A powerful investigative tool in biology is to consider not a single mathematical model but a collection of models designed to explore different working hypotheses and select the best model in that collection.In these...A powerful investigative tool in biology is to consider not a single mathematical model but a collection of models designed to explore different working hypotheses and select the best model in that collection.In these lecture notes,the usual workflow of the use of mathematical models to investigate a biological problem is described and the use of a collection of model is motivated.Models depend on parameters that must be estimated using observations;and when a collection of models is considered,the best model has then to be identified based on available observations.Hence,model calibration and selection,which are intrinsically linked,are essential steps of the workflow.Here,some procedures for model calibration and a criterion,the Akaike Information Criterion,of model selection based on experimental data are described.Rough derivation,practical technique of computation and use of this criterion are detailed.展开更多
An SL1L2I1I2A1A2R epidemic model is formulated that describes the spread of an epidemic in a population.The model incorporates an Erlang distribution of times of sojourn in incubating,symptomatically and asymptomatica...An SL1L2I1I2A1A2R epidemic model is formulated that describes the spread of an epidemic in a population.The model incorporates an Erlang distribution of times of sojourn in incubating,symptomatically and asymptomatically infectious compartments.Basic properties of the model are explored,with focus on properties important in the context of current COVID-19 pandemic.展开更多
基金SP is supported by a Discovery Grant of the Natural Sciences and Engineering Research Council of Canada(RGOIN-2018-04967).
文摘A powerful investigative tool in biology is to consider not a single mathematical model but a collection of models designed to explore different working hypotheses and select the best model in that collection.In these lecture notes,the usual workflow of the use of mathematical models to investigate a biological problem is described and the use of a collection of model is motivated.Models depend on parameters that must be estimated using observations;and when a collection of models is considered,the best model has then to be identified based on available observations.Hence,model calibration and selection,which are intrinsically linked,are essential steps of the workflow.Here,some procedures for model calibration and a criterion,the Akaike Information Criterion,of model selection based on experimental data are described.Rough derivation,practical technique of computation and use of this criterion are detailed.
基金The authors are supported in part by NSERC Discovery GrantsJA is also supported by CIHR through the Canadian 2019 Novel Coronavirus(COVID-19)Rapid Research Funding Opportunity+1 种基金The authors wish to thank Dr.Nicholas Ogden,Director of Public Health Risk Science(PHRS)at the National Microbiology Laboratory of the Public Health Agency of Canada,as well as DrsAamir Fazil and Erin Rees,also with PHRS,for helpful discussions during work on COVID-19.
文摘An SL1L2I1I2A1A2R epidemic model is formulated that describes the spread of an epidemic in a population.The model incorporates an Erlang distribution of times of sojourn in incubating,symptomatically and asymptomatically infectious compartments.Basic properties of the model are explored,with focus on properties important in the context of current COVID-19 pandemic.
