CN114707308A - Animal epidemic disease kinetic model prevention and control method and device based on livestock price - Google Patents
Animal epidemic disease kinetic model prevention and control method and device based on livestock price Download PDFInfo
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Abstract
The invention relates to a method and a device for preventing and controlling animal epidemic disease modeling based on livestock price, which comprises the steps of establishing a relational expression of livestock breeding quantity and livestock commodity market price in an area to be analyzed; constructing an animal epidemic disease kinetic model by using the relational expression; and (3) estimating the dynamic parameters of the constructed animal epidemic disease model by using a least square method, and performing parameter sensitivity analysis on the estimated parameters and the control parameters by using a Latin hypercube sampling method and a partial rank correlation coefficient method. And constructing an optimal control objective function of the animal epidemic disease, solving an optimal control solution by using the Pontryagin maximum value principle, and determining an optimal control strategy of the area to be analyzed. The method simultaneously considers the economic cost of population control and animal population epidemic disease control, finds the optimal control cost, and simultaneously needs to obtain the maximum profit in the breeding industry under the epidemic disease control.
Description
Technical Field
The invention relates to the technical field of computers, in particular to a method and a device for preventing and controlling an animal epidemic disease kinetic model based on livestock price.
Background
The outbreak of animal epidemic diseases can bring economic loss to animal breeding industry, some zoonosis can threaten human health at the same time, the animal epidemic diseases are divided into three types according to the degree of harm of the animal epidemic diseases to the production of the breeding industry and the human health, wherein one type of epidemic diseases is foot-and-mouth disease, African swine fever, highly pathogenic avian influenza and the like, the second type of epidemic diseases is rabies, brucellosis, grass carp hemorrhage and the like, the third type of epidemic diseases is colibacillosis, avian tuberculosis, turtle parotitis and the like, the three types of epidemic diseases can bring economic loss and harm of different degrees during the outbreak, and the economic loss and the harm are weakened from one degree to three degrees in sequence.
When epidemic diseases occur in the breeding process, livestock can not be slaughtered, killing, sterilization and burying treatment is needed, otherwise, the flowing of the disease to the market can cause great harm to human health, so economic loss can be caused to breeders, control and prevention measures must be taken for the epidemic diseases to reduce the economic loss, otherwise, serious consequences can be caused, part of cost needs to be spent in the process of taking the measures, and the breeders need to control breeding scale, slaughtering rate and control and prevention cost in the process, so that the disease can be controlled, and the maximum profit can be obtained with the minimum cost. In addition, if the epidemic disease is a disease of both human and livestock, the disease propagation conditions of animal populations and crowds need to be considered, and control and prevention measures are taken at the same time to better control the disease, government prevention and control personnel need to consider that the economic cost of both crowd prevention and control and animal population epidemic disease prevention and control is taken into consideration, so that the optimal control cost is found, and meanwhile, the maximum profit needs to be obtained in the breeding industry under the control of the epidemic disease.
Disclosure of Invention
The invention aims to solve the technical problem of the prior art and provides a method and a device for preventing and controlling an animal epidemic disease kinetic model based on livestock price.
The technical scheme for solving the technical problems is as follows:
a method for preventing and controlling animal epidemic disease dynamics model based on livestock price, which comprises the following steps:
establishing a relational expression of the livestock breeding quantity N and the livestock commodity market price p in an area to be analyzed:
wherein p is0Is the breeding price, alpha is the livestock slaughter rate, 0<α<1, f (p) is a demand function of the livestock commodity market price p, and the value of f (p) decreases with increasing livestock commodity market price p, ε is the livestock population growth rate coefficient, e is the average weight of slaughtered livestock, r is the livestock growth rate, K is the maximum value of the scale of farming,
is the growth rate of the livestock in unit time,
is the rate of price increase per unit time;
when the farmer is in a self-production and self-marketing mode, a first objective function is constructed and is solved by utilizing the maximum principle of Pontryagin to obtain a first optimal control solution, and when the farmer is in an outsourcing livestock mode, a second objective function is constructed and is solved by utilizing the maximum principle of Pontryagin to obtain a second optimal control solution;
and (3) constructing an animal epidemic disease kinetic model by using the relational expression:
obtaining estimation parameters of the animal epidemic disease kinetic model by using a least square method, performing parameter sensitivity analysis on the estimation parameters and the control parameters by using a Latin hypercube sampling LHS method and a partial rank correlation coefficient PRCC method, determining key parameters for epidemic disease control, constructing an animal epidemic disease optimal control objective function by using the animal epidemic disease kinetic model, and determining an optimal control strategy of the area to be analyzed by using the maximum value principle of Pontryagin and the key parameters.
The method has the beneficial effects that: the method comprises the steps of establishing a relational expression of livestock breeding quantity N and livestock commodity market price p of an area to be analyzed, constructing a first objective function when a farmer is in a self-production and self-marketing mode, solving by using the maximum principle of Pontryagin to obtain a first optimal control solution, constructing a second objective function when the farmer is in an outsourcing livestock mode, and solving by using the maximum principle of Pontryagin to obtain a second optimal control solution; the method comprises the steps of constructing an animal epidemic disease kinetic model by using the relational expression, obtaining estimation parameters of the animal epidemic disease kinetic model by using a least square method, carrying out parameter sensitivity analysis on the estimation parameters and the control parameters by using a Latin hypercube sampling LHS method and a partial rank correlation coefficient PRCC method, determining key parameters for epidemic disease control, constructing an animal epidemic disease optimal control target function by using the animal epidemic disease kinetic model, and determining an optimal control strategy of the region to be analyzed by using the maximum value principle of Pontryagin and the key parameters. The invention simultaneously considers the economic cost of population control and animal population epidemic disease control to find the optimal control cost, and simultaneously needs to obtain the maximum profit in the breeding industry under the epidemic disease control.
The invention also provides a device for preventing and controlling the animal epidemic disease kinetic model based on the price of the livestock, which comprises:
the relational expression establishing module is used for establishing a relational expression of the livestock breeding quantity N and the livestock commodity market price p in the area to be analyzed:
wherein p is0Is the breeding price, alpha is the livestock slaughter rate, 0<α<1, f (p) is a demand function of the livestock commodity market price p, and the value of f (p) decreases with increasing livestock commodity market price p, ε is the livestock population growth rate coefficient, e is the average weight of slaughtered livestock, r is the livestock growth rate, K is the maximum value of the scale of farming,
is the growth rate of the livestock in unit time,
is the rate of price increase per unit time;
the objective function establishing module is used for establishing a first objective function when the farmer is in a self-production and self-marketing mode, solving by utilizing the maximum principle of Pontryagin to obtain a first optimal control solution, and establishing a second objective function when the farmer is in an outsourcing livestock mode, solving by utilizing the maximum principle of Pontryagin to obtain a second optimal control solution;
the dynamic model building module is used for building an animal epidemic disease dynamic model by utilizing the relational expression:
the control strategy determination module is used for obtaining estimation parameters of the animal epidemic disease kinetic model by using a least square method, performing parameter sensitivity analysis on the estimation parameters and the control parameters by using a Latin hypercube sampling LHS method and a partial rank correlation coefficient PRCC method, determining key parameters for epidemic disease control, constructing an animal epidemic disease optimal control objective function by using the animal epidemic disease kinetic model, and determining an optimal control strategy of the area to be analyzed by using the maximum value principle of Pontryagin and the key parameters.
The invention also provides a computer readable storage medium, on which a computer program is stored, which when executed by a processor implements the steps of the method for preventing and controlling animal epidemic kinetic model based on livestock price in any one of the above technical solutions.
The invention also provides an electronic device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the program to realize the steps of the method for preventing and controlling the animal epidemic dynamic model based on the livestock price according to any one of the technical schemes.
Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments of the present invention or in the description of the prior art will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for controlling animal epidemic disease kinetic model based on livestock price according to an embodiment of the present invention;
fig. 2 is a block diagram of a control device for an animal epidemic kinetic model based on livestock price according to another embodiment of the 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 some, not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.
As shown in fig. 1, the method for preventing and controlling animal epidemic disease kinetic model based on livestock price in the embodiment of the invention comprises the following steps:
110. establishing a relational expression of the livestock breeding quantity N and the livestock commodity market price p in an area to be analyzed:
wherein p is0Is the breeding price, alpha is the livestock slaughter rate, 0<α<1, f (p) is a demand function of the livestock commodity market price p, and the value of f (p) decreases with increasing livestock commodity market price p, ε is the livestock population growth rate coefficient, e is the average weight of slaughtered livestock, r is the livestock growth rate, K is the maximum value of the scale of farming,
is the growth rate of the livestock in unit time,
is the rate of price increase per unit time.
120. When the farmer is in the self-production and self-marketing mode, a first objective function is constructed and solved by utilizing the maximum principle of Pontryagin to obtain a first optimal control solution, and when the farmer is in the outsourcing livestock mode, a second objective function is constructed and solved by utilizing the maximum principle of Pontryagin to obtain a second optimal control solution.
130. And constructing an animal epidemic disease kinetic model by using the relational expression.
140. And obtaining estimation parameters of the animal epidemic disease dynamics model by using a least square method, and performing parameter sensitivity analysis on the estimation parameters and the control parameters by using a Latin hypercube sampling LHS method and a partial rank correlation coefficient PRCC method to determine key parameters for epidemic disease control.
150. And constructing an optimal control objective function of the animal epidemic disease by using the animal epidemic disease kinetic model, and determining an optimal control strategy of the area to be analyzed by using the maximum value principle of Pontryagin and the key parameters.
It should be understood that the implementation of parameter sensitivity analysis, risk factor evaluation, and economic method evaluation for the advantages and disadvantages of each control strategy to obtain the optimization model selection strategy is a commonly used technical method at present, and the specific implementation manner may refer to the currently existing technology, which is not described in detail in this application, and only how to apply this application is discussed.
Based on the above embodiment, the demand function f (p) is D-bep, where D is the maximum demand of the livestock product and b is the price adjustment coefficient, the price transformation function is:
therefore, the relationship between the livestock breeding quantity N and the livestock commodity market price p is as follows:
further, in step 120, when the farmer is in the self-production and self-marketing mode, a first objective function is constructed, and the maximum value principle of pointryagin is utilized to solve, so as to obtain a first optimal control solution, which specifically includes:
the first objective function is:
wherein, C0N0The method is characterized in that the method comprises the steps of (1) the investment amount of initially buying livestock, the income is p alpha N, the unit time breeding cost of each livestock is C, the breeding cost is CN, dt is the integral of time, and T is the set terminal time;
solving an optimal control solution by using the maximum principle of Pontryagin, and constructing a Hamiltonian H:
wherein ep alpha N-CN is the profit per unit time,
and D-bep-aN is the right term of the differential equation, λ1And λ2As a companion matrixAnd (4) variable quantity.
Since H is linear with respect to the control variable α, (ep- λ)1-λ2) N is H and is expressed as sigma0(N,t)＝(ep-λ1-λ2)N；
A bang-bang control balance occurs according to the effect of the set variables described above, namely:
the optimal control solution under uncertainty is discussed below, namely:
based on the Hamiltonian H, the adjoint matrix and the terminal condition are satisfied, and the following equation is obtained:
the optimal control state is a stable equilibrium state, i.e.:
the above equation is therefore satisfied for the optimal control state,
and is
Obtaining:
thus, solving the following equation yields a first optimal control solution α*、N*And p*
Solving the equation to obtain
Wherein:
m3＝K2b2r3(-Kbr+6Db-6Dε)+27C2Kb(b+ε)4,
m4＝4D2r(b-ε)2(-3Kbr+2Db-2Dε),
m5＝m6(m6(m6-3Kbr+6Db-6Dε)-3Kbr(-Kbr+4Db-4Dε)+12D2((b-ε)2+ε2)),
m6＝4berεp0.
further, in step 120, when the farmer is in the outsourcing livestock mode, a second objective function is constructed, and the maximum value principle of pointryagin is utilized to solve, so as to obtain a second optimal control solution, which specifically includes:
the second objective function is:
wherein, ε e (p-p)0) Is the number of domestic animals bought inside and outside per unit time, C1Is the outsourcing price of each livestock;
the Hamiltonian is constructed similarly:
wherein λ1And λ2Is a companion matrix variable.
Since H is linear with respect to the control variables α and ε, (ep- λ)1-λ2) N and (lambda)1-C1)e(p-p0) For H linear coefficients of the control variables alpha and epsilon, note
σ1(N,t)＝(ep-λ1-λ2)N，σ2(p,t)＝(λ1-C1)e(p-p0).
A bang-bang control balance occurs according to the effects of the above set variables, in order to maximize H, then:
the optimal control solution under uncertainty is then:
the adjoint matrix and the terminal conditions are:
the optimal control state is a stable equilibrium state, i.e.:
therefore, the optimal control state of the above equation satisfies:
and is
Obtaining:
then the optimal control state is obtained:
the second optimal control solution alpha is obtained*、N*、p*And ε*。
The animal epidemic disease dynamics model based on the livestock price constructed in the step 130 specifically includes:
the following kinetic models were established:
wherein S is a susceptible animal, I is an infected animal, V is an immunized animal, W is Brucella in the environment, p is the livestock commercial market price, epsilon is the livestock population growth rate coefficient, e is the average weight of slaughtered livestock, p is0Is the breeding price, alpha is the livestock slaughter rate, and 0<α<1, D is the maximum demand of said livestock commodity, b is the price adjustment factor, beta1Is easy for the affected animalsInfection rate coefficient of animals, beta2Is the infection rate coefficient of bacteria in the environment to susceptible animals, v is the immunity rate of the susceptible animals, l is the immunity failure rate of the immunized animals, gamma is the clearance rate of the susceptible animals, k is the bacteria elimination rate of the infected animals, and delta is the natural mortality rate of the bacteria in the environment.
In step 140, the estimation parameters of the animal epidemic disease kinetic model are obtained by using a least square method, parameter sensitivity analysis is performed on the estimation parameters and the control parameters by using a latin hypercube sampling LHS method and a partial rank correlation coefficient PRCC method, and key parameters for epidemic disease control are determined, which specifically comprises the following steps:
the actual diseased livestock data is recorded as Y, and the set of estimation parameters is recorded as theta ═ beta1,β2K), estimating the unknown parameters by using a least square method,
is at tmThe animal epidemic kinetic model is in known parameters at the moment
And the theoretical solution, Y, under the unknown parameter thetamIs shown at tmThe real solution of the moment is the objective function of the least square method
The estimation parameter theta is changed into (beta) by utilizing a Latin hypercube sampling LHS method1,β2K) and the control parameter Δ ═ α, γ, v);
the estimation parameter Θ is (β) by using a partial rank correlation coefficient method PRCC1,β2K) and a control measure parameter Δ ═ α, Y, v);
using comparison of beta1、β2K, alpha, gamma and v determine key parameters for epidemic control according to the magnitude of the bias rank correlation coefficient values of the epidemic control strategy.
Further, in step 150, the constructing an optimal control objective function for the animal epidemic disease by using the animal epidemic disease kinetic model, and determining an optimal control strategy for the region to be analyzed by using the maximum value principle of pomtleria and the key parameters specifically includes:
constructing the optimal control objective function of the animal epidemic disease as
Wherein the control items are as follows: livestock slaughtering rate alpha and environmental sterilization rate u1And the immune rate v, C of susceptible animals2And C3Is the cost to be paid when the control item is controlled, C2For cost of disinfection, C3For the immunization cost, solving an optimal control solution by using the maximum value principle of Pontryagin, constructing a Hamiltonian and solving;
and evaluating the preset control strategy by combining a Latin hypercube sampling LHS method and a partial rank correlation coefficient PRCC method, and determining the optimal control strategy of the region to be analyzed.
It should be appreciated that the expressions are adjusted with reference to inventory of supply-demand relationship versus price of the commodity in consideration of livestock commodity market price factors in combination with cost control and economic loss gaming strategies. Further, in combination with the high market price of livestock, which may promote the farmers to breed more, the relationship between the livestock breeding amount N and the market price p of livestock commodity is defined as follows:
the first and second equations represent the variation of livestock farm N and livestock market price p, respectively, where r and K are the net growth rate of the model and the maximum livestock farm holding capacity, respectively, and ε e is the growth rate of the farm in price-based form. Alpha is the slaughter rate of the entire herd (0)<α<1) And f (p) is a demand function for the price p, which decreases as p increases, and f (p) tends to the maximum demand D as p tends to 0. In addition to the priceWhen the price of marketing is higher than the breeding price p0In the meantime, the farmers can enlarge the breeding scale and increase the livestock group input for profit, and conversely, when the marketing price is less than the breeding price, the breeding scale can be reduced and the livestock group input is reduced. Now taking the demand function f (p) as D-bep, where D is the maximum demand of the livestock commodity, b is the price adjustment factor, and e is the average weight of the slaughtered livestock, the price transformation function is:
therefore, the relationship between the livestock breeding amount N and the livestock commodity market price p may be changed as follows:
in livestock breeding, profit is the ultimate goal, and since price is affected by supply and demand to cause fluctuation, in order to obtain the maximum economic profit, it is necessary to control the slaughter rate of slaughtered livestock at each stage so that the maximum economic profit can be obtained in the final population breeding. Because the scale of the livestock is not increased in a logical stett form any more, but is influenced by price fluctuation in order to obtain the maximum benefit, the fluctuation coefficient of the population influenced by the price is assumed to be epsilon in the model, and farmers introduce two modes in production life every year, namely, self-production and self-sale, namely, the livestock does not need to be bought from other farms; another is that self-production is limited, and self-production by itself is not enough to maintain the scale of self-breeding, and livestock needs to be bought from other farms. The two modes lead to the difference of an objective function and a control item, in the former, only the slaughter rate is considered as the control item, the change of the fluctuation coefficient epsilon cannot be optimally controlled, in the latter, part of cost is spent due to the purchase of epsilon, so that the income is influenced, and in the case that both the slaughter rate and the fluctuation coefficient epsilon are considered as the control items, the income is maximized due to the common regulation of the two items.
1. Self-production self-marketing mode: the objective function in this case is defined as:
wherein, C0N0In order to initially buy the investment amount of the livestock, according to the cost-benefit theory, the payment function is 'benefit-cost', in the livestock breeding process, the obtained main benefit is the benefit obtained by selling the livestock in a fence, the price of each livestock in the fence is p, so the benefit is 'p alpha N', the breeding cost of the livestock comprises material and service cost, labor cost and land cost, the costs are averaged in the model to obtain the breeding cost per unit time of each livestock as C, the breeding cost is CN, and T is the set terminal time.
The maximum principle of Pontryagin is used to solve the optimal control solution. First, a Hamiltonian H is constructed:
wherein ep α N-CN is a profit per unit time,
and D-bep-aN is the right-hand term of the differential equation, λ1And λ2Is a companion matrix variable.
Since H is linear with respect to the control variable α, (ep- λ)1-λ2) N is H and is expressed as sigma0(N,t)＝(ep-λ1-λ2)N。
A bang-bang control balance occurs according to the effect of the set variables described above, namely:
the optimal control solution under uncertainty is discussed below, namely:
based on the Hamiltonian H, the adjoint matrix and the terminal condition are satisfied, and the following equation is obtained:
the optimal control state is a stable equilibrium state, i.e.:
the above equation is therefore satisfied for the optimal control state,
and is
Obtaining:
thus, solving the following equation yields a first optimal control solution α*、N*And p*
Solving the equation can be obtained
Wherein:
m3＝K2b2r3(-Kbr+6Db-6Dε)+27C2Kb(b+ε)4,
m4＝4D2r(b-ε)2(-3Kbr+2Db-2Dε),
m5＝m6(m6(m6-3Kbr+6Db-6Dε)-3Kbr(-Kbr+4Db-4Dε)+12D2((b-ε)2+ε2)),
m6＝4berεp0.
2. outsourcing livestock mode: the objective function in this mode is:
on the basis of the self-production self-sale objective function, the cost of purchasing livestock receiving price fluctuation is increased, epsilon e (p-p)0) Is the number of outsourcing livestock in unit time, C1Is the price of livestock.
The Hamiltonian is constructed similarly:
wherein λ1And λ2Is a companion matrix variable.
Since H is linear with respect to the control variables α and ε, (ep- λ)1-λ2) N and (lambda)1-C1)e(p-p0) For H linear coefficients of the control variables alpha and epsilon, note
σ1(N,t)＝(ep-λ1-λ2)N，σ2(p,t)＝(λ1-C1)e(p-p0).
A bang-bang control balance occurs according to the effects of the above set variables, in order to maximize H, then:
the optimal control solution under uncertainty is then:
the adjoint matrix and termination conditions are:
the optimal control state is a stable equilibrium state, i.e.:
therefore, the optimal control state of the above equation satisfies:
and is
Obtaining:
then the optimal control state is obtained:
the second optimal control solution alpha is obtained*、N*、p*And ε*。
Based on the above discussion, further considering animal epidemic diseases, the following kinetic model can be established:
wherein S is a susceptible animal, I is an infected animal, V is an immunized animal, W is Brucella in the environment, p is the livestock commercial market price, epsilon is the livestock population growth rate coefficient, e is the average weight of slaughtered livestock, p is0Is the breeding price, alpha is the livestock slaughter rate, and 0<α<1, D is the maximum demand of said livestock commodity, b is the price adjustment factor, beta1Is the infection rate coefficient of the infected animal to the susceptible animal, beta2Is the infection rate coefficient of bacteria in the environment to susceptible animals, v is the immunity rate of the susceptible animals, l is the immunity failure rate of the immunized animals, gamma is the clearance rate of the susceptible animals, k is the bacteria elimination rate of the infected animals, and delta is the natural mortality rate of the bacteria in the environment.
And (3) combining animal epidemic disease inter-animal morbidity data in certain regions, estimating model kinetic parameters by using a least square method by using MATLAB mathematical software, fitting a numerical solution of the model with actual data, and verifying the rationality of the model. And predicting the epidemic trend of the animal in the region through numerical simulation. And (3) carrying out global sensitivity analysis on each relevant control parameter of the basic regeneration number of the model by utilizing a Latin hypercube sampling/partial rank correlation coefficient method (LHS/PRCC) to determine the rationality of prevention and control measures (such as immunity and killing).
1. Least square method
Recording the actual data of the ill livestock as Y and the set of known parameters as Y
The set of parameters to be estimated is denoted as Θ ═ β1,β2K), estimating unknown parameters by using a least square method: note the book
Is at tkAt the moment the kinetic model is at a known parameter
And the theoretical solution, Y, under the unknown parameter thetakIs shown at tkAnd (3) solving the real solution of the moment, wherein the objective function of the least square method is as follows:
2. latin Hypercube Sampling (LHS)
Latin hypercube sampling is a method for approximate random sampling from multivariate parameter distribution, belongs to a layered sampling technology, and is commonly used for computer experiments or Monte Carlo integration and the like. The working principle is as follows: for the estimated parameter Θ ═ β1,β2K) and the control measure parameter Δ ═ (α, γ, v) are sampled. The sampling principle is that approximate random sampling is carried out in multivariate parameter distribution, each input is divided into N rows with equal probability by defining the number N of each parameter of sampling participating in computer operation, so the total number of the sampling is 6N; further defining the sampling range of each parameter as beta1∈(X10,X1N)，β2∈(X20,X2N)，k∈(X30,X3N)，α∈(X40,X4N)，γ∈(X50,X5N) And v ∈ (X)60,X6N) (ii) a The following expression is satisfied for the ith parameter, Xi0<Xi1<Xi2<…<Xin<…<XiNX denotes a sampling matrix of 6 parameters,
and is provided with
Only one sample is taken for each column, and the positions of the samples are random;
3. partial Rank Correlation Coefficient (PRCC)
The correlation coefficient is a statistical index used for reflecting the degree of closeness of correlation between variables. The following four common correlation coefficients are available: pearson Correlation Coefficient (CC), Partial Correlation Coefficient (PCC), Spearman Rank Correlation Coefficient (RCC), Partial Rank Correlation Coefficient (PRCC). The corresponding expressions are respectively:
correlation coefficient:
partial correlation coefficient:
rank correlation coefficient:
bias rank correlation coefficient:
wherein x is (x)1,x2,…,xn) And y ═ y1,y2,…,yn) Respectively, the two sets of data are shown,
and
denotes the mean value of the data x and y, r (x)i) And r (y)i) Respectively representing the rank of the ith data in data x and y,
and
mean values of data x and y ranks, respectively.
The estimated parameter Θ is (β) determined by using Partial Rank Correlation Coefficient (PRCC) method1,β2K) and the control measure parameter Δ ═ α, γ, v). The magnitude of the partial rank correlation coefficient value of each input parameter relative to the epidemic disease control strategy is in direct proportion to the correlation of the parameter to the epidemic disease control strategy, namely, the larger the partial rank correlation coefficient value of the parameter is, the larger the influence of the parameter on the epidemic disease control strategy is. By comparing these six parameters (. beta.)1,β2And k, alpha, gamma and v) the magnitude of the partial rank correlation coefficient value of the epidemic disease control strategy can judge the superiority and inferiority of the parameters on controlling diseases, and finally, the optimal parameters for controlling the diseases are given.
And (3) control measure evaluation: further according to the practical measure implementation situation, the optimal control objective function for constructing the animal epidemic disease is as follows:
wherein the control items are as follows: livestock slaughtering rate alpha and environmental sterilization rate u1And the immune rate v, C of the susceptible animal2And C3Is the cost to be paid when the control item is controlled, C2For cost of disinfection, C3For the immunization cost, the maximum principle of Pontryagin is used for solving the optimal control solution, and the Hamiltonian is constructed and solved. Evaluating the advantages and disadvantages of each strategy selection by using economics evaluation and optimal control theoryAnd giving an optimal control strategy of animal epidemic diseases in the undetermined area.
The prevention and control method for animal epidemic disease modeling based on the livestock price provided by the embodiment comprises the following steps: establishing a relational expression of the livestock breeding quantity N and the livestock commodity market price p in an area to be analyzed: when the farmer is in a self-production and self-marketing mode, a first objective function is constructed and is solved by utilizing the maximum principle of Pontryagin to obtain a first optimal control solution, and when the farmer is in an outsourcing livestock mode, a second objective function is constructed and is solved by utilizing the maximum principle of Pontryagin to obtain a second optimal control solution; constructing an animal epidemic disease kinetic model by using the relational expression; estimating animal epidemic disease kinetic model parameters by using a least square method, performing parameter sensitivity analysis on estimation parameters and control parameters by using a Latin Hypercube Sampling (LHS) method and a Partial Rank Correlation Coefficient (PRCC) method, evaluating risk factors, and determining which parameters play a key role in epidemic disease control; and constructing an optimal control objective function of the animal epidemic disease, solving an optimal control solution by using the maximum value principle of Pontryagin, evaluating the advantages and disadvantages of the preset control strategies by using an economic evaluation method, and determining the optimal control strategy of the area to be analyzed. The invention simultaneously considers the economic cost of population control and animal population epidemic disease control to find the optimal control cost, and simultaneously needs to obtain the maximum profit in the breeding industry under the epidemic disease control.
As shown in fig. 2, a prevention and control apparatus for an animal epidemic disease model based on livestock prices comprises:
the relational expression establishing module is used for establishing a relational expression of the livestock breeding quantity N and the livestock commodity market price p in the area to be analyzed:
wherein p is0Is the breeding price, alpha is the livestock slaughter rate, 0<α<1, f (p) is a demand function of the livestock commodity market price p, and the value of f (p) depends on the livestockThe commodity market price p is increased and decreased, epsilon is the growth rate coefficient of livestock population, e is the average weight of livestock on slaughter, r is the growth rate of livestock, K is the maximum value of the breeding scale,
is the growth rate of the livestock in unit time,
is the rate of price increase per unit time;
the objective function establishing module is used for establishing a first objective function when the farmer is in a self-production and self-marketing mode, solving by utilizing the maximum principle of Pontryagin to obtain a first optimal control solution, and establishing a second objective function when the farmer is in an outsourcing livestock mode, solving by utilizing the maximum principle of Pontryagin to obtain a second optimal control solution;
the dynamic model building module is used for building an animal epidemic dynamic model by utilizing the relation formula:
the control strategy determination module is used for obtaining estimation parameters of the animal epidemic disease dynamic model by using a least square method, performing parameter sensitivity analysis on the estimation parameters and the control parameters by using a Latin hypercube sampling LHS method and a partial rank correlation coefficient PRCC method, determining key parameters for epidemic disease control, constructing an animal epidemic disease optimal control objective function by using the animal epidemic disease dynamic model, and determining an optimal control strategy of the area to be analyzed by using the maximum value principle of Pontryagin and the key parameters.
The invention also provides a computer readable storage medium, on which a computer program is stored, which when executed by a processor implements the steps of the method for preventing and controlling animal epidemic kinetic model based on livestock price according to any one of the above technical solutions.
The invention also provides an electronic device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the program to realize the steps of the method for preventing and controlling the animal epidemic dynamic model based on the livestock price according to any one of the technical schemes.
While the invention has been described with reference to specific embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (9)
1. A method for preventing and controlling animal epidemic disease kinetic model based on livestock price is characterized by comprising the following steps:
establishing a relational expression of livestock breeding quantity N and livestock commodity market price p in an area to be analyzed:
wherein p is0Is the breeding price, alpha is the livestock slaughter rate, 0<α<1, f (p) is a demand function of the livestock commodity market price p, and the value of f (p) decreases with increasing livestock commodity market price p, ε is the livestock population growth rate coefficient, e is the average weight of slaughtered livestock, r is the livestock growth rate, K is the maximum value of the scale of farming,
is the growth rate of the livestock in unit time,
is the rate of price increase per unit time;
when the farmer is in a self-production and self-marketing mode, a first objective function is constructed and is solved by utilizing the maximum principle of Pontryagin to obtain a first optimal control solution, and when the farmer is in an outsourcing livestock mode, a second objective function is constructed and is solved by utilizing the maximum principle of Pontryagin to obtain a second optimal control solution;
and (3) constructing an animal epidemic disease kinetic model by utilizing the relation:
obtaining estimation parameters of the animal epidemic disease kinetic model by using a least square method, performing parameter sensitivity analysis on the estimation parameters and the control parameters by using a Latin hypercube sampling LHS method and a partial rank correlation coefficient PRCC method, determining key parameters for epidemic disease control, constructing an animal epidemic disease optimal control objective function by using the animal epidemic disease kinetic model, and determining an optimal control strategy of the area to be analyzed by using the maximum value principle of Pontryagin and the key parameters.
2. The method for preventing and controlling the animal epidemic disease kinetic model based on the livestock price according to claim 1, wherein when the farmer is in a self-production self-sale mode, a first objective function is constructed and solved by using the maximum principle of Pontryagin to obtain a first optimal control solution, specifically comprising:
the first objective function is
Wherein the breeding cost per livestock per unit time is C, and the investment amount for initially buying each livestock is C0，N0Is the number of the initial bought livestock, dt is the integral of time, and t is the set terminal time;
solving an optimal control solution by using the maximum principle of Pontryagin, and constructing a Hamiltonian H:
wherein D is the maximum demand of livestock goods, b is a price adjustment coefficient,
and D-bep-aN is the right-hand term of the differential equation, λ1And λ2For the adjoint matrix variables, a first optimal control solution alpha is obtained*、N*And p*。
3. The method for preventing and controlling the animal epidemic disease kinetic model based on the livestock price according to claim 2, wherein when the farmer is in the outsourcing livestock mode, a second objective function is constructed and solved by using the maximum value principle of Pontryagin to obtain a second optimal control solution, specifically comprising:
the second objective function is
Wherein, C1Is the outsourcing price of each livestock;
structure Hamiltonian
Wherein λ1And λ2Obtaining the second optimal control solution alpha for the adjoint matrix variable*、N*、p*And ε*。
4. The method for controlling animal epidemic kinetic model based on livestock price according to claim 3, wherein the constructing animal epidemic kinetic model by using the relationship formula specifically comprises:
establishing the animal epidemic disease kinetic model:
wherein S is the number of susceptible animals, I is the number of infected animals, V is the number of immunized animals, W is the number of Brucella in the environment, b is the price adjustment factor, beta1Is the infection rate coefficient of the infected animal to the susceptible animal, beta2Is the infection rate coefficient of bacteria in the environment to susceptible animals, v is the immunity rate of the susceptible animals, l is the immunity failure rate of the immunized animals, gamma is the clearance rate of the susceptible animals, k is the bacteria elimination rate of the infected animals, and delta is the natural mortality rate of the bacteria in the environment.
5. The method for preventing and controlling the animal epidemic disease kinetic model based on the livestock price according to claim 4, wherein the estimation parameters of the animal epidemic disease kinetic model are obtained by using a least square method, parameter sensitivity analysis is carried out on the estimation parameters and the control parameters by using a Latin hypercube sampling LHS method and a partial rank correlation coefficient PRCC method, and key parameters for epidemic disease control are determined, and the method specifically comprises the following steps:
the actual diseased livestock data is recorded as Y, and the set of estimation parameters is recorded as theta ═ beta1,β2K), estimating the unknown parameters by using a least square method,
is at tmThe animal epidemic kinetic model is in known parameters at the moment
And the theoretical solution, Y, under the unknown parameter thetamIs shown at tmThe real solution of the moment is the objective function of the least square method
The estimation parameter theta is changed into (beta) by utilizing a Latin hypercube sampling LHS method1,β2K) and the control parameter Δ ═ α, γ, v);
PRCC algorithm using partial rank correlation coefficientThe estimated parameter Θ ═ β (β)1,β2K) and a control measure parameter Δ ═ α, γ, v);
using comparison of beta1、β2K, alpha, gamma and v determine key parameters for epidemic control according to the magnitude of the bias rank correlation coefficient values of the epidemic control strategy.
6. The method for preventing and controlling the animal epidemic disease kinetic model based on the livestock price according to claim 5, wherein the animal epidemic disease kinetic model is utilized to construct an animal epidemic disease optimal control objective function, and the optimal control strategy of the area to be analyzed is determined by using the maximum value principle of Pontryagin and the key parameters, and specifically comprises the following steps:
constructing the optimal control objective function of the animal epidemic disease as
Wherein the control items are as follows: livestock slaughtering rate alpha and environmental sterilization rate u1And the immune rate v, C of susceptible animals2And C3Is the cost that needs to be paid when the control item is controlled, wherein C2For cost of disinfection, C3For the immunization cost, solving an optimal control solution by using the maximum value principle of Pontryagin, constructing a Hamiltonian and solving;
and evaluating the preset control strategy by combining a Latin hypercube sampling LHS method and a partial rank correlation coefficient PRCC method, and determining the optimal control strategy of the region to be analyzed.
7. An apparatus for preventing and controlling animal epidemic kinetic model based on livestock price, which is characterized in that the apparatus comprises:
the relational expression establishing module is used for establishing a relational expression of the livestock breeding quantity N and the livestock commodity market price p in the area to be analyzed:
wherein p is0Is the breeding price, alpha is the livestock slaughter rate, 0<α<1, f (p) is a demand function of the livestock commodity market price p, and the value of f (p) decreases with increasing livestock commodity market price p, ε is the livestock population growth rate coefficient, e is the average weight of slaughtered livestock, r is the livestock growth rate, K is the maximum value of the scale of farming,
is the growth rate of the livestock in unit time,
is the rate of price increase per unit time;
the objective function establishing module is used for establishing a first objective function when the farmer is in a self-production and self-marketing mode, solving by utilizing the maximum principle of Pontryagin to obtain a first optimal control solution, and establishing a second objective function when the farmer is in an outsourcing livestock mode, solving by utilizing the maximum principle of Pontryagin to obtain a second optimal control solution;
the dynamic model building module is used for building an animal epidemic disease dynamic model by utilizing the relational expression:
the control strategy determination module is used for obtaining estimation parameters of the animal epidemic disease dynamic model by using a least square method, performing parameter sensitivity analysis on the estimation parameters and the control parameters by using a Latin hypercube sampling LHS method and a partial rank correlation coefficient PRCC method, determining key parameters for epidemic disease control, constructing an animal epidemic disease optimal control objective function by using the animal epidemic disease dynamic model, and determining an optimal control strategy of the area to be analyzed by using the maximum value principle of Pontryagin and the key parameters.
8. A computer-readable storage medium, on which a computer program is stored, which program, when being executed by a processor, is adapted to carry out the steps of the method for controlling a livestock-based animal epidemic kinetic model according to any one of claims 1-6.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor when executing the program implements the steps of the method for controlling animal epidemic kinetic model based on livestock price according to any one of claims 1 to 6.
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