A measles transmission dynamic prediction and immunization strategy optimization method

Abstract

The present application relates to the technical field of medical informatics, in particular to a measles transmission dynamic prediction and immunization strategy optimization method, which comprises the following steps: constructing a non-autonomous SVEIR dynamic model containing susceptible, vaccination, latent, infected and recovered populations, adopting Fourier series fitting time-varying transmission rate, combining with measured data to derive time-varying vaccination rate, and making up the defect that traditional constant parameter model cannot reflect seasonal prevalence of measles. The adaptive Metropolis-Hastings MCMC algorithm is used to complete the Bayesian estimation of model parameters relying on specific monitoring data, and the goodness of model fitting reaches 0.91. The present application introduces vaccination intensity as a control variable, combines with the principle of maximum of Pontriagin to solve the optimal vaccination strategy, and calculates the basic reproductive number to determine the critical threshold of the epidemic. Through multi-scene simulation, the present application can simulate the epidemic development trend under different vaccination rates, quantify the benefits and risks of vaccination strategies, and effectively shorten the epidemic cycle and reduce the number of infected cases by preferentially vaccinating high-risk groups aged 0-24 months.

Description

Technical Field

[0001] This invention relates to the field of medical informatics technology, specifically to a method for predicting the dynamics of measles transmission and optimizing immunization strategies. Background Technology

[0002] Measles is a highly contagious respiratory disease caused by the measles virus. Although vaccines are available globally, its high transmissibility can still lead to periodic outbreaks in areas with insufficient vaccination coverage. Traditional infectious disease dynamics models (such as SEIR and SVEIR models) typically assume constant transmission and vaccination rates, failing to adequately account for seasonal fluctuations in transmission rates, the timeliness of vaccine protection, and population mobility characteristics. This results in limited accuracy in predicting measles transmission, particularly in areas with high population mobility, making it difficult to support precise immunization strategies.

[0003] The existing technology has the following main shortcomings:

[0004] (1) Insufficient model adaptability: The constant parameter model cannot accurately fit the actual seasonal and periodic characteristics of measles incidence, resulting in large prediction bias.

[0005] (2) Lack of focus on key populations: Previous studies have often overlooked the key role of the high-risk core population of infants aged 0-24 months in the spread of the virus and the differences in immune coverage among mobile populations.

[0006] (3) Insufficient quantification of intervention strategies: Most models fail to incorporate optimal control theory to quantify the long-term dynamic intervention benefits of different vaccination strategies, making it difficult to determine the optimal scheme for maintaining the herd immunity threshold. Summary of the Invention

[0007] The purpose of this invention is to provide a method for dynamic prediction of measles transmission and optimization of immunization strategies. It aims to construct an infectious disease dynamics model that characterizes the seasonal fluctuations in disease transmission and the dynamic changes in immunization coverage, thereby solving the problems of inaccurate prediction and imprecise strategy evaluation in existing models.

[0008] To achieve the above objectives, the present invention provides a method for dynamic prediction of measles transmission and optimization of immunization strategies, comprising the following steps:

[0009] Step 1: Construct a non-autonomous SVEIR dynamic model, which includes five compartments: S, V, E, I, and R, and N is the total population.

[0010] Step 2: Model parameter estimation and validation;

[0011] Step 3: Perform dynamic analysis and strategy optimization;

[0012] Step 4: Numerical simulation and benefit assessment.

[0013] Optionally, the five wards in step 1 correspond to five groups of people: S: susceptible individuals, V: vaccinated individuals, E: latent individuals, I: infected individuals, and R: recovered individuals.

[0014] During the execution of step 1, the time-varying transmission rate was fitted using an 8th-order Fourier series based on historical weekly incidence data. Based on the annual reported vaccination rate, the time-varying vaccination rate was deduced. ; and explicitly included vaccine protection rates .

[0015] Optionally, the state equations of the non-autonomous SVEIR dynamic model are as follows:

[0016]

[0017] in, For population import rate, For removal rate, The incubation period, This is the infection period.

[0018] Optionally, in step 2, the adaptive Metropolis-Hastings MCMC algorithm is used to estimate the parameters and 20,000 iterations are performed.

[0019] Optionally, a control variable can be introduced in step 3. The intensity of vaccination implementation is characterized, and an optimal control problem is constructed with the objectives of minimizing the number of susceptible individuals, the number of infected individuals, and control costs. The dynamic optimal control strategy is then solved using the Pontryagin maximum principle. The parsing expression.

[0020] Optionally, in step 4, the trained model is used to simulate the disease trend in future years under different constant vaccination rates; at the same time, the differences in infection scale, epidemic cycle and cumulative number of infections are simulated and compared between the two scenarios of implementing the optimal control strategy and not implementing the strategy, so as to quantify the effect of the strategy.

[0021] This invention provides a method for dynamic prediction of measles transmission and optimization of immunization strategies. It constructs a non-autonomous SVEIR dynamic model encompassing susceptible, vaccinated, latent, infected, and recovered populations, uses Fourier series to fit the time-varying transmission rate, and derives the time-varying vaccination rate based on measured data, overcoming the limitation of traditional constant-parameter models in reflecting the seasonality of measles outbreaks. The adaptive Metropolis-Hastings MCMC algorithm is employed, relying on specific monitoring data to complete Bayesian estimation of model parameters, achieving a goodness-of-fit of 0.91. This invention introduces vaccination intensity as a control variable, combining the Pontryagin maximum principle to solve for the optimal vaccination strategy, while simultaneously calculating the basic reproduction number to determine the critical threshold for epidemic spread. Through multi-scenario simulations, it can simulate the epidemic development trend under different vaccination rates, quantify the benefits and risks of vaccination strategies, and prioritize vaccination of high-risk groups aged 0-24 months to effectively shorten the epidemic cycle and reduce infection cases. This invention offers high prediction accuracy, enabling quantitative optimization of vaccination strategies and early warning of epidemic risks, providing a scientific basis for precise measles prevention and control and immunization program development. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a schematic diagram of the non-autonomous SVEIR model compartment flow according to a specific embodiment of the present invention.

[0024] Figure 2 This is a system structure diagram of a specific embodiment of the present invention.

[0025] Figure 3 The parameters in the specific embodiments of the present invention relate to the basic reproduction number. A schematic diagram of the affected grid.

[0026] Figure 4 This is provided in a specific embodiment of the present invention. Histogram of posterior distribution and model bifurcation diagram.

[0027] Figure 5 This invention provides a specific embodiment showing the model's fit to historical data, future prediction trends under different vaccination rates, and time-varying propagation rates. Time series plot.

[0028] Figure 6 This is a comparison chart of the dynamic changes of the population under the implementation of the optimal control strategy and without the implementation of the strategy in a specific embodiment of the present invention.

[0029] Figure 7 This is a three-dimensional graph showing the sensitivity analysis of vaccination rate and vaccine protection rate parameters provided in a specific embodiment of the present invention. Detailed Implementation

[0030] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0031] This invention provides a method for predicting the dynamics of measles transmission and optimizing immunization strategies, comprising the following steps:

[0032] Step 1: Construct a non-autonomous SVEIR dynamic model, which includes five compartments: S, V, E, I, and R, and N is the total population.

[0033] Step 2: Model parameter estimation and validation;

[0034] Step 3: Perform dynamic analysis and strategy optimization;

[0035] Step 4: Numerical simulation and benefit assessment.

[0036] Please see Figures 1 to 7 The present invention will be further described below with reference to specific embodiments:

[0037] The method for dynamic prediction of measles transmission and optimization of immunization strategies described in this invention specifically includes four steps: model construction, parameter estimation, strategy optimization, and simulation evaluation.

[0038] First, such as Figure 1 As shown, based on the transmission mechanism and immunological characteristics of measles, a dynamic model comprising five compartments (S, V, E, I, and R) is constructed. The core concept is defining a time-varying parameter: the transmission rate. An 8th-order Fourier series was used for fitting, and the formula is as follows: ,in ,parameter The vaccination rate was determined through subsequent data fitting. Annual reported vaccination rate The relationship is: .like Figure 2As shown, this embodiment relates to a system for predicting the dynamics of measles transmission and optimizing immunization strategies. This system is a comprehensive prediction and decision support system integrating data processing, model building, theoretical analysis, and strategy evaluation. Its overall architecture revolves around the dynamic mechanism of infectious diseases, and through specific mathematical models and numerical analysis methods, it achieves accurate prediction of measles transmission trends and scientific optimization of immunization strategies.

[0039] The equations of the non-autonomous SVEIR model are as follows:

[0040] (1)

[0041] in, For population import rate, For removal rate, The incubation period, This is the infection period.

[0042] Secondly, model parameter estimation and validation were performed. The weekly measles case count I(t) in Guangdong Province from 2005 to 2021 was used as the observed data Y(t), and the adaptive Metropolis-Hastings MCMC algorithm was employed to estimate the parameters. The model was run for 20,000 iterations, and the posterior sample mean was used as the parameter estimate. As shown in Table 1, the key parameter values ​​were derived from monitoring data, literature, or MCMC estimates. The model fitting results are as follows: Figure 5 As shown, the predicted curve matches the historical data well.

[0043] Table 1. Estimated parameter values ​​of the model

[0044]

[0045] Subsequently, dynamic analysis and strategy optimization were performed. The basic regeneration number of the model was calculated. Its sensitivity to various parameters is as follows: Figure 3 As shown, the propagation rate Vaccination rate Vaccine protection rate and recovery rate right The impact is most significant. Estimates for Guangdong Province. =0.87 (95% CI: 0.43–1.3), and its distribution is as follows: Figure 4 As shown. Bifurcation analysis confirms... =1 is the critical threshold between disease extinction and endemicity.

[0046] Based on this, an optimal control problem is constructed. In model equation (1), control variables are used... Replacing the original inoculation rate term, we form a system of state equations (2):

[0047] (2)

[0048] Define the objective function for the optimal control problem:

[0049] (3)

[0050] in The weighting coefficients are designed to minimize the number of susceptible individuals and those infected, as well as control costs.

[0051] Applying Pontryagin's maximum principle, the optimal control is derived. The expression:

[0052] (4)

[0053] in These are the accompanying variables, obtained by solving the system of state equations.

[0054] Finally, numerical simulations and benefit assessments are conducted. For example... Figure 5 As shown, simulations predict that if the vaccination rate remains at 99% or 99.5%, the incidence rate will remain at a very low level before 2030; if the vaccination rate drops to 98.5%, the number of cases will rise sharply after 2027.

[0055] Figure 6 The simulation compared scenarios where the optimal control strategy was implemented with those where no strategy was implemented. The simulation showed that the optimal control strategy could reduce the final size of the epidemic by 30%, shorten the epidemic cycle by 32.8%, and avoid a large number of cumulative infections. Figure 7 Further parameter sensitivity analysis showed that small fluctuations in vaccination rate and vaccine protection rate around the critical value (approximately 99%, 0.95) can lead to an order-of-magnitude jump in the cumulative number of cases, confirming the criticality of maintaining a vaccination rate above 99%.

[0056] This invention achieves more accurate prediction of measles transmission dynamics by constructing a refined model that integrates time-varying parameters and optimal control, and can provide public health departments with quantitative and optimizable vaccination strategies, which is of great significance for controlling and even eliminating measles.

[0057] In summary, the present invention has the following beneficial effects:

[0058] 1. Accurate Prediction: By incorporating time-varying transmission rates and vaccination rates, the model can better capture the seasonal and periodic epidemic characteristics of measles, demonstrating a high degree of goodness of fit to case data from Guangdong Province. It can reach 0.91, making predictions more accurate.

[0059] 2. Clear Threshold: Through model analysis, the basic reproduction number was clearly defined. This is a critical threshold determining whether measles cases resolve or persist. The estimation method applied to Guangdong Province... The value of 0.87 indicates that the current spread is under control.

[0060] 3. Strategy Optimization: Provides quantifiable optimal control strategies that can scientifically guide the dynamic allocation of vaccination resources. Simulations show that prioritizing vaccination of the 0-2 year old group combined with real-time monitoring can shorten the epidemic cycle by 30% and cumulatively prevent approximately 80 million infections between 2005 and 2021.

[0061] 4. Early warning function: The model can sensitively assess the long-term risks of declining vaccination rates. Simulations show that if the vaccination rate drops from 99% to 98.5%, it is expected to trigger a surge in morbidity to 0.9% in 3 years (2030), providing research support for maintaining high vaccination rates.

[0062] The above description discloses only one preferred embodiment of the present invention, and should not be construed as limiting the scope of the present invention. Those skilled in the art will understand that all or part of the processes of the above embodiments can be implemented, and equivalent changes made in accordance with the claims of the present invention are still within the scope of the invention.

Claims

1. A method for dynamic prediction of measles transmission and optimization of immunization strategies, characterized in that, Includes the following steps: Step 1: Construct a non-autonomous SVEIR dynamic model, which includes five compartments: S, V, E, I, and R, and N is the total population. Step 2: Model parameter estimation and validation; Step 3: Perform dynamic analysis and strategy optimization; Step 4: Numerical simulation and benefit assessment.

2. The method for dynamic prediction of measles transmission and optimization of immunization strategies as described in claim 1, characterized in that, In step 1, the five wards correspond to five groups of people: S: susceptible individuals, V: vaccinated individuals, E: latent individuals, I: infected individuals, and R: recovered individuals. During the execution of step 1, the time-varying transmission rate was fitted using an 8th-order Fourier series based on historical weekly incidence data. Based on the annual reported vaccination rate, the time-varying vaccination rate was deduced. ; And explicitly include vaccine protection rate .

3. The method for dynamic prediction of measles transmission and optimization of immunization strategies as described in claim 2, characterized in that, The state equations of the non-autonomous SVEIR dynamic model are as follows: in, For population import rate, For removal rate, The incubation period This is the infection period.

4. The method for dynamic prediction of measles transmission and optimization of immunization strategies as described in claim 3, characterized in that, In step 2, the adaptive Metropolis-Hastings MCMC algorithm is used to estimate the parameters and 20,000 iterations are performed.

5. The method for dynamic prediction of measles transmission and optimization of immunization strategies as described in claim 4, characterized in that, Introducing control variables in step 3 The intensity of vaccination implementation is characterized, and an optimal control problem is constructed with the objectives of minimizing the number of susceptible individuals, the number of infected individuals, and control costs. The dynamic optimal control strategy is then solved using the Pontryagin maximum principle. The parsing expression.

6. The method for dynamic prediction of measles transmission and optimization of immunization strategies as described in claim 5, characterized in that, In step 4, the trained model is used to simulate the disease trend in future years under different constant vaccination rates; Simultaneously, the differences in infection scale, epidemic cycle, and cumulative number of infections were simulated and compared between implementing the optimal control strategy and not implementing the strategy, quantifying the effect of the strategy.

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