A Bayesian model calibration framework for stochastic compartmental models with both time-varying and timeinvariant parameters  

作　　者：Brandon Robinson Philippe Bisaillon Jodi D.Edwards Tetyana Kendzerska Mohammad Khalil Dominique Poirel Abhijit Sarkar 

机构地区：[1]Department of Civil and Environmental Engineering,Carleton University,Ottawa,ON K1S 5B6,Canada [2]School of Epidemiology and Public Health,University of Ottawa and University of Ottawa Heart Institute,Ottawa,Ontario,Canada [3]ICES,Ottawa,Ontario,Canada [4]The Ottawa Hospital Research Institute,Ottawa,Ontario,Canada [5]Department of Medicine,Faculty of Medicine,Division of Respirology,University of Ottawa,Ottawa,Ontario,Canada [6]Quantitative Modeling&Analysis Department,Sandia National Laboratories,Livermore,CA,USA [7]Department of Mechanical and Aerospace Engineering,Royal Military College of Canada,Kingston,ON,Canada

出　　处：《Infectious Disease Modelling》2024年第4期1224-1249,共26页传染病建模（英文）

基　　金：the funding from the New Frontiers in Research Fund(NFRF)2022 Special Call e Research for Postpandemic Recovery(Grant no:NFRFR-2022-00395).

摘　　要：We consider state and parameter estimation for compartmental models having both timevarying and time-invariant parameters.In this manuscript,we first detail a general Bayesian computational framework as a continuation of our previous work.Subsequently,this framework is specifically tailored to the susceptible-infectious-removed(SIR)model which describes a basic mechanism for the spread of infectious diseases through a system of coupled nonlinear differential equations.The SIR model consists of three states,namely,the susceptible,infectious,and removed compartments.The coupling among these states is controlled by two parameters,the infection rate and the recovery rate.The simplicity of the SIR model and similar compartmental models make them applicable to many classes of infectious diseases.However,the combined assumption of a deterministic model and time-invariance among the model parameters are two significant impediments which critically limit their use for long-term predictions.The tendency of certain model parameters to vary in time due to seasonal trends,non-pharmaceutical interventions,and other random effects necessitates a model that structurally permits the incorporation of such time-varying effects.Complementary to this,is the need for a robust mechanism for the estimation of the parameters of the resulting model from data.To this end,we consider an augmented state vector,which appends the time-varying parameters to the original system states whereby the time evolution of the time-varying parameters are driven by an artificial noise process in a standard manner.Distinguishing between time-varying and time-invariant parameters in this fashion limits the introduction of artificial dynamics into the system,and provides a robust,fully Bayesian approach for estimating the timeinvariant system parameters as well as the elements of the process noise covariance matrix.This computational framework is implemented by leveraging the robustness of the Markov chain Monte Carlo algorithm permits the estimation of time

关 键 词：Time-varying parameter estimation Bayesian inference Stochastic compartmental models 

分 类 号：R51[医药卫生—内科学]