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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

Research by experts published in Nature
2011-06-02

 
The members of the research group are, from the left, front: Christelle van Rooyen, Mariana Erasmus, Prof. Esta van Heerden; back: Armand Bester and Prof. Derek Litthauer.
Photo: Gerhard Louw

A  research article on the work by a team of experts at our university, under the leadership of Prof. Esta van Heerden, and counterparts in Belgium and the USA has been published in the distinguished academic journal Nature today (Thursday, 2 June 2011).

The article – Nematoda from the terrestrial deep subsurface of South Africa – sheds more light on life in the form of a small worm living under extreme conditions in deep hot mines. It was discovered 1,3 km under the surface of the earth in the Beatrix Goldmine close to Welkom and is the first multi-cellular organism that was found so far beneath the surface of the earth. The worm (nematode) was found in between a rock face that is between 3 000 and 12 000 years old.

The research can shed some new light on the possibility of life on other planets, previously considered impossible under extreme conditions. It also expands the possibilities into new areas where new organisms may be found.

These small invertebrates live in terrestrial soil subjected to stress almost for 24 hours They live through sunshine, rain, scorching temperatures and freezing conditions. Through time they developed a means to cope with harsh conditions. Terrestrial nematodes (roundworms, not to be confused or related to earthworms) are among those very tough small invertebrates that deal with those conditions everywhere. After insects they are the most dominant multi-cellular (metazoan) species on the planet having a general size of 0,5 to 1 mm and are among the oldest metazoans on the planet, Nature says in a statement on the article.

They inhabit nearly every imaginable habitat form the deep seas to the acid in pitcher . Some nematodes simply eat bacteria and these are the ones we study here. Terrestrial nematodes have developed a survival stage that can take them through hard times (absence of food, extreme temperatures, too little oxygen, crowding, and more).

At the head of the research was Prof. Gaetan Borgonie of the Ghent University in Belgium and a world leader in the discipline of nematode research. He was brought into contact with the South African research leader, Prof. Esta van Heerden, who set up a cooperation agreement with the University of Ghent and Prof. Borgonie. Prof. Van Heerden manages the Extreme Biochemistry group at the UFS and the research was funded by several research grants.

The search for worms began in earnest in 2007, but it was soon clear that the sampling strategy was insufficient. A massive sampling campaign in 2008-2009 in several mines led to the discovery of several nematodes and the new nematode species Halicephalobus mephisto. It is named after the legend of Faust where the devil, also known as the lord of the underworld is called Mephistopheles.

Nature says special filters had to be designed and installed on various boreholes. Unfortunately, there is no easy way of finding a magic formula and designs had to be adapted by trial and error; improving existing designs all the time. The work of the UFS Mechanical Workshop, which manufactured, adapted and helped design it, was crucial in this respect. Filters were left on the holes for varying periods, sometimes for a few hours and sometimes for months. Prof. Derek Litthauer from the UFS played a big role in sampling, filter designs and coming up with ideas for names for the new nematode with Prof. Borgonie.

Research showed that the nematodes can live in the deep for up to 12 000 years. Three students – Armand Bester, Mariana Erasmus and Christelle van Rooyen from the UFS – did the work on this.

The importance of multi-cellular animals living in the ultra-deep subsurface is twofold: The nematodes graze on the existing bacterial population and influence their turnover. Secondly, if more complex multi-cellular organisms can survive in the deep subsurface on earth, this may be good news when looking for life on other planets where the surface is considered too inhospitable (e.g. Mars). Complex life forms can be found in ecosystems previously thought to be uninhabitable. Nature says this expands the possibilities into new areas where new organisms may be discovered.

Future research will focus on selective boreholes to look for more metazoans, so that a better idea of the complexity of the ecosystems there can be obtained. It will also look for metazoans in the deep subsurface on other continents to determine similarities and differences.

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