establishing simplified SIS model from probability angle according to the mechanism of transmission of SIS class infectious disease.
2. carrying out time domain-frequency domain conversion to SIS model is simplified according to Laplace shift theory
3. being simplified analytic solutions of the SIS model in frequency domain by arranging；
4. converting time solution for the Frequency Domain Solution for simplifying SIS model using Laplace inverse transformation, simplified SIS is finally obtained
Solution to model analysis solution；
5. according to the SIS solution to model analysis solution analysis dynamic variation characteristic of infectious disease is simplified, influence of the initial value to propagation, most
The time of whole stable state and arrival stable state.
Pulmonary tuberculosis data (- 2017 years 2 months 2012 12 provided with the Notifiable disease report of Chinese Disease Control and Prevention Center publication
Month) it is correlation data, to simplify SIS analytical model solution as fitting frame, system initial value, probability of infection, treatment rate are carried out most
Small two multiply fitting, and gained optimal solution substituted into simplify SIS model and form theoretical curve and is compared with Disease Control and Prevention Center data, say
Bright invented simplification SIS model can describe the trend of infectious disease transmission, meet the basic demand of Epidemic Model.Wherein,
Data are handled by Linear Amplifer, and treatment process is detailed in Detailed description of the invention.
Pulmonary tuberculosis data of the data source in the Notifiable disease report that Chinese Disease Control and Prevention Center issues, period 2011
Year 2 months 2018 July-, data pass through Linear Amplifer, and total number of people is 1,000,000,000 orders of magnitude, e.g., in July, 2011 Pulmonary Tuberculosis Infection
Number is 112647 people, population magnitude 1.09, infection proportion 1.12647*10-4, it is 0.112647 after Linear Amplifer processing.
Claims (5)
1. a kind of foundation of simplification SIS model for describing infectious disease transmission process and Laplace are analyzed, which is characterized in that
Start with from the mechanism of transmission of SIS class infectious disease, be based on " warehouse modeling " thought, establishes a SIS propagation model simplified, and
The simplification SIS model established is analyzed based on Laplace transform method.
2. the foundation of the simplification SIS model of description infectious disease transmission process according to claim 1 and Laplace are analyzed,
It is characterized in that,
Simplify SIS model:
1) the simplification SIS infectious disease propagation model based on infectious disease transmission mechanism is intuitive, is easy to understand；
2) it can satisfy the basic demand of description SIS class infectious disease transmission process.
3. the foundation of the simplification SIS model of description infectious disease transmission process according to claim 1 and Laplace are analyzed,
It is characterized in that, being analyzed based on Laplace transform method SIS model is simplified；
1) the SIS Epidemic Model simplified can use Laplace transformation and be analyzed, and obtain solution to model analysis solution；
It 2) being capable of influence of the analysis system initial value to SIS class infectious disease transmission；
3) state parameter that communication process reaches stable state can be obtained.
4. the foundation of the simplification SIS model of description infectious disease transmission process according to claim 1 and Laplace are analyzed,
It is characterized in that,
Simplify the foundation of SIS model；
For first deficiency of compartment model, under the premise of meeting the requirement of description infectious disease transmission process, from probability angle
Start with, abbreviation is carried out to the classical SIS model based on bilinearity infection rate；The SIS model that abbreviation obtains is more intuitive, readily understood
And it can be analyzed by the method that Laplace is converted；The analytic solutions for analyzing available system, are passed by analytic solutions
Catch an illness propagation dynamic characteristic, can analyze influence of the system initial value to infectious disease transmission process；The following institute of model abbreviation process
Show:
This core concept for simplifying SIS model is to extract node from network node at random, certain shape probability of state is equivalent to
With the ratio of the state node in network.
5. the foundation of the simplification SIS model of description infectious disease transmission process according to claim 1 and Laplace are analyzed,
It is characterized in that,
Simplify the Laplace analysis of SIS model；
The advantage analyzed in differential system is converted using Laplace, and the simplification SIS model established is analyzed, is
The analytic solutions of system (2) are as follows:
Analytically solution kind is easy to obtain the stable state of infectious disease and dynamic convergence process, and available system initial value s (0), i
(0) it on communication process influences.
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| CN109192319A (en) * | 2018-07-11 | 2019-01-11 | 辽宁石油化工大学 | A kind of description method for the viral transmission process considering dynamic network structure |
| CN110458324A (en) * | 2019-07-04 | 2019-11-15 | 重庆金融资产交易所有限责任公司 | Calculation method, device and the computer equipment of risk probability |
| WO2021189516A1 (en) * | 2020-03-27 | 2021-09-30 | 中国科学院深圳先进技术研究院 | Method and system for simulating process of temporal and spatial circulation of influenza with massive trajectory data |
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Application publication date: 20190111 |