Models of coronavirus ‘underestimate its peak and overestimate its duration’

Coronavirus models underestimate the epidemic’s peak and overestimate its duration, an expert has said.

Comparison of a new approach with a published model of Covid-19 in Wuhan, China, before isolation and social distancing measures were imposed suggests the standard model underestimates the peak infection rate by a factor of three.

This means it could be three times higher – and substantially overestimates how long the epidemic will continue after the peak.

Mathematical models are widely used to understand and predict the dynamics of epidemics, and to assess the likely effectiveness of different disease management measures.

Some track the progress of the disease through individuals, but most publications that model the Covid-19 epidemic use what is known as a compartment or SEIR model.

This tracks numbers of individuals that are susceptible to the disease, have been exposed but not yet showing symptoms, are infected (showing symptoms) or recovering.

These models group all individuals in a compartment together, and do not consider the actual time since they were infected.

They then predict the course of the epidemic from information on rates of transmission and the average time an individual takes before showing symptoms, and then to recover.

In his paper Alastair Grant, of the University of East Anglia’s school of environmental sciences, argues that while SEIR and other compartment models can predict how far the disease transmission rate needs to be reduced to stop an epidemic growing, they do a poor job of predicting the path of an epidemic that is growing.

He says this problem was identified in the research literature at least 15 years ago, but the available solutions to it are far more difficult to use than the SEIR model.

Prof Grant, who has previously introduced key methodological tools into matrix population modelling, presents a new approach that tracks the time since individuals were infected.

But due to the rapid-response nature of this research, it has not yet been peer-reviewed.

Prof Grant said: “Standard compartment models of disease, such as SEIR, are being widely used to model the dynamics of the Covid‐19 epidemic.

“However, they do not accurately capture the distribution of times that an individual spends in each compartment, so do not accurately capture the transient dynamics of epidemics.

“Our explicit time model shows that the peak of infection may be either earlier or later than the peak in the simple SEIR model.

He added: “If SEIR models use parameter values estimated independently from data they will underestimate the proportion of the population which will be infected at the epidemic’s peak.

“But, if inverse modelling uses SEIR models to estimate parameters from disease time series, they may give estimates that are too pessimistic.

“National policies are guided by a range of disease models, including ones which deal more effectively with the known time course of infection within individuals, but details of this modelling work are not always made public.

“However, the domination of the published scientific literature by compartment models may be in danger of creating a discontinuity between the views held in the research community and the modelling that is informing national decision-making about the management of Covid-19.”

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