Mathematics Involved Behind the COVID – 19 Containment



A well paced article written by Martin Enserink and Kaikupferschmidt in, highlights the importance of epidemic modelers in containing the corona break down and the models’ limitations, by incorporating the views of various experts in this field.

Wallinga – the Mathematician and the Chief Epidemic Modeler

COVID-19 isn’t the first infectious disease scientists have modeled.  For example, Ebola and Zika but never has so much depended on their work.  Many epidemic modelers provide time to time statistics and analysis to track and tackle this outbreak. 

A high-stake reality check is what Jacco Wallinga’s computer simulations are about to face.  He is a mathematician and the chief epidemic modeler at the National Institute for Public Health and the Environment (RIVM).  It advises the Dutch government on what actions, such as closing schools and businesses, will help control the spread of the novel coronavirus in the country.

Wallinga’s models predict that the number of infected people needing hospitalization.  But if the models are wrong, the demand for intensive care beds could outstrip supply, as it has, tragically, in Italy and Spain.

Netherlands’ response to RIVM’s Expertise

  • The Netherlands has so far chosen a softer set of measures than most Western European countries. 
  • Prime Minister Mark Rutte rejected “working endlessly to contain the virus” and “shutting down the country completely.”
  • Instead, he opted for “controlled spread” of the virus among the groups least at risk of severe illness. 

“It has suddenly become very visible how much the response to infectious diseases is based on models,” Wallinga says.  For the entire cities and countries have been locked down based on hastily done forecasts that often haven’t been peer reviewed.

A huge responsibility for modelers

For the modelers, “it’s a huge responsibility,” says epidemiologist Caitlin Rivers of the Johns Hopkins University Center for Health Security, who co-authored a report about the future of outbreak modeling in the United States.  

Scenario 1 – The U.K government at first implemented fewer measures 

These models have become vital and influential in the first two weeks of March for the United Kingdom.  Based partly on modeling work by a group at Imperial College London, the U.K. government at first implemented fewer measures than many other countries.

Scenario 2 – The U.K government announced a strict lockdown

Whereas, in the 2nd week of March, the Imperial College group published a dramatically revised model that concluded—based on fresh data from the United Kingdom and Italy—that even a reduced peak would fill twice as many intensive care beds as estimated previously, overwhelming capacity. 

The only choice, they concluded, was to go all out on control measures. At best, strict measures might be periodically eased for short periods, the group said. The U.K. government shifted course within days and announced a strict lockdown.

All models are wrong but some useful

Epidemic modelers are the first to admit their projections can be off. “All models are wrong, but some are useful,” statistician George Box supposedly once said—a phrase that has become a cliché in the field.

U.K. control measures could be let up once in a while, a model suggests, until demand for intensive care unit (ICU) beds hits a threshold.

Wallinga’s Mathematical approach to epidemic model

  • The RIVM team knows how many contacts people of different ages have at home, school, work, and during leisure.
  • Equations determine how many people move between compartments as weeks and months pass.
  • The model outcomes vary widely depending on the characteristics of a pathogen and the affected population.
  • As the virus that causes COVID-19 is new, modelers need estimates for key model parameters.
  • He spent a lot of time estimating R0 for SARS-Cov-2, the virus that causes COVID-19, and felt sure it’s just over two.
  • He is also confident about his estimate that 3 to 6 days elapse between the moment someone is infected and the time they start to infect others.

Compartment model vs day-to-day model

Compartment models assume the population is homogeneously mixed, a reasonable assumption for a small country like the Netherlands. 

Other modeling groups don’t use compartments but simulate the day-to-day interactions of millions of individuals. Such models can depict heterogeneous countries, such as the United States, or all of Europe.

Scenario 3 – Possible Corona outbreak from January in the U.K

 A widely publicized, controversial modeling study published by a group at the University of Oxford argues that the deaths observed in the United Kingdom could be explained by a very different scenario from the currently accepted one. 

Rather than SARS-CoV-2 spreading in recent weeks and causing severe disease in a significant percentage of people, as most models suggest, the virus might have been spreading in the United Kingdom since January.  could have already infected up to half of the population, causing severe disease only in a tiny fraction. 

Both scenarios are equally plausible, says Sunetra Gupta, the theoretical epidemiologist who led the Oxford work. “I do think it is missing from the thinking that there is an equally big possibility that a lot of us are immune,” she says.

The model itself cannot answer the question, she says; only widespread testing for antibodies can, and that needs to be done urgently.

Possible measures to tackle the COVID-19 epidemic

Caitlin Rivers of the Johns Hopkins University Center for Health Security, says “It would be more effective if they could be on-site with the government, working side by side with decision makers.”

Rivers argues for the creation of a National Infectious Disease Forecasting Center, akin to the National Weather Service. It would be the primary source of models in a crisis and strengthen outbreak science in “peacetime.”

Models are at their most useful when they identify something that is not obvious. 

There’s also a lot that models don’t capture.  Long lockdowns to slow a disease can also have catastrophic economic impacts that may themselves affect public health. The economic fallout isn’t something epidemic models address.

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Source: ScienceMag


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