Study Group Problems

Industry: Attractions (Tourism Sector)

Industry Representative: Dr. Lombuso Precious Shabalala, University of South Africa

Moderators: Dr. Simphiwe Simelane, University of Johannesburg

                       Dr. Matthews Sejeso, University of the Witwatersrand  

Problem Statement:

The Bushbuckridge Nature Reserve (Figure 1) is geographically located in the north of Mpumalanga Province, under Bushbuckridge Local Municipality.  It shares a boundary with Kruger National Park and local communities.  The area is about 7000 hectares, co-managed by the Mpumalanga Tourism and Parks Agency (MTPA) and Communal Property Associations (CPA) through Integrated Management.  Interestingly, it is 100% land claimed by Sisonke CPA (95%) and Injaka Watervaal (5%). 

Figure 1: Bushbuckridge Nature Reserve 
Source:  Bushbuckridge Local Municipality, 2022.

This nature reserve presents an opportunity to restore and conserve the ecosystem because it used to be one of the province's well-operational and well-preserved natural reserves.  Through eco-tourism, the preservation and enhancement of the restored natural wonders could be realised.  Eventually, sustainable benefits will come into life.   Partnerships with local communities that honor their traditions and values, including discussions around human-wildlife conflict, become paramount. Creating employment in restoration and conservation while integrating scientific activities and fully reopening doors to tourists can be considered a significant contributor to the Tourism Sector as part of South Africa's tourism Gross Domestic Production (GDP) from this region.

The Bushbuckridge Nature Reserve aims to be a world-class Nature Reserve that maintains the integrity of its biodiversity through conservation while permitting sustainable utilisation of its natural resources by neighboring communities. In addition, it plans to offer its visitors and future generations a safe and unique nature experience at its best (Bushbuckridge Nature Reserve Management Plan, 2016-2022).   Biodiversity is described by Noss (1990) as the composition, structure, and function inferred at four levels of organisation – regional-landscape, community-ecosystem, population-species, and genetic. Therefore, through management authorities such as Mpumalanga Tourism and Parks Agency (MTPA), South Africa has recognised the importance of biodiversity protection through legislation.   Hence, effective management of declared protected areas must consider biodiversity conservation. 

Areas adjacent to the Reserve have undergone habitat losses, and the size and densities of human settlements have increased in Bushbuckridge (Coetzee et al., 2010). The activities of impoverished communities are seen as a major driver of landscape change. The increases seen in human-impacted vegetation suggest rural settlements depend on adjacent communal lands for cattle grazing, fuelwood, and medicinal plants, amongst other ecosystem services. These further stress the importance of the nature reserve as a conservation area and the need for detailed terrestrial biodiversity data.

In addition, Bushbuckridge Nature Reserve has the potential to contribute to conservation as mandated by the National Biodiversity Act (Act No. 10 of 2004) and the Mpumalanga Nature Conservation (Act No. 10 of 1998), and the Reserve's value as a significant catchment area, its position in the Kruger to Canyons Biosphere Reserve, as an ecological corridor should be viewed as an added advantage. The envisaged activities in the nature reserve will link the Blyde River Canyon Nature Reserve and the Kruger National Park in order to maintain and improve the movement of animals and plants through reserves and potentially improve the resilience of ecosystems to climate change.

On the other hand, as is experienced in other nature reserves, human-wildlife conflict and coexistence are serious challenges. This is not an exception for Bushbuckridge Nature Reserve, which includes livestock of the communities residing in the boundary that enters the Reserve since some of the fence is down. Nyhus (2016) is under the impression that human interactions with wildlife are a defining experience of human existence, although these interactions can be positive or negative. It is understood that naturally, people compete with wildlife for food and resources and have eradicated dangerous species, co-opted and domesticated valuable species, and applied a wide range of social, behavioral, and technical approaches to reduce negative interactions with wildlife (Nyhus, 2016:147).   If such conflicts are not addressed, unfortunately, they eventually lead to the extinction and reduction of numerous species and uncountable human deaths and economic losses.

 The problem to investigate:

• Design or develop a mathematical model to determine what can be done to revive the ecosystem of Bushbuckridge Nature Reserve since there is currently no life or meaningful activity.
• This design should also assist with presenting viable tools for controlling the ecosystem versus human-wildlife conflict.

References

1. Bushbuckridge Local Municipality. Bushbuckridge Nature Reserve Management Plan 2016-2022.
2. Coetzee, M. and Van Averbeke, W., 2010. Poverty, land and food production in South African townships. In: Reforming Land and Resource Use in South Africa, Routledge, pp. 291-309.
3. Mpumalanga Nature Conservation (Act No. 10 of 1998). Available from: https://www.fao.org/faolex/results/details/en/c/LEX-FAOC093357/#:~:text=It%20provides%20for%2C%20among%20other,animals%2C%20freshwater%20pollution%20and%20enforcement.
4. National Environmental Management Biodiversity Act, 2004 (No. 10 of 2004). Available from: https://www.fao.org/faolex/results/details/en/c/LEX-FAOC045083/#:~:text=An%20Act%20to%20provide%20for,the%20fair%20and%20equitable%20sharing.
5. Nyhus, P.J., 2016. Human–wildlife conflict and coexistence. Annual review of environment and resources, 41(1), pp.143-171.

Supporting material

Presentation

Report-back presentation

Industry: Global Health

Industry Representatives:

Professor Gideon Ngwa, Applied Mathematical and Computer Assisted Modelling Unit, Department of Mathematics, University of Buea, Cameroon

Professor Calistus Ngonghala, Department of Mathematics, University of Florida, USA

Moderator:

足球竞彩app排名 Moderator:

Problem Statement

Mosquito-borne diseases continue to be a major global health challenge, causing millions of cases and hundreds of thousands of deaths annually, primarily in sub-Saharan Africa. Beyond its health toll, mosquito-borne diseases result in significant economic losses, estimated in the billions of dollars annually due to treatment costs, lost productivity, and prevention efforts. 

Mosquito-borne diseases are transmitted to humans through the bite of female mosquitoes infected with pathogens in their quest for blood that is required for reproduction. Mosquitoes exhibit distinct biting behaviour that supports their role in disease transmission. After emerging from breeding sites, adult female mosquitoes swarm near these sites to mate. Once mated, they begin questing for blood by seeking out non-human vertebrates and human habitats, where they use environmental cues like body heat, carbon dioxide, and scent to locate hosts. If a mosquito's initial attempt to blood feed (on a human) is unsuccessful. it may continue to search and make multiple attempts until it acquires blood. This might result in the mosquito being killed. After a successful blood meal, mosquitoes that fed on human blood will typically rest in or near human habitats to digest the meal and allow the development of eggs. Once the eggs are ready, the mosquito returns to a breeding site to lay them, completing the reproductive cycle. This behaviour allows mosquitoes to effectively transmit diseases like mosquito-borne disease between humans.

Insecticide-treated nets (ITNs) are a key intervention for mosquito-borne disease control, effectively reducing mosquito bites, mosquito-borne disease transmission, and infection rates. They work by providing a physical barrier that keeps mosquitoes away from humans while they sleep and by killing or repelling mosquitoes through the insecticide-treated fabric. ITNs also lower local mosquito populations, offering a community-wide protective effect for both net users and non-users. However, ITNs can impact immunity development. Repeated exposure to pathogens (such as {\it Plasmodium} parasites that cause malaria) typically builds immunity, especially in endemic areas. By reducing infection rates, ITNs may limit this immunity build-up, potentially leaving individuals more susceptible to severe mosquito-borne disease in the future when exposure resumes.

This project aims to explore how widespread ITN use impacts long-term mosquito-borne discase transmission and immunity development. using a mathematical model to assess the trade-off between ITNs and immunity build-up. It will also investigate how complementary interventions, like vaccines. can mitigate this trade-off and improve mosquito-borne disease control strategics, ultimately seeking an optimal balance that enhances long-term effectiveness while reducing vulnerability from over-reliance on nets. In the case of malaria disease in humans. immunity is sustained by continuing exposure, so that sustained use of ITNs will cut down exposure to malaria transmission and at the same time curtail the immunity build-up.

Research Question. How do widespread ITN interventions impact long-term mosquito-borne disease transmission dynamics and immunity development, and what role can complementary interventions, like vaccines, play in mitigating the trade-offs between reduced exposure and immunity build-up?

References

[1] Ngwa G A. On the population dynamics of the malaria vector, Bulletin of Mathematical Biology, 68(2006) pp 2161-2189.

[2] Ngwa G A, Wankah T T, Fomboh-Nforba M Y, Ngonghala C N, Teboh-Ewungkem M I. On a reproductive stage-structured model for the population dynamics of the malaria vector, Bulletin of Mathematical Biology, 76 (2014) pp 2476-2516.

[3] Ngonghala C N, Del Valle S Y, Zhao R, Mohammed-Awel J. Quantifying the impact of decay in bednet efficacy on malaria transmission, Journal of Theoretical Biology, 363 (2014) pp 247-261.

[4] Ngonghala C N, Mohammed-Awel J, Zhao R, Prosper O. Interplay between insecticide-treated bed-netsand mosquito demography: implications for malaria control, Journal of Theoretical Biology, 397 (2017) pp 179-192.

[5] Ngwa G A, Teboh-Ewungkem M I, Dumont Y, Quifki R, Banasiak J. On a three-stage structured modelfor the dynamics of malaria transmission with human treatment, adult vector demographics and oneaquatic stage, Journal of Theoretical Biology, 481 (2019) pp 202-222.

[6] Ghakanyuy B M, Teboh-Ewungkem M I, Schneider K A, Ngw G A. Investigating the impact of multiplefeeding attempts on mosquito dynamics via mathematical models, Mathematical Biosciences,350 (2022) 108832.

[7] Ngwa G A, Teboh-Ewungkem M I, Njongwe J A. Continuous-time predator-prey-like systems used toinvestigate the question: Can human consciousness help eliminate temporary mosquito breeding sites fromaround human habitats?, Mathematics and Computers in Simulation, 206 (2023) pp 437 469.

[8] Keegan L T, Dushoff J, Population-level effects of clinical immunity to malaria. BMC infectious diseases,13 (2013) pp 1-11.

[9] Aron J L. Dynamics of acquired immunity boosted by exposure to infection, Mathematical Biosciences, 64(1983) pp 249-259.

[10] Fowkes F, McGready R, Cross N, Hommel M, Simpson J, Elliott S, Richards J, Lackovic K,Viladpai- Nguen J, Narum D, Tsuboi D, Anders R, Nosten F, Beeson J. New insights into acquisition,boosting, and longevity of immunity to malaria in pregnant women, The Journal of Infectious Diseases,206 (2012) 1612-21.

[11] Langhorne J, Ndungu F M, Sponaas A-M, Marsh K. Immunity to malaria: more questions thananswers, Nature Immunology, 9 (2008) pp 725-732. 

Supporting Material  

First-day Presentation

Report-back Presentation

Industry:

Sugar Cane Processing

Industrial Representative:

Richard Loubser, Sugar Milling Research Institute NPC,

c/o University of KwaZulu-Natal, Durban.

Moderator:

足球竞彩app排名 Moderator:

Problem Statement:

The production of sugar from sugar cane involves several steps:

• Preparation – the sugar cane is shredded into small pieces
• Extraction – the sugar (and other dissolved solids) is washed out of the shredded cane in a diffuser
• Evaporation – the extracted juice is thickened using evaporators
• Boiling – vacuum pans are used to evaporate more water and produce sugar crystals
• Centrifuging – the crystals are separated from the mother liquor giving raw sugar and molasses

The mixture of sugar and molasses (massecuite) enters at the hub of the basket of the centrifuge. The centrifuge rotates continuously at about 2000 rev per min. The basket is conical in shape so the massecuite migrates up the basket towards the rim. At the same time, the molasses separates and passes through the screen. The ideal situation is when the sugar arrives at the rim of the basket free of molasses. Water is mixed with the massecuite as it enters the centrifuge to facilitate separation of the molasses. The degree of separation has a positive relationship to the amount of water added.

The Sugar Milling Research Institute NPC (SMRI) has been developing a camera-based system to control the quantity of water added to a sugar centrifuge Loubser et al (2024). The system consists of a camera mounted on top of a centrifuge focussed on the centrifuge screen. A triggered light emitting diode (LED) stroboscope arrangement is used to freeze the frames so that the flow on the screen can be observed. The intention is to use image analysis to assess the quality of the sugar and hence generate a control action.

 A typical frame is shown in the figure below. The massecuite can be seen as a dark band as it enters the basket at the hub basket. It migrates up the screen until clean sugar remains or it passes over the rim of the centrifuge. Depending on the nature of the feed, it will form finger-like patterns on the screen surface. If too many of these fingers reach the rim, too much non-sugar is reprocessed. If, however, the sugar is too clean, this could indicate an excess of added water and possible dissolving and loss of the sugar to molasses.

In the trials, the image was analysed using a threshold technique to binarise the image. The image was then reduced to a control value by determining the number of ‘white’ pixels in a rectangle adjacent to the rim of the basket (excluding the washwater pipe). The added water was successfully adjusted using a proportional control loop approach to give a consistent sugar quality despite disturbances, in the form of varying throughput, that were introduced.

The performance of the system is dependent on the quality and uniformity of the lighting and the threshold setting. Poor lighting in the extremities of the image can lead to false detection of massecuite. Otsu thresholding was explored as an option but was abandoned when it could not distinguish between completely dark and completely light images. It would be a great advantage if a technique, or recipe, could be identified that is immune to the lighting conditions.

Numerous images with sugar analyses are available for testing any proposed algorithm.

References

Supporting Material

First-day Presentation

Report-back Presentation

Industry: Conservation, Tourism, and Sustainability

Industry Representative: Mr Mukhtaar Waja, University of the Witwatersrand, Ms Thea Juanita Earnest, University of the Witwatersrand

Moderators:

足球竞彩app排名 Moderators:

Problem Statement:

Climate change poses a major threat to the survival of the African penguin population – which has already been classified as Critically Endangered – as it may adversely impact the species’ access to food, potentially disrupting the African penguin’s breeding patterns, while also exposing African penguins to dangerous levels of heat stress, and habitat degradation. 

Climate change is inducing changes in sea temperatures, ocean currents, and upwelling, resulting in changes to the timing of the movement of sardines and anchovies, which are the African penguin’s primary source of food. The annual sardine run – which occurs along the coast of South Africa between May and July – is a crucial feeding event for African penguins, which rely on the sardine run to satisfy their energy requirements during the breeding season, when adult penguins must feed their offspring and themselves. Research suggests that the sardine run is occurring at a later period with each passing year, due to warming ocean temperatures. African penguins may thus struggle to synchronise their feeding and breeding patterns with the changing timing of the sardine run, resulting in a species mismatch. Increasing ocean temperatures and acidification may also lead to a decline in fish stocks which African penguins rely on as a food source, potentially forcing African penguins to have to travel greater distances to locate sufficient food during critical periods. 

Rising ocean and air temperatures caused by climate change will likely place the African penguin at risk of experiencing prolonged heat stress. While African penguins can survive in relatively warm, temperate coastal climates, they are still vulnerable to extreme heat, which has the potential to overwhelm their thermoregulatory mechanisms, potentially resulting in reduced survival rates and lower reproductive success. African penguins’ eggs are especially vulnerable to temperature fluctuations, and an increase in the frequency and intensity of heat waves may severely compromise the ability of adult penguins to maintain suitable conditions for their eggs and offspring. 

Lastly, climate change may threaten the African penguin’s habitat, due to an increase in the intensity and frequency of extreme weather events. Tropical cyclones and intense storms may result in the flooding of breeding colonies and nesting sites, and the destabilisation of penguin colonies, forcing African penguins to relocate to areas with suboptimal conditions.

The problem to Investigate:

Model a projection of the year at which the African penguin species will likely face a significant threat to its survival, potentially leading to its extinction.

References:

Sherley, R.B., Crawford, R.J., de Blocq, A.D., Dyer, B.M., Geldenhuys, D., Hagen, C., Kemper, J., Makhado, A.B., Pichegru, L., Tom, D. and Upfold, L., 2020. The conservation status and population decline of the African penguin deconstructed in space and time. Ecology and Evolution, 10(15), 8506-8516. 
(Download PDF: Sherley et al. 2020. The conservation status and population decline of the African Penguin)

Sherley, R.B., Underhill, L.G., Barham, B.J., Barham, P.J., Coetzee, J.C., Crawford, R.J., Dyer, B.M., Leshoro, T.M. and Upfold, L., 2013. Influence of local and regional prey availability on breeding performance of African penguins Spheniscus demersus. Marine Ecology Progress Series, 473, 291-301.
(Download PDF: Sherley et al. 2013. Influence of local and regional prey availability)

Welman, S., Green, J.A., Ryan, P.G., Parsons, N.J. and Pichegru, L., 2024. Body temperature and thermoregulatory behaviour in the Endangered African Penguin Spheniscus demersus. Bird Conservation International, 34, 1-8.
(Download PDF: Welman et al. 2024. Body temperature and thermoregulatory behaviour)

Supporting Material

First-Day Presentation

Report-back Presentation

Industry: Drinking Water Treatment Plant

Industry Representatives:

 Dr Alba Cabrera Codony, University of Girona, Spain

Professor Tim Myers, Centre de Recerca Matematica, Barcelona, Spain

Moderator:

足球竞彩app排名 Moderator

Problem Statement

1. INTRODUCTION

Waterborne diseases are a significant global challenge and the provision of safe drinking water is a fundamental public health requirement. Disinfection plays a crucial role in water treatment processes by eliminating pathogenic microorganisms that can cause severe illness. Due to their proven efficacy, ease of application, and relatively low cost Chlorine-based disinfectants, such as sodium hypochlorite (NaClO) and chlorine dioxide (ClO?), are among the most widely used methods for ensuring microbial safety in drinking water systems. They are capable of inactivating a broad range of microorganisms, including bacteria, viruses, and protozoa. However, despite their extensive use, chlorine-based disinfectants face increasing scrutiny due to challenges including the increased microbial resistance, and the formation of potentially harmful disinfection by-products (DBPs) due to the reaction with dissolved organic matter.

The reaction between chlorine and organic matter not only reduces the concentration of free chlorine available for microbial inactivation but also leads to the production of potentially toxic compounds. As regulatory standards for DBPs continue to tighten, there is a growing need for disinfection methods that can achieve effective microbial control while minimizing the risk of DBP formation. This is particularly important in reclaimed or recycled water systems, where organic matter concentrations may be higher, increasing the likelihood of DBP formation during chlorine treatment.

To address these limitations, ultraviolet (UV) radiation has been explored as a complementary disinfection method. UV-C light disrupts microbial DNA by causing the formation of thymine dimers, which block replication and transcription, ultimately leading to cell death. The combination of UV radiation with chlorine-based disinfectants presents a promising strategy for improving disinfection efficacy. Additionally, the use of UV light may allow for lower chlorine dosages while maintaining or even improving disinfection performance, potentially reducing the formation of DBPs.

2. MODELLING

Current mathematical models for the process are very basic. In the absence of irradiation a standard model is that of Chick-Watson

where N is the number of bacteria, C₀ the initial chlorine concentration and k_c a rate constant. This may be integrated under the assumption of constant C₀ and then k_a determined through fitting to data. However this clearly neglects the decrease in chlorine concentration. To arrive at better results the time dependence is often changed to t^m, providing another fitting parameter (and naturally a better fit to data). This choice is arbitrary.

In fact the literature is littered with arbitrary unjustified extensions, a common example s replacing

where C_c is the concentration where the chlorine kills the bacteria.

In reality the decrease will depend on the time-dependent chlorine concentration, which then requires a second equation tracking the chlorine. Subsequently we must consider the effect of irradiation. As a starting point we will apply the Beer-Lambert law, which states that the intensity decreases exponentially with depth,

 This will add a further term to the rate equations, where the bacteria die due to irradiation and chlorine. It also introduces also the possibility of space dependence.

Advances may then be possible through a sequence of modifications, starting from time-dependent population type models to later include spatial variation. 

Questions:

1. Can we obtain a better model for the basic process? Specifically including chlorine decay into the kinetics. Can we justify current, apparently arbitrary, models?
2. Can we extend the model to include irradiation effects? Once this model is obtained can we adjust conditions to improve efficiency?
3. Can we provide a simple method to determine unknown rate constants?

Results will be verified against experimental data to be provided at the MISG.

References:

Supporting Material

First-day Presentation

Report-back Presentation