Public health officials are increasingly recognizing the need to develop disease-forecasting systems to respond to epidemic and pandemic outbreaks.For instance,simple epidemic models relying on a small number of param...Public health officials are increasingly recognizing the need to develop disease-forecasting systems to respond to epidemic and pandemic outbreaks.For instance,simple epidemic models relying on a small number of parameters can play an important role in characterizing epidemic growth and generating short-term epidemic forecasts.In the absence of reliable information about transmission mechanisms of emerging infectious diseases,phenomenological models are useful to characterize epidemic growth patterns without the need to explicitly model transmission mechanisms and the natural history of the disease.In this article,our goal is to discuss and illustrate the role of regularization methods for estimating parameters and generating disease forecasts using the generalized Richards model in the context of the 2014e15 Ebola epidemic in West Africa.展开更多
In recent years,advanced regularization techniques have emerged as a powerful tool aimed at stable estimation of infectious disease parameters that are crucial for future projections,prevention,and control.Unlike othe...In recent years,advanced regularization techniques have emerged as a powerful tool aimed at stable estimation of infectious disease parameters that are crucial for future projections,prevention,and control.Unlike other system parameters,i.e.,incubation and recovery rates,the case reporting rate,Ψ,and the time-dependent effective reproduction number,R_(e)t,are directly influenced by a large number of factors making it impossible to pre-estimate these parameters in any meaningful way.In this study,we propose a novel iteratively-regularized trust-region optimization algorithm,combined with SuSvIuIvRD compartmental model,for stable reconstruction ofΨand R_(e)t from reported epidemic data on vaccination percentages,incidence cases,and daily deaths.The innovative regularization procedure exploits(and takes full advantage of)a unique structure of the Jacobian and Hessian approximation for the nonlinear observation operator.The proposed inversion method is thoroughly tested with synthetic and real SARS-CoV-2 Delta variant data for different regions in the United States of America from July 9,2021,to November 25,2021.Our study shows that case reporting rate during the Delta wave of COVID-19 pandemic in the US is between 12%and 37%,with most states being in the range from 15%to 25%.This confirms earlier accounts on considerable under-reporting of COVID-19 cases due to the impact of”silent spreaders”and the limitations of testing.展开更多
We propose a versatile model with a flexible choice of control for an early-pandemic outbreak prevention when vaccine/drug is not yet available.At that stage,control is often limited to non-medical interventions like ...We propose a versatile model with a flexible choice of control for an early-pandemic outbreak prevention when vaccine/drug is not yet available.At that stage,control is often limited to non-medical interventions like social distancing and other behavioral changes.For the SIR optimal control problem,we show that the running cost of control satisfying mild,practically justified conditions generates an optimal strategy,u(t),t∈[0,T],that is sustainable up until some moment τ∈[0,T).However,for any t∈[τ,T],the function u(t)will decline as t approaches T,which may cause the number of newly infected people to increase.So,the window from 0 to τ is the time for public health officials to prepare alternative mitigation measures,such as vaccines,testing,antiviral medications,and others.In addition to theoretical study,we develop a fast and stable computational method for solving the proposed optimal control problem.The efficiency of the new method is illustrated with numerical examples of optimal control trajectories for various cost functions and weights.Simulation results provide a comprehensive demonstration of the effects of control on the epidemic spread and mitigation expenses,which can serve as invaluable references for public health officials.展开更多
基金Dr.Gerardo Chowell acknowledges financial support from NSF grant 1414374 as part of the joint NSF-NIH-USDA Ecology and Evolution of Infectious Diseases programUK Biotechnology and Biological Sciences Research Council grant BB/M008894/1 and NSF grant 1610429.
文摘Public health officials are increasingly recognizing the need to develop disease-forecasting systems to respond to epidemic and pandemic outbreaks.For instance,simple epidemic models relying on a small number of parameters can play an important role in characterizing epidemic growth and generating short-term epidemic forecasts.In the absence of reliable information about transmission mechanisms of emerging infectious diseases,phenomenological models are useful to characterize epidemic growth patterns without the need to explicitly model transmission mechanisms and the natural history of the disease.In this article,our goal is to discuss and illustrate the role of regularization methods for estimating parameters and generating disease forecasts using the generalized Richards model in the context of the 2014e15 Ebola epidemic in West Africa.
基金Supported by NSF award 2011622(DMS Computational Mathematics).
文摘In recent years,advanced regularization techniques have emerged as a powerful tool aimed at stable estimation of infectious disease parameters that are crucial for future projections,prevention,and control.Unlike other system parameters,i.e.,incubation and recovery rates,the case reporting rate,Ψ,and the time-dependent effective reproduction number,R_(e)t,are directly influenced by a large number of factors making it impossible to pre-estimate these parameters in any meaningful way.In this study,we propose a novel iteratively-regularized trust-region optimization algorithm,combined with SuSvIuIvRD compartmental model,for stable reconstruction ofΨand R_(e)t from reported epidemic data on vaccination percentages,incidence cases,and daily deaths.The innovative regularization procedure exploits(and takes full advantage of)a unique structure of the Jacobian and Hessian approximation for the nonlinear observation operator.The proposed inversion method is thoroughly tested with synthetic and real SARS-CoV-2 Delta variant data for different regions in the United States of America from July 9,2021,to November 25,2021.Our study shows that case reporting rate during the Delta wave of COVID-19 pandemic in the US is between 12%and 37%,with most states being in the range from 15%to 25%.This confirms earlier accounts on considerable under-reporting of COVID-19 cases due to the impact of”silent spreaders”and the limitations of testing.
基金Supported by NSF award 2011622(DMS Computational Mathematics)Supported by NSF award 2152960(DMS CDS&E)and 2307466(DMS Applied Mathematics).
文摘We propose a versatile model with a flexible choice of control for an early-pandemic outbreak prevention when vaccine/drug is not yet available.At that stage,control is often limited to non-medical interventions like social distancing and other behavioral changes.For the SIR optimal control problem,we show that the running cost of control satisfying mild,practically justified conditions generates an optimal strategy,u(t),t∈[0,T],that is sustainable up until some moment τ∈[0,T).However,for any t∈[τ,T],the function u(t)will decline as t approaches T,which may cause the number of newly infected people to increase.So,the window from 0 to τ is the time for public health officials to prepare alternative mitigation measures,such as vaccines,testing,antiviral medications,and others.In addition to theoretical study,we develop a fast and stable computational method for solving the proposed optimal control problem.The efficiency of the new method is illustrated with numerical examples of optimal control trajectories for various cost functions and weights.Simulation results provide a comprehensive demonstration of the effects of control on the epidemic spread and mitigation expenses,which can serve as invaluable references for public health officials.
