Physical distancing and related safety precautions around COVID-19 make both health and business sense, according to two new – and very different – studies.

In the first, medical researchers suggest that physical distancing orders issued by all 50 US states and the District of Columbia during March significantly slowed the epidemic, leading to a reduction of more than 600,000 cases within three weeks of implementation.

In the second, mathematicians say their modelling shows that businesses reopening after lockdown “may stand a good opportunity to generate positive net profit” only if “necessary protection measures are strictly implemented”.

The first study, described in a paper in the journal PLOS Medicine, was run by Massachusetts General Hospital, in collaboration with Harvard University and the University of Pennsylvania in the US, and University College London, UK.

Clinicians analysed data from the first five months of the epidemic, comparing changes in COVID-19 cases and attributed deaths before and after implementation of statewide government-ordered physical distancing measures.

They found, they say, that the average daily case growth rate began declining about one incubation period (four days) after implementation of the first measures. The time required for the number of cases to double increased from four to eight days within three weeks.

Overall, the model suggests that statewide measures reduced the total number of reported COVID-19 cases by about 1600 cases by one week after implementation and – due to the exponential growth of the spread – by about 621,000 by three weeks after implementation.

“The results show the timing of government-issued orders correlated strongly with reductions in both cases and deaths. In short, these measures work…” says Harvard’s Mark J Siedner.

The researchers do flag limitations to the analysis, however, notably that implementation was not a controlled experiment. If state governments intensified physical distancing measures in response to worsening local epidemics, they say, the analysis would likely have shown the policies to be less effective.

They also note that in many states people may have begun spontaneously changing their behaviour in response to a worsening local epidemic even prior to any statewide measures.

In the second study, researchers from the University of Texas Health Science Centre argue that mathematically, under a wide range of parameters, reopening a business is only feasible if at least six safety measures are adopted: social distancing; wearing goggles, gloves and masks when with others; frequent hand washing; routine floor cleaning; monitoring body temperature; and quarantine of exposed and sick employees.

These measures won’t only control the spread of COVID-19 within the company, they say, but also “increase your net profit under the assumptions of the model”.

As described in a paper Frontiers in Applied Mathematics and Statistics, Hongyu Miao and colleagues first developed five differential equations for the numbers of susceptible, infectious, quarantined, deceased, and recovered employees within a company.

These assumed that all workers who can work from home do so; that they self-quarantine as soon as they present symptoms or have been in close contact with a carrier; that infected employees who aren’t detected or are apparently recovered but still infectious can continue to infect others as “silent spreaders”; and that sick and quarantined workers receive full pay.

The authors then modelled net profit, based on the average salary and productivity of US workers, the cost of PPE and other safety measures, and the reduction in productivity expected from a limit on working hours and the need for distancing. They estimated values for key parameters, such as the effectiveness of PPE in preventing transmission, the expected cost of these measures, and the dynamics of infection.

When a well-known company was used as a hypothetical example, the model suggested that under the least-safe scenario, where no safety measures are taken, the prevalence of COVID-19 within the company steadily rises to become 30-fold higher than in the general US population, indicating that reopening wouldn’t be feasible.

Under the safest scenario, where all possible measures are adopted, its prevalence falls to “104-fold lower than in the population, resulting in a higher and more stable net profit”.

Results are similar under the second-safest scenario, where only the most expensive measures – such as non-contact sensors for real-time fever detection and UV purification –  are omitted, but if employees drop the use of PPE, the workplace again quickly becomes a “hot spot” of infection, resulting in a lower net profit.