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Prof Abdon Atangana develops new concept to test Ebola waves

05 September 2022 | Story Andrè Damons | Photo Andrè Damons

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

Fight against Ebola virus requires more research

2014-10-22

Dr Abdon Atangana
Photo: Ifa Tshishonge

Dr Abdon Atangana, a postdoctoral researcher in the Institute for Groundwater Studies at the University of the Free State (UFS), wrote an article related to the Ebola virus: Modelling the Ebola haemorrhagic fever with the beta-derivative: Deathly infection disease in West African countries.

“The filoviruses belong to a virus family named filoviridae. This virus can cause unembellished haemorrhagic fever in humans and nonhuman monkeys. In literature, only two members of this virus family have been mentioned, namely the Marburg virus and the Ebola virus. However, so far only five species of the Ebola virus have been identified, including: Ivory Coast, Sudan, Zaire, Reston and Bundibugyo.

“Among these families, the Ebola virus is the only member of the Zaire Ebola virus species and also the most dangerous, being responsible for the largest number of outbreaks.

“Ebola is an unusual, but fatal virus that causes bleeding inside and outside the body. As the virus spreads through the body, it damages the immune system and organs. Ultimately, it causes the blood-clotting levels in cells to drop. This leads to severe, uncontrollable bleeding.

Since all physical problems can be modelled via mathematical equation, Dr Atangana aimed in his research (the paper was published in BioMed Research International with impact factor 2.701) to analyse the spread of this deadly disease using mathematical equations. We shall propose a model underpinning the spread of this disease in a given Sub-Saharan African country,” he said.

The mathematical equations are used to predict the future behaviour of the disease, especially the spread of the disease among the targeted population. These mathematical equations are called differential equation and are only using the concept of rate of change over time.

However, there is several definitions for derivative, and the choice of the derivative used for such a model is very important, because the more accurate the model, the better results will be obtained. The classical derivative describes the change of rate, but it is an approximation of the real velocity of the object under study. The beta derivative is the modification of the classical derivative that takes into account the time scale and also has a new parameter that can be considered as the fractional order.

“I have used the beta derivative to model the spread of the fatal disease called Ebola, which has killed many people in the West African countries, including Nigeria, Sierra Leone, Guinea and Liberia, since December 2013,” he said.

The constructed mathematical equations were called Atangana’s Beta Ebola System of Equations (ABESE). “We did the investigation of the stable endemic points and presented the Eigen-Values using the Jacobian method. The homotopy decomposition method was used to solve the resulted system of equations. The convergence of the method was presented and some numerical simulations were done for different values of beta.

“The simulations showed that our model is more realistic for all betas less than 0.5. The model revealed that, if there were no recovery precaution for a given population in a West African country, the entire population of that country would all die in a very short period of time, even if the total number of the infected population is very small. In simple terms, the prediction revealed a fast spread of the virus among the targeted population. These results can be used to educate and inform people about the rapid spread of the deadly disease,” he said.

The spread of Ebola among people only occurs through direct contact with the blood or body fluids of a person after symptoms have developed. Body fluid that may contain the Ebola virus includes saliva, mucus, vomit, faeces, sweat, tears, breast milk, urine and semen. Entry points include the nose, mouth, eyes, open wounds, cuts and abrasions. Note should be taken that contact with objects contaminated by the virus, particularly needles and syringes, may also transmit the infection.

“Based on the predictions in this paper, we are calling on more research regarding this disease; in particular, we are calling on researchers to pay attention to finding an efficient cure or more effective prevention, to reduce the risk of contamination,” Dr Atangana said.

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