Recent evidences show that individuals who recovered from COVID-19 can be reinfected.However,this phenomenon has rarely been studied using mathematical models.In this paper,we propose an SEIRE epidemic model to descri...Recent evidences show that individuals who recovered from COVID-19 can be reinfected.However,this phenomenon has rarely been studied using mathematical models.In this paper,we propose an SEIRE epidemic model to describe the spread of the epidemic with reinfection.We obtain the important thresholds R_(0)(the basic reproduction number)and R_(c)(a threshold less than one).Our investigations show that when R_(0)>1,the system has an endemic equilibrium,which is globally asymptotically stable.When R_(c)<R_(0)<1,the epidemic system exhibits bistable dynamics.That is,the system has backward bifurcation and the disease cannot be eradicated.In order to eradicate the disease,we must ensure that the basic reproduction number R_(0) is less than R_(c).The basic reinfection number is obtained to measure the reinfection force,which turns out to be a new tipping point for disease dynamics.We also give definition of robustness,a new concept to measure the dificulty of completely eliminating the disease for a bistable epidemic system.Numerical simulations are carried out to verify the conclusions.展开更多
The numerical approximation of stochastic partial differential equations(SPDEs),particularly those including q-diffusion,poses considerable challenges due to the requirements for high-order precision,stability amongst...The numerical approximation of stochastic partial differential equations(SPDEs),particularly those including q-diffusion,poses considerable challenges due to the requirements for high-order precision,stability amongst random perturbations,and processing efficiency.Because of their simplicity,conventional numerical techniques like the Euler-Maruyama method are frequently employed to solve stochastic differential equations;nonetheless,they may have low-order accuracy and lower stability in stiff or high-resolution situations.This study proposes a novel computational scheme for solving SPDEs arising from a stochastic SEIR model with q-diffusion and a general incidence rate function.A proposed computational scheme can be used to solve stochastic partial differential equations.For spatial discretization,a compact scheme is chosen.The compact scheme can provide a sixth-order accurate solution.The proposed scheme can be considered an extension of the Euler Maruyama method.Stability and consistency in the mean square sense are also provided.For application purposes,the stochastic SEIR model is considered using q-diffusion effects.The scheme is used to solve the stochastic model and compared with the Euler-Maruyama method.The scheme is also compared with nonstandard finite difference method for solving deterministic models.In both cases,it performs better than existing schemes.Incorporating q-diffusion further enhanced the model’s ability to represent realistic spatial-temporal disease dynamics,especially in scenarios where classical diffusion is insufficient.展开更多
针对一类改进的SVEIR流感传播动力学模型,探讨了参数估计与拟合方法,并分析了疫苗接种对流感传播的影响。首先,假设现有确诊病例数遵循泊松分布,通过Bootstrap方法生成时间序列样本,采用马尔可夫链蒙特卡洛(MCMC)算法实现后验分布的高...针对一类改进的SVEIR流感传播动力学模型,探讨了参数估计与拟合方法,并分析了疫苗接种对流感传播的影响。首先,假设现有确诊病例数遵循泊松分布,通过Bootstrap方法生成时间序列样本,采用马尔可夫链蒙特卡洛(MCMC)算法实现后验分布的高效采样对模型参数进行估计。随后,为验证模型的有效性,利用实际流感数据进行检验,结果表明模型能够较好地捕捉流感的传播动态。进一步,通过敏感性分析,评估了疫苗接种率v对基本再生数ℜ0和最终感染规模的影响。研究发现,提高疫苗接种率可显著降低流感的传播风险。For a class of improved SVEIR influenza transmission dynamics model, parameter estimation and fitting methods are discussed, and the impact of vaccination on influenza transmission is analyzed. First, assuming that the number of confirmed cases follows a Poisson distribution, the Bootstrap method is used to generate time series samples, and the Markov Chain Monte Carlo (MCMC) algorithm is used to achieve efficient sampling of the posterior distribution to estimate the model parameters. Subsequently, in order to verify the effectiveness of the model, actual influenza data were used for testing, and the results showed that the model can better capture the transmission dynamics of influenza. Furthermore, through sensitivity analysis, the impact of vaccination rate von the basic reproduction number ℜ0and the final infection scale was evaluated. The study found that increasing the vaccination rate can significantly reduce the risk of influenza transmission.展开更多
基金supported by the National Natural Science Foundation of China(U21A20206)Natural Science Foundations of Henan(192102310089,202300410045).
文摘Recent evidences show that individuals who recovered from COVID-19 can be reinfected.However,this phenomenon has rarely been studied using mathematical models.In this paper,we propose an SEIRE epidemic model to describe the spread of the epidemic with reinfection.We obtain the important thresholds R_(0)(the basic reproduction number)and R_(c)(a threshold less than one).Our investigations show that when R_(0)>1,the system has an endemic equilibrium,which is globally asymptotically stable.When R_(c)<R_(0)<1,the epidemic system exhibits bistable dynamics.That is,the system has backward bifurcation and the disease cannot be eradicated.In order to eradicate the disease,we must ensure that the basic reproduction number R_(0) is less than R_(c).The basic reinfection number is obtained to measure the reinfection force,which turns out to be a new tipping point for disease dynamics.We also give definition of robustness,a new concept to measure the dificulty of completely eliminating the disease for a bistable epidemic system.Numerical simulations are carried out to verify the conclusions.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2501).
文摘The numerical approximation of stochastic partial differential equations(SPDEs),particularly those including q-diffusion,poses considerable challenges due to the requirements for high-order precision,stability amongst random perturbations,and processing efficiency.Because of their simplicity,conventional numerical techniques like the Euler-Maruyama method are frequently employed to solve stochastic differential equations;nonetheless,they may have low-order accuracy and lower stability in stiff or high-resolution situations.This study proposes a novel computational scheme for solving SPDEs arising from a stochastic SEIR model with q-diffusion and a general incidence rate function.A proposed computational scheme can be used to solve stochastic partial differential equations.For spatial discretization,a compact scheme is chosen.The compact scheme can provide a sixth-order accurate solution.The proposed scheme can be considered an extension of the Euler Maruyama method.Stability and consistency in the mean square sense are also provided.For application purposes,the stochastic SEIR model is considered using q-diffusion effects.The scheme is used to solve the stochastic model and compared with the Euler-Maruyama method.The scheme is also compared with nonstandard finite difference method for solving deterministic models.In both cases,it performs better than existing schemes.Incorporating q-diffusion further enhanced the model’s ability to represent realistic spatial-temporal disease dynamics,especially in scenarios where classical diffusion is insufficient.
文摘针对一类改进的SVEIR流感传播动力学模型,探讨了参数估计与拟合方法,并分析了疫苗接种对流感传播的影响。首先,假设现有确诊病例数遵循泊松分布,通过Bootstrap方法生成时间序列样本,采用马尔可夫链蒙特卡洛(MCMC)算法实现后验分布的高效采样对模型参数进行估计。随后,为验证模型的有效性,利用实际流感数据进行检验,结果表明模型能够较好地捕捉流感的传播动态。进一步,通过敏感性分析,评估了疫苗接种率v对基本再生数ℜ0和最终感染规模的影响。研究发现,提高疫苗接种率可显著降低流感的传播风险。For a class of improved SVEIR influenza transmission dynamics model, parameter estimation and fitting methods are discussed, and the impact of vaccination on influenza transmission is analyzed. First, assuming that the number of confirmed cases follows a Poisson distribution, the Bootstrap method is used to generate time series samples, and the Markov Chain Monte Carlo (MCMC) algorithm is used to achieve efficient sampling of the posterior distribution to estimate the model parameters. Subsequently, in order to verify the effectiveness of the model, actual influenza data were used for testing, and the results showed that the model can better capture the transmission dynamics of influenza. Furthermore, through sensitivity analysis, the impact of vaccination rate von the basic reproduction number ℜ0and the final infection scale was evaluated. The study found that increasing the vaccination rate can significantly reduce the risk of influenza transmission.
