Motivated by the need for robust models of the Covid-19 epidemic that adequately reflect the extreme heterogeneity of humans and society,this paper presents a novel framework that treats a population of N individuals ...Motivated by the need for robust models of the Covid-19 epidemic that adequately reflect the extreme heterogeneity of humans and society,this paper presents a novel framework that treats a population of N individuals as an inhomogeneous random social network(IRSN).The nodes of the network represent individuals of different types and the edges represent significant social relationships.An epidemic is pictured as a contagion process that develops day by day,triggered by a seed infection introduced into the population on day 0.Individuals’social behaviour and health status are assumed to vary randomly within each type,with probability distributions that vary with their type.A formulation and analysis is given for a SEIR(susceptible-exposed-infective-removed)network contagion model,considered as an agent based model,which focusses on the number of people of each type in each compartment each day.The main result is an analytical formula valid in the large N limit for the stochastic state of the system on day t in terms of the initial conditions.The formula involves only one-dimensional integration.The model can be implemented numerically for any number of types by a deterministic algorithm that efficiently incorporates the discrete Fourier transform.While the paper focusses on fundamental properties rather than far ranging applications,a concluding discussion addresses a number of domains,notably public awareness,infectious disease research and public health policy,where the IRSN framework may provide unique insights.展开更多
This paper provides a mathematical model that makes it clearly visible why the underestimation of r,the fraction of asymptomatic COVID-19 carriers in the general population,may lead to a catastrophic reliance on the s...This paper provides a mathematical model that makes it clearly visible why the underestimation of r,the fraction of asymptomatic COVID-19 carriers in the general population,may lead to a catastrophic reliance on the standard policy intervention that attempts to isolate all confirmed infectious cases.The SE(AþO)R model with infectives separated into asymptomatic and ordinary carriers,supplemented by a model of the data generation process,is calibrated to standard early pandemic datasets for two countries.It is shown that certain fundamental parameters,critically r,are unidentifiable with this data.A general analytical framework is presented that projects the impact of different types of policy intervention.It is found that the lack of parameter identifiability implies that some,but not all,potential policy interventions can be correctly predicted.In an example representing Italy in March 2020,a hypothetical optimal policy of isolating confirmed cases that aims to reduce the basic reproduction number R0 of the outbreak from 4.4 to 0.8 assuming r¼0,only achieves 3.8 if it turns out that r¼40%.展开更多
基金This project was funded by the Natural Sciences and Engineering Research Council of Canada and the McMaster University COVID-19 Research Fund.
文摘Motivated by the need for robust models of the Covid-19 epidemic that adequately reflect the extreme heterogeneity of humans and society,this paper presents a novel framework that treats a population of N individuals as an inhomogeneous random social network(IRSN).The nodes of the network represent individuals of different types and the edges represent significant social relationships.An epidemic is pictured as a contagion process that develops day by day,triggered by a seed infection introduced into the population on day 0.Individuals’social behaviour and health status are assumed to vary randomly within each type,with probability distributions that vary with their type.A formulation and analysis is given for a SEIR(susceptible-exposed-infective-removed)network contagion model,considered as an agent based model,which focusses on the number of people of each type in each compartment each day.The main result is an analytical formula valid in the large N limit for the stochastic state of the system on day t in terms of the initial conditions.The formula involves only one-dimensional integration.The model can be implemented numerically for any number of types by a deterministic algorithm that efficiently incorporates the discrete Fourier transform.While the paper focusses on fundamental properties rather than far ranging applications,a concluding discussion addresses a number of domains,notably public awareness,infectious disease research and public health policy,where the IRSN framework may provide unique insights.
文摘This paper provides a mathematical model that makes it clearly visible why the underestimation of r,the fraction of asymptomatic COVID-19 carriers in the general population,may lead to a catastrophic reliance on the standard policy intervention that attempts to isolate all confirmed infectious cases.The SE(AþO)R model with infectives separated into asymptomatic and ordinary carriers,supplemented by a model of the data generation process,is calibrated to standard early pandemic datasets for two countries.It is shown that certain fundamental parameters,critically r,are unidentifiable with this data.A general analytical framework is presented that projects the impact of different types of policy intervention.It is found that the lack of parameter identifiability implies that some,but not all,potential policy interventions can be correctly predicted.In an example representing Italy in March 2020,a hypothetical optimal policy of isolating confirmed cases that aims to reduce the basic reproduction number R0 of the outbreak from 4.4 to 0.8 assuming r¼0,only achieves 3.8 if it turns out that r¼40%.
