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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

Profiling of small businesses discussed
2010-06-03

From the left are: Mr Christoff van der Merwe, businessman from Pretoria, Ms Jackie Ntshingila, Provincial Manager of SEDA in the Free State, Prof. Tienie Crous, Dean: Faculty of Economic and Management Sciences at the UFS, Mr Barry Chang from Mijona International in Bloemfontein and Mr Hendrik van der Merwe, businessman from Pretoria.
Photo: Stephen Collett


“We need some kind of innovation to help small businesses in the Free State grow to their full potential.” These were the words of Ms Jackie Ntshingila, Provincial Manager of the Small Enterprise Development Agency (SEDA) in the Free State at a breakfast presented by the Faculty of Economic and Management Sciences of the University of the Free State (UFS) in Bloemfontein.

The faculty and SEDA presented the breakfast after identifying the need to profile small business development agencies and to get the role-players in the province together to discuss the development of small business enterprises.

“It is important that we start to profile small agencies in the province and a university is a good neutral ground to start an initiative like this,” said Prof. Tienie Crous, Dean of the Faculty of Economic and Management Sciences at the UFS.

“Small business development agencies are working in silos, there are fragmented reporting lines, a duplication of services and the service is rotated among the same group of small, medium and micro enterprises,” said Ms Ntshingila.

“Students do not see themselves as job creators and entrepreneurs are not contributing optimally to the gross domestic product of the province. Job creation opportunities are also not efficiently reported and there is a competitive approach amongst different business associations,” she said.

Ms Ntshingila proposed a couple solutions: “Establish an electronic database, do government reporting through a systems or database administrator and make a presentation to government for adequate funding for these projects,” she said.

At the breakfast it was proposed that the small business development agencies will now be identified and follow-up meetings will be arranged by the faculty and SEDA.


Media Release
Issued by: Lacea Loader
Assistant Director: Media Liaison
Tel: 051 401 2584
Cell: 083 645 2454
E-mail: loaderl.stg@ufs.ac.za  
2 June 2010

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