It was reported at the weekend that Vietnam had recorded its first case of the transmission of the coronavirus after 100 days, when a 57-year-old man in the city of Danang tested positive. The discovery of the new case came as a shock to citizens and the government alike, according to The New York Times, and many people have reportedly cancelled travel plans in central Vietnam, a popular destination for domestic and foreign travellers.

Vietnam, one of the world’s few remaining communist states, has been among the most successful in the world in containing the virus, largely attributed to the public embracing the wearing of masks. As of July 25, the country had reported 416 cases and no deaths. Its last known case of local transmission was in mid-April.

Here in South Africa, precautions have also been put in place to “flatten the curve”. Yet, there is great ambiguity in what it means to flatten the curve. Is this when recoveries outnumber the infection rate? According to epidemiology, flattening the curve is slowing the spread of the virus so that fewer people need treatment at any given time, which allows healthcare services to better manage the volume of patients.

In this context, the curve is the estimated number of people who will contract Covid-19 over a period of time. The number of confirmed cases of Covid-19 is plotted on one axis while the time since the first case is plotted on the other axis. This is a mathematical description, but there is no other way of understanding this pandemic except to use mathematics.

As there is no vaccine or specific treatment for Covid-19, countries have implemented physical distancing guidelines to spur collective action to prevent the spread of the virus. Physical distancing is not new in South Africa – it has long been an integral part of our way of life. In African societies, for example, people traditionally lived far apart and the clustering of people into densely populated areas is a new phenomenon. In addition, when African people greeted, traditionally there was no physical contact. In fact, there was a distance maintained between the people greeting. Contact greeting such as the shaking of hands or hugging came with the Westernisation of our society. Perhaps, we need to return to our ways of life to tackle the problem of the coronavirus.

As countries around the globe begin a slow reopening, we have to ask whether it is time for us to follow suit, and how. Just last week, South Africa became the fifth-worst affected country globally as the number of local coronavirus infections topped 364,000. Cases are continuing to rise. How do we determine when the right time is to reopen the economy? In probability theory in mathematics, there is a concept called the optimal stopping problem, which identifies the time to take an action in order to maximise the outcome.

There are two theories that can lead us to this answer. The first is the Secretary Problem. The basis of this theory is a hypothetical situation, where an administrator wants to hire the best secretary out of the applicants. Each applicant is interviewed, and a decision is made immediately and cannot be retracted.

As the administrator learns information about the applicant, they are ranked. Of course, the administrator, in doing this, is unaware of the quality of the applicants that have not been seen yet.

In the case of lockdown, exploration is equivalent to identifying the impact of rules in each lockdown phase and easing them to find which are necessary while exploitation is opening up as much of the economy as possible during the pandemic. Exploitation takes advantage of the best option that we know, following the risks and short-term sacrifices made during the exploration period.

The difficulty in this theory is that a decision must be made immediately without weighing it against other options. The first official solution to this problem, in print at least, was proposed by British statistician Dennis Lindley in 1961. The optimal candidate could be found by observing the first 37% of the sample and ranking them and then choosing the first person better than any of the 37%.

The idea is that you have a one-in-three chance of choosing the most suitable candidate overall with this system. As the Secretary Problem demonstrates, there needs to be a certain amount of time spent exploring before you implement what has been learned.

We, of course, have incomplete information in this instance of Covid-19. We do not know how many people are infected, nor the number of people who are infectious. We only know the number of confirmed cases. Yet we use the information we have to make the best possible decision, taking some risk with the unknown variables. This algorithm, of course, can be deployed for any choice – such as deciding when to end a lockdown.

Here we can look at where we are in terms of infections, for instance, and look at what other countries did at the same point, where they might have ended lockdown, when they peaked and base a prediction on this sample set.

Another possible solution arises from the multi-armed bandit problem. In this problem, a gambler is faced with a row of slot machines and has to decide which machines to play, how many to play, in what order to play and whether to continue playing on a machine or switch to another one.

The probability distribution for a reward corresponding to each lever is different and is unknown to the gambler. Because there is no prior knowledge of the potential rewards, this requires a balance between exploration, or trying a lot of slot machines, and exploitation, or repeatedly pulling the best levers to narrow down selections.

In the case of lockdown, exploration is equivalent to identifying the impact of rules in each lockdown phase and easing them to find which are necessary while exploitation is opening up as much of the economy as possible during the pandemic. Exploitation takes advantage of the best option that we know, following the risks and short-term sacrifices made during the exploration period.

There is a distinct need to tap into our AI capabilities to aid in our decisions as we figure out whether the lockdown is still effective. Of course, the decision to lift the lockdown does not mean that things will return to normal. We will still need to wash our hands, sanitise, self-isolate and maintain social distancing – but we may be able to do this without putting the economy at further risk. DM