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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

Inaugural lecture: Prof. Phillipe Burger
2007-11-26

 

Attending the lecture were, from the left: Prof. Tienie Crous (Dean of the Faculty of Economic and Management Sciences at the UFS), Prof. Phillipe Burger (Departmental Chairperson of the Department of Economics at the UFS), and Prof. Frederick Fourie (Rector and Vice-Chancellor of the UFS).
Photo: Stephen Collet

 
A summary of an inaugural lecture presented by Prof. Phillipe Burger on the topic: “The ups and downs of the South African Economy: Rough seas or smooth sailing?”

South African business cycle shows reduction in volatility

Better monetary policy and improvements in the financial sector that place less liquidity constraints on individuals is one of the main reasons for the reduction in the volatility of the South African economy. The improvement in access to the financial sector also enables individuals to manage their debt better.

These are some of the findings in an analysis on the volatility of the South African business cycle done by Prof. Philippe Burger, Departmental Chairperson of the University of the Free State’s (UFS) Department of Economics.

Prof. Burger delivered his inaugural lecture last night (22 November 2007) on the Main Campus in Bloemfontein on the topic “The ups and downs of the South African Economy: Rough seas or smooth sailing?”

In his lecture, Prof. Burger emphasised a few key aspects of the South African business cycle and indicated how it changed during the periods 1960-1976, 1976-1994 en 1994-2006.

With the Gross Domestic Product (GDP) as an indicator of the business cycle, the analysis identified the variables that showed the highest correlation with the GDP. During the periods 1976-1994 and 1994-2006, these included durable consumption, manufacturing investment, private sector investment, as well as investment in machinery and non-residential buildings. Other variables that also show a high correlation with the GDP are imports, non-durable consumption, investment in the financial services sector, investment by general government, as well as investment in residential buildings.

Prof. Burger’s analysis also shows that changes in durable consumption, investment in the manufacturing sector, investment in the private sector, as well as investment in non-residential buildings preceded changes in the GDP. If changes in a variable such as durable consumption precede changes in the GDP, it is an indication that durable consumption is one of the drivers of the business cycle. The up or down swing of durable consumption may, in other words, just as well contribute to an up or down swing in the business cycle.

A surprising finding of the analysis is the particularly strong role durable consumption has played in the business cycle since 1994. This finding is especially surprising due to the fact that durable consumption only constitutes about 12% of the total household consumption.

A further surprising finding is the particularly small role exports have been playing since 1960 as a driver of the business cycle. In South Africa it is still generally accepted that exports are one of the most important drivers of the business cycle. It is generally accepted that, should the business cycles of South Africa’s most important trade partners show an upward phase; these partners will purchase more from South Africa. This increase in exports will contribute to the South African economy moving upward. Prof. Burger’s analyses shows, however, that exports have generally never fulfil this role.

Over and above the identification of the drivers of the South African business cycle, Prof. Burger’s analysis also investigated the volatility of the business cycle.

When the periods 1976-1994 and 1994-2006 are compared, the analysis shows that the volatility of the business cycle has reduced since 1994 with more than half. The reduction in volatility can be traced to the reduction in the volatility of household consumption (especially durables and services), as well as a reduction in the volatility of investment in machinery, non-residential buildings and transport equipment. The last three coincide with the general reduction in the volatility of investment in the manufacturing sector. Investment in sectors such as electricity and transport (not to be confused with investment in transport equipment by various sectors) which are strongly dominated by the government, did not contribute to the decrease in volatility.

In his analysis, Prof. Burger supplies reasons for the reduction in volatility. One of the explanations is the reduction in the shocks affecting the economy – especially in the South African context. Another explanation is the application of an improved monetary policy by the South African Reserve Bank since the mid 1990’s. A third explanation is the better access to liquidity and credit since the mid 1990’s, which enables the better management of household finance and the absorption of financial shocks.

A further reason which contributed to the reduction in volatility in countries such as the United States of America’s business cycle is better inventory management. While the volatility of inventory in South Africa has also reduced there is, according to Prof. Burger, little proof that better inventory management contributed to the reduction in volatility of the GDP.

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