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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

Moshoeshoe - lessons from an African icon - by Prof Frederick Fourie
2004-11-03

(The full text of the article that appeared in City Press and Sunday Independent)

Our understanding of history informs our understanding of the present. No wonder the contestation over historical figures in South Africa’s past is so fierce and so divisive.
The question is: could it be any other way? I would like to think that it could; that black and white South Africans, across linguistic, cultural, religious and other divides, can develop a shared appreciation of our history – at least with certain periods and personalities as a starting point.

One such personality whose legacy I believe offers a possible platform for unifying our still divided country is King Moshoeshoe, who lived from 1786 to 1870, and is acknowledged as the founder of the Basotho.

King Moshoeshoe is the topic of a documentary that has been commissioned by the University of the Free State as part of its Centenary celebrations this year. It is part of a larger project to honour and research the legacy of Moshoeshoe. The documentary will be screened on SABC 2 at 21:00 on November 4th.

Moshoeshoe rose to prominence at a time of great upheaval and conflict in South Africa – the 19th century, a time when British colonialism was entrenching itself, when the Boer trekkers were migrating from the Cape and when numerous indigenous chiefdoms and groupings were engaged in territorial conquests. It was the time of the Difaqane, a period when society in the central parts of the later South Africa and Lesotho was fractured, destabilised and caught in a cycle of violence and aggression.

In this period Moshoeshoe displayed a unique and innovative model of leadership that resulted in reconciliation, peace and stability in the area that later became Lesotho and Free State. It made him stand out from many of his contemporaries and also caught the attention of his colonial adversaries.

Such an evaluation is not a judgment about which model of leadership is right and which is wrong, or which leader was better than another; but merely an attempt to explore what we can learn from a particular exemplar.
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Historians point to the many progressive leadership qualities displayed by Moshoeshoe which he used effectively in establishing the Basotho nation and in defending it.
First, there is his humanism and sense of justice worthy of any great statesman. Confronted by a situation in which cannibals murdered and devoured his grandfather, Moshoeshoe chose not to take revenge. Instead he opted to rehabilitate them and feed them as he believed hunger drove them to cannibalism.

Secondly, there is his skilful alliance-building with his contemporaries such as Shaka in an attempt to neutralize those rivals who were intent on attacking his followers. This is also displayed in the way he sought the protection of the British to keep the Boer forces at bay.
Thirdly, his emphasis on peaceful options is also seen in his defensive military strategy which saw him retreat to a mountain fortress to be able to protect and build a burgeoning nation in the face of the many forces threatening its survival.

Fourthly, there is his remarkable inclusivity and tolerance for diversity which saw him unite disparate groups of refugees from the violence and hunger that displaced them and then weld them into the Basotho nation. He also engaged with French missionaries, inviting them to stay with him and advise him on Western thought, technology and religion.
These are but some of the qualities which belie the notion that all 19th century African leaders were merely marauders and conquerors that gained their ascendancy through violence. Instead Moshoeshoe is a prime example of the human-centred, democratic and pluralist roots of South African, indeed African society.

The Moshoeshoe project that we have initiated (of which the documentary, called “The Renaissance King”, forms but one part) derives from our location as a university in the Free State, a province with a particular history and a particular political culture that developed as a result of this very model of leadership. This province has benefited tremendously from leaders such as Moshoeshoe and president MT Steyn, both of whom many observers credit with establishing a climate of tolerance, respect for diversity of opinion, political accommodation and peaceful methods of pursuing political objectives in the province. Their legacy is real – and Moshoeshoe’s role can not be overstated.
In addition the project derives from the University of the Free State being a site of higher learning in a broader geo-political sense. As a university in Africa we are called upon to understand and critically engage with this history, this context and this legacy.
Besides the documentary, the UFS is also planning to establish an annual Moshoeshoe memorial lecture which will focus on and interrogate models of African leadership, nation-building, reconciliation, diversity management and political tolerance.

In tackling such projects, there may be a temptation to engage in myth-making. It is a trap we must be wary of, especially as an institution of higher learning. We need to ask critical questions about some aspects of Moshoeshoe’s leadership but of current political leadership as well. Thus there is a need for rigorous academic research into aspects of the Moshoeshoe legacy in particular but also into these above-mentioned issues.
While the documentary was commissioned to coincide with the University of the Free State’s centenary and our country’s ten years of democracy, it is a project that has a much wider significance. It is an attempt to get people talking about our past and about our future, as a campus, as a province and as a country – even as a continent, given the NEPAD initiatives to promote democracy and good governance.

The project therefore has particular relevance for the continued transformation of institutions such as universities and the transformation of our society. Hopefully it will assist those who are confronted by the question how to bring about new institutional cultures or even a national political culture that is truly inclusive, tolerant, democratic, non-sexist, non-racial, multilingual and multicultural.

I believe that the Moshoeshoe model of leadership can be emulated and provide some point of convergence. A fractured society such as ours needs points of convergence, icons and heroes which we can share. Moshoeshoe is one such an African icon – in a world with too few of them.

Prof Frederick Fourie is the Rector and Vice-Chancellor of the University of the Free State

* The documentary on “Moshoeshoe: The Renaissance King” will be screened on SABC2 on 4 November 2004 at 21:00.

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