Infectious disease time-varying forward sequence interval distribution inference method

Abstract

The invention discloses an infectious disease time-varying forward sequence interval distribution inference method, and belongs to the technical field of intelligent medical treatment. In order to reasonably deduce forward sequence interval distribution at related time points, the method comprises the following steps: constructing a basic transmission chain model of infectious diseases; based on the constructed basic propagation chain model of the infectious disease, establishing an inequality constraint of an effective regeneration number of the time point # imgabs0 #; based on the inequality constraint of the effective regeneration number of the obtained time point # imgabs1 #, establishing a relation between forward sequence interval distribution and reverse sequence interval distribution; constructing a forward sequence spaced distribution inference target; and constructing a forward sequence interval distribution inference method. The forward sequence interval distribution provided by the invention allows dynamic change along with time so as to better conform to the actual situation. And when the true situation of # imgabs2 is sub-exponential growth, the forward sequence interval distribution difference deduced under the assumption that the # imgabs2 is exponential growth and the assumption that the # imgabs2 is sub-exponential growth is compared, so that the necessity of reasonably constructing the initial growth mode of the infectious disease is explained.

Description

Technical Field

[0001] The present invention belongs to the field of smart medical technology, and specifically relates to a method for inferring the interval distribution of a time-varying positive sequence of an infectious disease. Background Art

[0002] In recent years, more and more infectious diseases have attracted people's attention. For example, after the outbreak of COVID-19, relevant key parameters and indicators of infectious diseases can provide reference information for the formulation of subsequent prevention and control measures, such as basic reproduction number, effective reproduction number, etc. (Effective reproduction number), generation time interval, forward serial interval, backward serial interval, incubation period. After being infected, patients may need to go through an incubation period before they develop symptoms, and the onset of symptoms at this time is also called "onset". In actual observation, it is difficult to directly observe when a patient is infected, but it is possible to directly observe when the patient develops the disease.

[0003] In previous studies, it is necessary to give a preset growth pattern for the number of cases at each point in time. It can be given explicitly, for example, it is usually assumed to be early exponential growth; it can also be given implicitly, for example, a transmission mechanism of the infectious disease is assumed (such as SIR, SEIR, etc.). Recent studies have shown that in reality, due to contact patterns, spatial effects, inhomogeneous mixing, reactive behavior changes or other mechanisms, the early growth pattern of a large number of infectious diseases is not exponential growth, but subexponential growth. Different preset growth patterns may have a greater impact on the subsequent inference of related infectious disease parameters, such as the inference of the positive sequence interval distribution. Basic reproduction number (the average number of secondary infections caused by primary infection), the effective reproduction number, and the growth rate of the number of cases are key parameters of infectious diseases, which are linked by generation intervals, incubation periods, etc. Since the generation interval is the time delay between the time when the transmitter and the infected person are infected, it is difficult to observe directly, so the serial interval is generally used as a direct substitute or inferred from the serial interval through the incubation period. Therefore, the serial interval is the key to linking these core parameters or indicators, and the positive serial interval distribution can more accurately evaluate the relevant parameters of infectious diseases. However, in actual observation statistics, it is easier to obtain the reverse serial interval distribution, because when the reverse serial interval distribution is statistically calculated, only the information of the infected person at the time point that has already occurred needs to be searched. In contrast, when the positive serial interval distribution is statistically calculated, some transmission pairs may be missed because some infected people have not yet developed the disease. Therefore, it is key to reasonably infer the positive serial interval distribution at the relevant time point. Summary of the invention

[0004] The problem to be solved by the present invention is to reasonably infer the interval distribution of the positive sequence at relevant time points, and to propose a method for inferring the time-varying interval distribution of the positive sequence of infectious diseases.

[0005] To achieve the above object, the present invention is implemented through the following technical solutions: A method for inferring the interval distribution of a time-varying positive sequence of an infectious disease comprises the following steps: S1. Construct a basic transmission chain model for infectious diseases; S2. Based on the basic transmission chain model of infectious diseases constructed in step S1, establish the time point Inequality constraints on the effective reproduction number of ; S3. Based on the time point obtained in step S2 The inequality constraint of the effective reproduction number is used to establish the relationship between the forward sequence interval distribution and the reverse sequence interval distribution; S4. Constructing the inference target of the positive serial interval distribution; S5. Inference methods for constructing positive serial interval distributions.

[0006] Furthermore, the specific implementation method of step S1 includes the following steps: S1.1. Set the basic transmission situation of the infectious disease to local transmission and no imported infections; S1.2. Setting the time point in the transmission chain The number of nodes on , used to represent the number of patients with the disease. In the transmission pair, the initiator of infection is called the Infector, and the patient infected by the Infector is called the Infectee. The Infectee is the successor Infectee of the Infector, and the Infector is the predecessor Infectee of the Infector. S1.3. Let the maximum interval in the distribution of serial intervals of the propagation chain be , define the time point The nodes on the have the property of complete observation, which means that they have the property of observation up to the time point The predecessor propagation node and the successor sensing node of each node; S1.4. Assumption represents the effective time point length of the transmission chain, then the time point length of the transmission chain is ,set up It represents the maximum continuous observation time point of the transmission chain, completing the construction of the basic transmission chain model of the infectious disease.

[0007] Furthermore, the specific implementation method of step S2 includes the following steps: S2.1. Consider The right time point The effective reproduction number Based on the basic transmission chain model of infectious diseases obtained in step S1, the infection starts at , then when at the time point Time, from the time point The node before must be part of a continuous transmission chain; The nodes are determined by The nodes are connected and are located at the time point The node is not an isolated node, so The nodes on must all be connected by edges; and The nodes on the The out-degree edge on , that is, The edges sent from All nodes on have a unique predecessor propagation node, then the expression is: (1) in, For the i The number of nodes at a time point, i for t Any one of For the i The effective reproduction number at a point in time; S2.2. Based on The outgoing edges do not need to make all the edges in All nodes have unique predecessor propagation nodes, then: (2) then , the number of nodes at each time point , the maximum interval in the distribution of serial intervals of the propagation chain as well as , satisfying the following inequality constraints: (3) S2.3. Further consider the following situation: When considering the time point on Time, time point on For known ,have: (4) Therefore, we have: (5) in, for At the point in time The lower bound of the upper for At the point in time The upper bound of the upper; The expression is: (6) The expression is: (7) S2.4. Based on Inequality constraints Make estimates; Consider based on exist It is known that on According to formula (5), when considering the time point When: (8) Based on the assignment method, take the ratio of the upper and lower bounds , which can be set to change over time or take random values, then: (9) in, Time point An estimate of the effective reproduction number; Next, use calculate and , and then use the same method to obtain Repeat the above process until be estimated; Therefore, ,have: (10) in, is the length of the time delay between the onset of the disease in the transmitter and the onset of the disease in the corresponding recipient; (11) (12).

[0008] Furthermore, the specific implementation method of step S3 includes the following steps: S3.1. Construction time The effective reproduction number , Time The total number of outgoing edges from the nodes on and time point The number of nodes on The relationship formula is: (13); S3.2. Definitions Indicates that the starting point is from the time point , the end point is at time The total number of out-degree edges of , then the construction time The positive serial interval distribution of It is defined by the following formula: (14); S3.3. The distribution of the intervals of the reverse sequence is the time point from the reverse perspective Facing the past The angle definition of the time point is Reverse serial interval distribution The formula is: (15); S3.4. According to , as well as The formula is , there is the following formula: (16) And because It is easy to derive from observations that At any point in time, it is known that Depend on The inequality estimate is given, and the formula for the relationship between the forward sequence interval distribution and the reverse sequence interval distribution is: (17).

[0009] Furthermore, the specific implementation method of step S4 includes the following steps: S4.1. Assumptions is the maximum continuous observation time point of the transmission chain, indicating that the time interval can be observed The ability to propagate chains from the reverse perspective of all nodes; S4.2. Assume that the node is at time The above is a fully observed property, then The relevant links on the above are known quantities, then at the time point on , as well as All are known quantities; For , set in the time interval Get The effective part of for subsequent calculation or inference, so set: (18) Right now: (19) Since the considered propagation chain only provides The above has the property of being fully observed, so Theoretically, the maximum ,get: (20); S4.3. Calculation exist The true value of S4.4. Constructing a forward serial interval distribution where the inference target is a time interval Positive serial interval distribution on .

[0010] Furthermore, the specific implementation method of step S5 includes the following steps: S5.1. Construct the inference matrix Inference Matrix, whose Row, No. The elements of the column represent the time points And the time delay length The forward sequence interval The value of and , set the time and , so the inference matrix Inference Matrix has Line and Columns, the matrix size is ; S5.2. Setting time point Inference Matrix The time points represented by the rows are: (twenty one) Then when and When the following inequality is satisfied, the inference matrix Inference Matrix Row, No. The elements of the column have the capabilities inferred from formula (17): (twenty two) Right now: (twenty three) According to the above formula, we can get the inference matrix from the first row to the first column. The element values ​​of the column are calculated by formula (17); like and To satisfy the above inequality, take , , then the first Row, No. The elements of the column are given by the following formula: (twenty four); S5.3. Each row of the inference matrix represents a probability distribution. , there is the following formula: (25) Then when , of The value is given by formula (24), so the first row of The columns are given by the following formula: (26); S5.4. Assuming that the change in the distribution of the positive sequence interval is continuous when the external intervention intensity remains unchanged, then the current time point of Compared with before The differences between the average distributions of time should be as small as possible; for Time and , average distribution Given by: (27) set up , then the inference matrix The status of the line Calculated at the time And the probability value in the forward serial interval distribution to be inferred The status is as follows:

[0011] in, In In the above formula, the values ​​are ; S5.5. Define the difference between the two distributions obtained in step S5.4 for: (28) Then define the difference function for: (29) According to formula (25), there are the following constraints: (30) Then write the above expression as: (31) In summary, the inference method for constructing the positive sequence interval distribution is to calculate the constraints under Minimize: (32); S5.6. Constructing Lagrangian functions as follows: (33) in, is the Lagrange multiplier; Right now: (34) Then, combine the following equations: (35) get: (36) The above formula is as well as All are established; If it appears , then set the , and then recalculate the other value; Then, the inference matrix Inference Matrix is ​​calculated by using formulas (24) and (26) to satisfy Elements The value of , where the element The value is The value of , and then calculate the element values ​​at other positions using formula (36).

[0012] Beneficial effects of the present invention: The method for inferring the time-varying positive sequence interval distribution of infectious diseases described in the present invention is similar to The growth pattern is not mandatory and can be assumed to be exponential growth, sub-exponential growth, or other growth patterns.

[0013] The method for inferring the time-varying forward sequence interval distribution of an infectious disease described in the present invention does not require the forward / reverse sequence interval distribution to be fixed, but rather a time-varying distribution that is closer to the actual situation, and does not require the pre-assumption of a certain type of special distribution.

[0014] The present invention provides a method for inferring the time-varying positive sequence interval distribution of infectious diseases. Over time Changing constraints ( Inequality), this constraint condition does not require too many additional assumptions, which can guide subsequent research based on the observed To reasonably presume .

[0015] The invention discloses a method for inferring time-varying positive sequence interval distribution of an infectious disease, and proposes a method for inferring positive sequence interval distribution, wherein the positive sequence interval distribution varies with time.

[0016] The present invention provides a method for inferring the time-varying positive sequence interval distribution of infectious diseases, focusing on more reasonable In the growth mode (sub-exponential growth), the distribution of positive sequence intervals over time is inferred. Through further derivation and exploration, the present invention There is no mandatory assumption on the growth mode, which can be either exponential growth or sub-exponential growth, or other forms of growth mode; and the forward sequence interval distribution of the present invention allows dynamic changes over time to be more in line with the actual situation. When the actual situation is sub-exponential growth, comparing the difference in the distribution of positive sequence intervals inferred under the assumption of exponential growth and the assumption of sub-exponential growth shows the necessity of reasonably constructing the initial growth model of infectious diseases. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1It is a flow chart of a method for inferring time-varying forward sequence interval distribution of infectious diseases according to the present invention; Figure 2 For the present invention Auxiliary schematic diagram of meaning; Figure 3 For the present invention Schematic diagram of the impact that the last observation time point may have on the calculation of the forward sequence interval distribution; Figure 4 For the present invention Schematic diagram of the reverse sequence interval perspective as an example; Figure 5 For the present invention Schematic diagram of the forward sequence interval perspective as an example; Figure 6 For the present invention Schematic diagram of parameters or distributions that can be calculated when the time point is fully observable; Figure 7 It is a schematic diagram of each key time point of the present invention; Figure 8 This is a schematic diagram of the time points at which the present invention can directly calculate the interval distribution of the forward sequence. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solution and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the specific embodiments described are only part of the embodiments of the present invention, rather than all of the specific embodiments. The components of the specific embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0019] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents the selected specific embodiments of the present invention. Based on the specific embodiments of the present invention, all other specific embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0020] In order to further understand the content, features and effects of the present invention, the following specific implementation methods are given as examples, and the attached Figure 1 -Attached Figure 8 The detailed instructions are as follows: A method for inferring the interval distribution of a time-varying positive sequence of an infectious disease comprises the following steps: S1. Construct a basic transmission chain model for infectious diseases; Furthermore, the specific implementation method of step S1 includes the following steps: S1.1. Set the basic transmission situation of the infectious disease to local transmission and no imported infections; S1.2. Setting the time point in the transmission chain The number of nodes on , used to represent the number of patients with the disease. In the transmission pair, the initiator of infection is called the Infector, and the patient infected by the Infector is called the Infectee. The Infectee is the successor Infectee of the Infector, and the Infector is the predecessor Infectee of the Infector. S1.3. Let the maximum interval in the distribution of serial intervals of the propagation chain be , define the time point The nodes on the have the property of complete observation, which means that they have the property of observation up to the time point The predecessor propagation node and the successor sensing node of each node; S1.4. Assumption represents the effective time point length of the transmission chain, then the time point length of the transmission chain is ,set up It represents the maximum continuous observation time point of the transmission chain, completing the construction of the basic transmission chain model of the infectious disease.

[0021] Furthermore, except for the node at the initial time point, each node at each time point must have a unique predecessor transmission node, but not necessarily a subsequent infection node (this means that the node does not transmit the infectious disease to other nodes / individuals). represents the effective time length of the transmission chain, then the time length involved in the transmission chain is , which means that in the considered transmission chain, the time interval The nodes are "fully observable" and are in The predecessor propagation nodes of the nodes on must come from the time interval In addition, in the considered propagation chain, The nodes on the network must not have subsequent infected nodes, because the main focus is on the transmission chain. The infection and infection status of the previous node, and the extended time interval Just to ensure that The subsequent infected nodes of the nodes above will not be missed. represents the maximum continuous observation time point of the transmission chain, which means that we can know The exact and unique predecessor propagation node of all nodes on the network, but the subsequent infection nodes of these nodes are not necessarily known. Subsequent infected nodes of the node on may appear At this point in time, in this case, the link will not be observed.

[0022] S2. Based on the basic transmission chain model of infectious diseases constructed in step S1, establish the time point Inequality constraints on the effective reproduction number of ; Furthermore, the specific implementation method of step S2 includes the following steps: S2.1. Consider The right time point The effective reproduction number Based on the basic transmission chain model of infectious diseases obtained in step S1, the infection starts at , then when at the time point Time, from the time point The node before must be part of a continuous transmission chain; The nodes are determined by The nodes are connected and are located at the time point The node is not an isolated node, so The nodes on must all be connected by edges; and The nodes on the The out-degree edge on , that is, The edges sent from All nodes on have a unique predecessor propagation node, then the expression is: (1) in, For the i The number of nodes at a time point, i for t Any one of For the i The effective reproduction number at a point in time; Furthermore, The outgoing edges do not need to make all the edges in Each node has a unique predecessor propagation node, because The nodes on the Nodes on ; S2.2. Based on The outgoing edges do not need to make all the edges in All nodes have unique predecessor propagation nodes, then: (2) when The outgoing edges from When all nodes on , the equality sign on the right side of the above inequality holds.

[0023] then , the number of nodes at each time point , the maximum interval in the distribution of serial intervals of the propagation chain as well as , satisfying the following inequality constraints: (3) S2.3. Further consider the following situation: When considering the time point on Time, time point on For known ,have: (4) Therefore, we have: (5) in, for At the point in time The lower bound of the upper for At the point in time The upper bound of the upper; The expression is: (6) The expression is: (7) Furthermore, when NPI (Non-Pharmaceutical Intervention) changes, Follow If the change The upper and lower bounds also change accordingly. Inequality constraints can not only be used to check the current Does the value meet the numerical requirements and can guide Estimates.

[0024] S2.4. Based on Inequality constraints Make estimates; Consider based on exist It is known that on According to formula (5), when considering the time point When: (8) Based on the assignment method, take the ratio of the upper and lower bounds , then: (9) in, Time point An estimate of the effective reproduction number; Next, use calculate and , and then use the same method to obtain Repeat the above process until be estimated; Therefore, ,have: (10) in, is the length of the time delay between the onset of the disease in the transmitter and the onset of the disease in the corresponding recipient; (11) (12).

[0025] S3. Based on the time point obtained in step S2 The inequality constraint of the effective reproduction number is used to establish the relationship between the forward sequence interval distribution and the reverse sequence interval distribution; Furthermore, the specific implementation method of step S3 includes the following steps: S3.1. Construction time The effective reproduction number , Time The total number of outgoing edges from the nodes on and time point The number of nodes on The relationship formula is: (13); S3.2. Definitions Indicates that the starting point is from the time point , the end point is at time The total number of out-degree edges, set , then the construction time The positive serial interval distribution of It is defined by the following formula: (14); Forward Serial Interval Distribution is a distribution that stands at a point in time. Looking to the future The Backward Serial Interval Distribution is defined from the perspective of the reverse time point. Facing the past Obviously, since the minimum time point is , so when At the time and time point There is no directed edge between them, that is, Since the transmission chain is continuous, each The node must be an infected node, which means that The node at time has only one predecessor node. The total number of in-degree edges of the previous node must be .

[0026] S3.3. The distribution of the intervals of the reverse sequence is the time point from the reverse perspective Facing the past The angle definition of the time point is Reverse serial interval distribution The formula is: (15); S3.4. According to , as well as The formula is , there is the following formula: (16) And because It is easy to derive from observations that At any point in time, it is known that Depend on The inequality estimate is given, and the formula for the relationship between the forward sequence interval distribution and the reverse sequence interval distribution is: (17).

[0027] S4. Constructing the inference target of the positive serial interval distribution; It is necessary to clarify the specific target to be inferred is the forward serial interval distribution (ForwardSerial Interval Distribution) in which time period. Since the transmission chain considered has a transmission time of (also referred to as effective time in the above text) and the maximum sequence interval delay is assumed to be , so the maximum duration of the propagation chain is , which allows the propagation chain to obtain superior and The true value of Therefore, we first need to clarify which time intervals The true value can be directly calculated, which time intervals What needs to be inferred and has the possibility of inference, and what time intervals cannot be inferred.

[0028] set up is the maximum observation time, which indicates the time interval that can be observed The propagation chain of the reverse view of all nodes on Figure 2 ). This means that each The only predecessor infector node of the node above, but its successor infectee node may not be observed. The successor node of the node at time point may appear in At this point in time, in this case, the link cannot be observed (see Figure 3 ).

[0029] A node is called at a point in time The meaning of “fully observable” is: (1) from the reverse perspective, we know that The predecessor propagation node of the node at the time point (see Figure 4 ); (2) From a positive perspective, we know that the The subsequent sensing node at the time point (see Figure 5 ).

[0030] Therefore, if the node is at time is fully observable (meaning that The relevant links on the above can be observed), then at time on , as well as can be calculated (see Figure 6 ).

[0031] Furthermore, the specific implementation method of step S4 includes the following steps: S4.1. Assumptions is the maximum continuous observation time point of the transmission chain, indicating that the time interval can be observed The ability to propagate chains from the reverse perspective of all nodes; S4.2. Assume that the node is at time The above is a fully observed property, then The relevant links on the above are known quantities, then at the time point on , as well as All are known quantities; For , set in the time interval Get The effective part of for subsequent calculation or inference, so set: (18) Right now: (19) Since the considered propagation chain only provides The above has the property of being fully observed, so Theoretically, the maximum ,get: (20); S4.3. Calculation exist The true value of Furthermore, from a positive perspective, if we can observe the time point All out-degree edges of the nodes (considering at most ), you can calculate the time point on Value. ,So , which means that we can calculate exist The true value of Figure 8 As shown; On the other hand, the timing and time point , formula (17) gives and Since the growth pattern of the number of nodes over time is assumed to be known (for example, the number of nodes grows in a sub-exponential manner), and Known. exist can be calculated accurately and directly from the observed transmission chains, and exist can be estimated using formula (10-12). Therefore, for a specific and , to calculate Need to know The value of is recorded as: For example, Therefore, when calculating accurately, it is necessary to accurately calculate The value of On the point in time value. The maximum value that can be obtained is on Value. ,but , so it can be accurately calculated at most on value.

[0032] S4.4. Constructing a forward serial interval distribution where the inference target is a time interval Positive serial interval distribution on .

[0033] Furthermore, from a macro perspective The inferential boundary of Initially, no links or infection information between nodes can be observed, only information about and information; Obviously, for a given and There are many possible ways to connect nodes, and different ways of connecting nodes will lead to different Get the value.

[0034] From a positive perspective, the timing and time point The node link between is the last time point with link or infection information, which cannot be observed. and If there is a link or infection information between them, it is inferred that the target is a time interval Positive serial interval distribution on .

[0035] S5. Inference methods for constructing positive serial interval distributions.

[0036] Furthermore, the specific implementation method of step S5 includes the following steps: S5.1. Construct the inference matrix Inference Matrix, whose Row, No. The elements of the column represent the time points And the time delay length The forward sequence interval The value of and , set the time and , so the inference matrix Inference Matrix has Line and Columns, the matrix size is ; S5.2. Setting time point Inference Matrix The time points represented by the rows are: (twenty one) Then when and When the following inequality is satisfied, the inference matrix Inference Matrix Row, No. The elements of the column have the capabilities inferred from formula (17): (twenty two) Right now: (twenty three) According to the above formula, we can get the inference matrix from the first row to the first column. The element values ​​of the column are calculated by formula (17); like and To satisfy the above inequality, take , , then the first Row, No. The elements of the column are given by the following formula: (twenty four); S5.3. Each row of the inference matrix represents a probability distribution. , there is the following formula: (25) Then when , of The value is given by formula (24), so the first row of The columns are given by the following formula: (26); Next, additional assumptions need to be added to enable the inference process to move forward. Assume that the intensity of external intervention remains unchanged (for example, the NPI does not change dramatically, the vaccine coverage does not change significantly, the vaccine efficacy does not change significantly, etc.); S5.4. Assuming that the change in the distribution of the positive sequence interval is continuous when the external intervention intensity remains unchanged, then the current time point of Compared with before The differences between the average distributions of time should be as small as possible; for Time and , average distribution Given by: (27) set up , then the inference matrix The status of the line Calculated at the time And the probability value in the forward serial interval distribution to be inferred The status is as follows:

[0037] in, In In the above formula, the values ​​are ; S5.5. Define the difference between the two distributions obtained in step S5.4 for: (28) Then define the difference function for: (29) According to formula (25), there are the following constraints: (30) Then write the above expression as: (31) In summary, the inference method for constructing the positive sequence interval distribution is to calculate the constraints under Minimize: (32); S5.6. Constructing Lagrangian functions as follows: (33) in, is the Lagrange multiplier; Right now: (34) Then, combine the following equations: (35) get: (36) The above formula is as well as All are established; If it appears , then set the , and then recalculate the other value; Then, the inference matrix Inference Matrix is ​​calculated by using formulas (24) and (26) to satisfy Elements The value of , where the element The value is The value of , and then calculate the element values ​​at other positions using formula (36).

[0038] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0039] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and parts thereof may be replaced with equivalents without departing from the scope of the present application. In particular, as long as there is no structural conflict, the various features in the specific embodiments disclosed in the present application may be used in combination with each other in any manner, and the fact that these combinations are not exhaustively described in this specification is only for the sake of omitting space and saving resources. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A method for inferring the interval distribution of a time-varying forward series of infectious diseases, characterized in that: The steps include: S1. Construct a basic transmission chain model for infectious diseases; S2. Based on the basic transmission chain model of infectious diseases constructed in step S1, establish the time point Inequality constraints on the effective reproduction number of ; S3. Based on the time point obtained in step S2 The inequality constraint of the effective reproduction number is used to establish the relationship between the forward sequence interval distribution and the reverse sequence interval distribution; S4. Constructing the inference target of the positive serial interval distribution; S5. Inference methods for constructing positive serial interval distributions.

2. A method for inferring time-varying positive sequence interval distribution of infectious diseases according to claim 1, characterized in that: The specific implementation method of step S1 includes the following steps: S1.

1. Set the basic transmission situation of the infectious disease to local transmission and no imported infections; S1.

2. Setting the time point in the transmission chain The number of nodes on , used to represent the number of patients with the disease. In the transmission pair, the initiator of infection is called the Infector, and the patient infected by the Infector is called the Infectee. The Infectee is the successor Infectee of the Infector, and the Infector is the predecessor Infectee of the Infector. S1.

3. Let the maximum interval in the distribution of serial intervals of the propagation chain be , define the time point The nodes on the have the property of complete observation, which means that they have the property of observation up to the time point The predecessor propagation node and the successor sensing node of each node; S1.

4. Assumption represents the effective time point length of the transmission chain, then the time point length of the transmission chain is ,set up It represents the maximum continuous observation time point of the transmission chain, completing the construction of the basic transmission chain model of the infectious disease.

3. The method for inferring the time-varying forward sequence interval distribution of an infectious disease according to claim 2, characterized in that: The specific implementation method of step S2 includes the following steps: S2.

1. Consider The right time point The effective reproduction number Based on the basic transmission chain model of infectious diseases obtained in step S1, the infection starts at , then when at the time point Time, from the time point The node before must be part of a continuous transmission chain; The nodes are determined by The nodes are connected and are located at the time point The node is not an isolated node, so The nodes on must all be connected by edges; and The nodes on the The out-degree edge on , that is, The edges sent from All nodes on have a unique predecessor propagation node, then the expression is: （1） in, For the i The number of nodes at a time point, i for t Any one of For the i The effective reproduction number at a point in time; S2.

2. Based on The outgoing edges do not need to make all the edges in All nodes have unique predecessor propagation nodes, then: （2） then , the number of nodes at each time point , the maximum interval in the distribution of serial intervals of the propagation chain as well as , satisfying the following inequality constraints: （3） S2.

3. Further consider the following situation: When considering the time point on Time, time point on For known ,have: （4） Therefore, we have: （5） in, for At the point in time The lower bound of the upper for At the point in time The upper bound of the upper; The expression is: （6） The expression is: （7） S2.

4. Based on Inequality constraints Make estimates; Consider based on exist It is known that on According to formula (5), when considering the time point When: （8） Based on the assignment method, take the ratio of the upper and lower bounds , then: （9） in, Time point An estimate of the effective reproduction number; Next, use calculate and , and then use the same method to obtain Repeat the above process until be estimated; Therefore, ,have: （10） in, is the length of the time delay between the onset of the disease in the transmitter and the onset of the disease in the corresponding recipient; （11） （12）。 4. A method for inferring the time-varying forward sequence interval distribution of an infectious disease according to claim 3, characterized in that: The specific implementation method of step S3 includes the following steps: S3.

1. Construction time The effective reproduction number , Time The total number of outgoing edges from the nodes on and time point The number of nodes on The relationship formula is: （13）； S3.

2. Definitions Indicates that the starting point is from the time point , the end point is at time The total number of out-degree edges of , then the construction time The positive serial interval distribution of It is defined by the following formula: （14）； S3.

3. The distribution of the intervals of the reverse sequence is the time point from the reverse perspective Facing the past The angle definition of the time point is Reverse serial interval distribution The formula is: （15）； S3.

4. According to , as well as The formula is , there is the following formula: （16） And because It is easy to derive from observations that At any point in time, it is known that Depend on The inequality estimate is given, and the formula for the relationship between the forward sequence interval distribution and the reverse sequence interval distribution is: （17）。 5. A method for inferring the time-varying forward sequence interval distribution of an infectious disease according to claim 4, characterized in that: The specific implementation method of step S4 includes the following steps: S4.

1. Assumptions is the maximum continuous observation time point of the transmission chain, indicating that the time interval can be observed The ability to propagate chains from the reverse perspective of all nodes; S4.

2. Assume that the node is at time The above is a fully observed property, then The relevant links on the above are known quantities, then at the time point on , as well as All are known quantities; For , set in the time interval Get The effective part of for subsequent calculation or inference, so set: （18） Right now: （19） Since the considered propagation chain only provides The above has the property of being fully observed, so Theoretically, the maximum ,get: （20）； S4.

3. Calculation exist The true value of S4.

4. Constructing a forward serial interval distribution where the inference target is a time interval Positive serial interval distribution on .

6. A method for inferring time-varying forward sequence interval distribution of infectious diseases according to claim 5, characterized in that: The specific implementation method of step S5 includes the following steps: S5.

1. Construct the inference matrix Inference Matrix, whose Row, No. The elements of the column represent the time points And the time delay length The forward sequence interval The value of and , set the time and , so the inference matrix Inference Matrix has Line and Columns, the matrix size is ; S5.

2. Setting time point Inference Matrix The time points represented by the rows are: （21） Then when and When the following inequality is satisfied, the inference matrix Inference Matrix Row, No. The elements of the column have the capabilities inferred from formula (17): （22） Right now: （23） According to the above formula, we can get the inference matrix from the first row to the first column. The element values ​​of the column are calculated by formula (17); like and To satisfy the above inequality, take , , then the first Row, No. The elements of the column are given by the following formula: （24）； S5.

3. Each row of the inference matrix represents a probability distribution. , there is the following formula: （25） Then when , of The value is given by formula (24), so the first row of The columns are given by the following formula: （26）； S5.

4. Assuming that the change in the distribution of the positive sequence interval is continuous when the external intervention intensity remains unchanged, then the current time point of Compared with before The differences between the average distributions of time should be as small as possible; for Time and , average distribution Given by: （27） set up , then the inference matrix The status of the line Calculated at the time And the probability value in the forward serial interval distribution to be inferred The status is as follows: ； in, In In the above formula, the values ​​are ; S5.

5. Define the difference between the two distributions obtained in step S5.4 for: （28） Then define the difference function for: （29） According to formula (25), there are the following constraints: （30） Then write the above expression as: （31） In summary, the inference method for constructing the positive sequence interval distribution is to calculate the constraints under Minimize: （32）； S5.

6. Constructing Lagrangian functions as follows: （33） in, is the Lagrange multiplier; Right now: （34） Then, combine the following equations: （35） get: （36） The above formula is as well as All are established; If it appears , then set the , and then recalculate the other value; Then, the inference matrix Inference Matrix is ​​calculated by using formulas (24) and (26) to satisfy Elements The value of , where the element The value is The value of , and then calculate the element values ​​at other positions using formula (36).

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