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05 September 2022 | Story Andrè Damons | Photo Andrè Damons
Prof Abdon Atangana
Prof Abdon Atangana, Professor of Applied Mathematics in the Institute for Groundwater Studies (IGS) and a highly cited mathematician for the years 2019-2021, says existing mathematical models are used to first fit collected data and then predict future events. It is for this reason he introduced a new concept that can be used to test whether the spread will have one or several waves.

With a new outbreak of the Ebola Virus Disease (EVD) reported this year in Democratic Republic of the Congo (DRC) – the 14th EVD outbreak in the country – researchers at the University of the Free State (UFS) introduced a new concept that can be used to test whether the spread will have one or several waves. They believe the focus should be to identify the source or the hosts of this virus for it to be a complete eradication. 

According to the Centers for Disease Control and Prevention (CDC), the Ministry of Health in the Democratic Republic of the Congo (DRC) declared an outbreak of Ebola in Mbandaka health zone, Equateur Province on April 23, 2022. EVD, formerly known as Ebola haemorrhagic fever, is a severe, often fatal illness affecting humans and other primates. The virus is transmitted to people from wild animals (such as fruit bats, porcupines and non-human primates) and then spreads in the human population through direct contact with the blood, secretions, organs or other bodily fluids of infected people, and with surfaces and materials (e.g. bedding, clothing) contaminated with these fluids, according to the World Health Organisation (WHO).
 
Prof Abdon Atangana, Professor of Applied Mathematics in the Institute for Groundwater Studies (IGS), says existing mathematical models are used to first fit collected data and then predict future events. Predictions help lawmakers to take decisions that will help protect their citizens and their environments. The outbreaks of COVID-19 and other infectious diseases have exposed the weakness of these models as they failed to predict the number of waves and in several instances; they failed to predict accurately day-to-day new infections, daily deaths and recoveries.

Solving the challenges of the current models

In the case of COVID-19 in South Africa, it is predicted that the country had far more infections than what was recorded, which is due to challenges faced by the medical facilities, poverty, inequality, and other factors. With Ebola in the DRC, data recorded are not far from reality due to the nature of the virus and its symptoms. However, the predictions show although some measures have been put in place in DRC and other places where the Ebola virus spread, they will still face some challenges in the future, as the virus will continue to spread but may have less impact. 

“To solve the challenges with the current models, we suggested a new methodology. We suggested that each class should be divided into two subclasses (Detected and undetected) and we also suggested that rates of infection, recovery, death and vaccination classes should be a function of time not constant as suggested previously. These rates are obtained from what we called daily indicator functions. For example, an infection rate should be obtained from recorded data with the addition of an uncertain function that represents non-recorded data (Here more work is still to be done to get a better approximation).

“I introduced a new concept called strength number that can be used to test whether the spread will have one or several waves. The strength number is an accelerative force that helps to provide speed changes, thus if this number is less than zero we have deceleration, meaning there will be a decline in the number of infections. If the number is positive, we have acceleration, meaning we will have an increase in numbers. If the number is zero, the current situation will remain the same,” according to Prof Atangana. 

To provide better prediction, he continues, reliable data are first fitted with the suggested mathematical model. This helps them to know if their mathematical model is replicating the dynamic process of the spread. The next step is to predict future events, to do this, we create three sub-daily indicator functions (minimum, actual, and maximum). These will lead to three systems, the first system represents the worst-case scenario, the second is the actual scenario, and the last is a best-case scenario.

Virus will continue to spread but with less impact

Using this method, Prof Atangana, a highly cited mathematician for the years 2019-2021, says he and Dr Seda Igret Araz, postdoctoral student, were able to predict that, although some measures have been put in place in DRC and other places where the Ebola virus spreads, they will still face some challenges in the future as the virus will continue to spread but may have less impact. 

To properly achieve the conversion from observed facts into mathematical formulations and to address these limitations, he had to ask fundamental questions such as what is the rate of infection, what is the strength of the infection, what are the crossover patterns presented by the spread, how can day-to-day new infected numbers be predicted and what differential operator should be used to model a dynamic process followed by the spread?

This approach was tested for several infectious diseases where we present the case of Ebola in Congo and Covid-19 in South Africa.  

News Archive

“To forgive is not an obligation. It’s a choice.” – Prof Minow during Reconciliation Lecture
2014-03-05

“To forgive is not an obligation. It’s a choice.” – Prof Minow during the Third Annual Reconciliation Lecture entitled Forgiveness, Law and Justice.
Photo: Johan Roux

No one could have anticipated the atmosphere in which Prof Martha Minow would visit the Bloemfontein Campus. And no one could have predicted how apt the timing of her message would be. As this formidable Dean of Harvard University’s Law School stepped behind the podium, a latent tension edged through the crowded audience.

“The issue of getting along after conflict is urgent.”

With these few words, Prof Minow exposed the essence of not only her lecture, but also the central concern of the entire university community.

As an expert on issues surrounding racial justice, Prof Minow has worked across the globe in post-conflict societies. How can we prevent atrocities from happening? she asked. Her answer was an honest, “I don’t know.” What she is certain of, on the other hand, is that the usual practice of either silence or retribution does not work. “I think that silence produces rage – understandably – and retribution produces the cycle of violence. Rather than ignoring what happens, rather than retribution, it would be good to reach for something more.” This is where reconciliation comes in.

Prof Minow put forward the idea that forgiveness should accompany reconciliation efforts. She defined forgiveness as a conscious, deliberate decision to forego rightful grounds of resentment towards those who have committed a wrong. “To forgive then, in this definition, is not an obligation. It’s a choice. And it’s held by the one who was harmed,” she explained.

Letting go of resentment cannot be forced – not even by the law. What the law can do, though, is either to encourage or discourage forgiveness. Prof Minow showed how the law can construct adversarial processes that render forgiveness less likely, when indeed its intention was the opposite. “Or, law can give people chances to meet together in spaces where they may apologise and they may forgive,” she continued. This point introduced some surprising revelations about our Truth and Reconciliation Commission (TRC).

Indeed, studies do report ambivalence, disappointment and mixed views about the TRC. Whatever our views are on its success, Prof Minow reported that people across the world wonder how South African did it. “It may not work entirely inside the country; outside the country it’s had a huge effect. It’s a touchstone for transitional justice.”

The TRC “seems to have coincided with, and maybe contributed to, the relatively peaceful political transition to democracy that is, frankly, an absolute miracle.” What came as a surprise to many is this: the fact that the TRC has affected transitional justice efforts in forty jurisdictions, including Rwanda, Sierra Leone, Cambodia and Liberia. It has even inspired the creation of a TRC in Greensborough, North Carolina, in the United States.

There are no blueprints for solving conflict, though. “But the possibility of something other than criminal trials, something other than war, something other than silence – that’s why the TRC, I think, has been such an exemplar to the world,” she commended.

Court decision cannot rebuild a society, though. Only individuals can forgive. Only individuals can start with purposeful, daily decisions to forgive and forge a common future. Forgiveness is rather like kindness, she suggested. It’s a resource without limits. It’s not scarce like water or money. It’s within our reach. But if it’s forced, it’s not forgiveness.

“It is good,” Prof Minow warned, “to be cautious about the use of law to deliberately shape or manipulate the feelings of any individual. But it is no less important to admit that law does affect human beings, not just in its results, but in its process.” And then we must take responsibility for how we use that law.

“A government can judge, but only people can forgive.” As Prof Minow’s words lingered, the air suddenly seemed a bit more buoyant.

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