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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

Is milk really so well-known, asks UFS’s Prof. Osthoff
2011-03-17

Prof. Garry Osthoff
Photo: Stephen Collett

Prof. Garry Osthoff opened a whole new world of milk to the audience in his inaugural lecture, Milk: the well-known (?) food, in our Department of Microbial, Biochemical and Food Biotechnology of the Faculty of Natural and Agricultural Sciences.

Prof. Osthoff has done his research in protein chemistry, immuno-chemistry and enzymology at the Council for Scientific and Industrial Research (CSIR) in Pretoria and post-doctoral research at the Bowman-Grey School of Medicine, North Carolina, USA. That was instrumental in establishing food chemistry at the university.
 
He is involved in chemical aspects of food, with a focus on dairy science and technology. He is also involved in the research of cheese processing as well as milk evolution and concentrated on milk evolution in his lecture. Knowledge of milk from dairy animals alone does not provide all the explanations of milk as food.
 
Some aspects he highlighted in his lecture were that milk is the first food to be utilised by young mammals and that it is custom-designed for each species. “However, mankind is an opportunist and has found ways of easy access to food by the practice of agriculture, where plants as well as animals were employed or rather exploited,” he said.
 
The cow is the best-known milk producer, but environmental conditions forced man to select other animals. In spite of breeding selection, cattle seem not to have adapted to the most extreme conditions such as high altitudes with sub-freezing temperatures, deserts and marshes.
 
Prof. Osthoff said the consumption of the milk as an adult is not natural; neither is the consumption of milk across species. This practice of mankind may often have consequences, when signs of malnutrition or diseases are noticed. Two common problems are an allergy to milk and lactose intolerance.
 
Allergies are normally the result of an immune response of the consumer to the foreign proteins found in the milk. In some cases it might help to switch from one milk source to another, such as switching from cow’s milk to goat’s milk.
 
Prof. Osthoff said lactose intolerance – the inability of adult humans to digest lactose, the milk sugar – is natural, as adults lose that ability to digest lactose. The symptoms of the condition are stomach cramps and diarrhoea. This problem is mainly found in the warmer climates of the world. This could be an indication of early passive development of dairy technology. In these regions milk could not be stored in its fresh form, but in a fermented form, in which case the lactose was pre-digested by micro-organisms, and the human population never adapted to digesting lactose in adulthood.
 
According to Prof. Osthoff, it is basically the lactose in milk that has spurred dairy technology. Its fermentation has resulted in the development of yoghurts and all the cheeses that we know. In turn, the intolerance to lactose has spurred a further technological solution: lactose-free milk is currently produced by pre-digestion of lactose with enzymes.
 
It was realised that the milks and products from different species differed in quality aspects such as keeping properties and taste. It was also realised that the nutritional properties differed as well as their effects on health. One example is the mentioned allergy against cow’s milk proteins, which may be solved by the consumption of goat’s milk. The nutritional benefits and technological processing of milk aroused an interest in more information, and it was realised that the information gained from human milk and that of the few domesticated species do not provide a complete explanation of the properties of milk as food. Of the 250 species of milk which have been studied, only the milk of humans and a few domesticated dairy animals has been studied in detail.

Media Release
15 March 2011
Issued by: Lacea Loader
Director: Strategic Communication
Tel: 051 401 2584
Cell: 083 645 2454
E-mail: news@ufs.ac.za

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