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Infectious Diseases

Updated 12 May 2020

Physical distancing works, according to mathematical modelling

During this time of immense uncertainty, if there is one thing that we can be sure of, it’s that physical distancing works, say University of Johannesburg researchers.

The pandemic that’s gripping the world has infected more than 4.1 million people and killed more than 282 000 worldwide, according to the latest stats by the Johns Hopkins Coronavirus Resource Centre.

Physical distancing, which has become a crucial factor in public health intervention in many countries, including South Africa, has become key in containing the new coronavirus, officially named SARS-CoV-2. And, according to mathematical modelling experts from the University of Johannesburg (UJ), this line of prevention works.

The team, led by UJ’s Professor Farai Nyabadza, an advanced researcher in mathematical epidemiology, Dr Faraimunashe Chirove, Dr Maria Visaya and Mr Williams Chukwu, performed numerous calculations and quantified the level of physical distancing that can reduce the transmission and infection rate substantially.

What mathematical modelling does

Mathematical modelling is, in essence, an abstract representation of a real-life situation, explains Nyabadza, adding that policy-making decisions by the government are driven by research evidence of this nature.

“They use a range of these models because the models are dependent on different questions, on what you want to investigate. Our team, for example, investigated physical distancing, but another model might investigate how many hospital beds our healthcare system will need, so that’s why, with our diverse expertise, each one of us can contribute to a range of models.”

In this particular scenario, the UJ team wanted to analyse a disease, i.e. Covid-19, that is spreading among the South African population, and how it is affected by physical distancing.

“What we wanted to do was create a sort of tool that we can use to represent a disease that is spreading, but in mathematical terms, and once we reached a mathematical equation, we translated that back to the real-life situation so that we could interpret what is actually happening – and find solutions to it.” 

The team found that if physical distancing is relaxed, which is expected to happen with the easing into the lower levels of lockdown, the following could happen:

  • Relaxing physical distancing by just 2% can result in a 23% rise in the number of cumulative cases.
  • Increasing the levels of physical distancing by 2% would reduce the number of cumulative cases by about 18%.

Nyabadza explains that the five levels of lockdown had not yet been introduced at the time of their research, and that the team analysed Google mobility data, which present insights into how people are moving around in local communities.

“We found that just before the lockdown, and during the lockdown, people were more at home. The percentage of people that were still moving, for various reasons (such as being essential workers), gave us a way of quantifying the level of physical distancing.

“The simulations show that if the optimal level of physical distancing is maintained at 55%, then the number of cumulative cases will continue to grow exponentially. On this basis, increasing the level of physical distancing from 55% to 57%, 59%, and 61% would avert the cumulative cases by about 18%, 32% and 53% respectively at the end of lockdown,” Nyabadza explains.

In simple terms, this means that increasing the level of physical distancing in the model means increasing people’s distancing from one another in real life, which in turn reduces the infection rate. However, Nyabadza believes that pushing it to 60% is quite aggressive, as it would greatly limit people's movements and is therefore not very practical.

Need for more aggressive approaches

According to Nyabadza, there is a need for “more aggressive and robust multi-control approaches that target reduction of the infection rate” as the current levels of physical distancing are inadequate. “You know, asking the population to stay at home is having a huge economic impact for so many people. We need to have interventions that are targeted at reducing contact or the way people interact, and as a result, the number of people that are infected.

“So from a policy perspective, they had to come up with a way of relaxing the levels so that people can start working and earn an income, but in the process of doing that, the President made it mandatory to wear a mask in public. And so, despite the relaxation of physical distancing, wearing a mask will now help to limit the spread of the virus.”

However, Nyabadza feels uneasy about the eventual allowing of inter-provincial travel in the country:

“This will have implications with respect to the spread of the disease. In some provinces, the disease is quite bad, whereas in the Northern Cape, for example, it currently does not have more than 27 cases.

“And some people will, for instance, want to visit and stay with their grandparents in provinces where the infection rate is very low, but we have to consider that they will travel from provinces with higher infection rates and could potentially carry the virus to the provinces with the lowest number of infections.

“People just need to understand that it’s such an important part to obey regulations, because they’re all based on science and minimising the spread of the disease,” says Nyabadza.

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