Mathematicians say lockdowns worked to limit spread of COVID-19

Despite South Africa reporting its first case of COVID-19 before Turkey, the spread was much slower in South Africa than in Turkey. Researchers devised mathematical models to understand why.

The COVID-19 pandemic began in 2020, and at the time scientists were still making and testing vaccines against the disease. Without vaccines, countries took other measures to reduce the spread of COVID-19, such as lockdowns (requiring citizens to stay at home) or social distancing. 

Despite the similarities in these practices, some countries, such as Turkey and South Africa, had very different responses. South Africa's lockdown was enforced slightly earlier and was somewhat more strict. But the difference in the number of infections between Turkey and South Africa was huge.

Researchers wanted to know why the number of infections and deaths in South Africa was so much lower than in Turkey. So, they created a new mathematical model to help them understand and predict how COVID-19 spreads. They also used the model to find out which aspects of the lockdown or social distancing were most effective.

They collected daily infections, deaths, and recoveries data from South Africa and Turkey from the first wave of infections until 3 May 2020. They then created multiple possible models of how COVID-19 spreads. Importantly, they made a model of how it may spread with a lockdown in place and another without a lockdown.

Their model predicted that COVID-19 would infect a whole country in about 2 months without a lockdown, and about 25% of people would not survive. On the other hand, if everyone followed lockdown rules, cases may drop by 90% in 2 weeks.

The researchers found that actions by individuals, such as social distancing, regular hand-washing, and wearing masks, are essential to limit the spread of COVID-19. Their models also predicted that government actions, such as banning alcohol sales and public smoking, are also useful.

The researchers however cautioned that they could not confirm some assumptions of their models, meaning their models may not be accurate when compared to the real world. They also did not explain what exactly caused the significant difference between South Africa and Turkey.

Researchers from South Africa, Turkey, and Taiwan worked together on this study. They said this work is important because it can suggest ways to save lives in a pandemic before vaccines are available.

Abstract

A comprehensive study about the spread of COVID-19 cases in Turkey and South Africa has been presented in this paper. An exhaustive statistical analysis was performed using data collected from Turkey and South Africa within the period of 11 March 2020 to 3 May 2020 and 05 March and 3 of May, respectively. It was observed that in the case of Turkey, a negative Spearman correlation for the number of infected class and a positive Spearman correlation for both the number of deaths and recoveries were obtained. This implied that the daily infections could decrease, while the daily deaths and number of recovered people could increase under current conditions. In the case of South Africa, a negative Spearman correlation for both daily deaths and daily infected people were obtained, indicating that these numbers may decrease if the current conditions are maintained. The utilization of a statistical technique predicted the daily number of infected, recovered, and dead people for each country; and three results were obtained for Turkey, namely an upper boundary, a prediction from current situation and lower boundary. The histograms of the daily number of newly infected, recovered and death showed a sign of lognormal and normal distribution, which is presented using the Bell curving method parameters estimation. A new mathematical model COVID-19 comprised of nine classes was suggested; of which a formula of the reproductive number, well-poseness of the solutions and the stability analysis were presented in detail. The suggested model was further extended to the scope of nonlocal operators for each case; whereby a numerical method was used to provide numerical solutions, and simulations were performed for different non-integer numbers. Additionally, sections devoted to control optimal and others dedicated to compare cases between Turkey and South Africa with the aim to comprehend why there are less numbers of deaths and infected people in South Africa than Turkey were presented in detail.

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