SA Graduate Modelling Camp Problems

Presenters:

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

Problem Statement

Mosquito-borne diseases remain a critical global health challenge, causing over a million cases and hundreds of thousands of deaths annually, particularly in sub-Saharan Africa. These diseases impose significant economic costs, with billions of dollars lost each year due to treatment, prevention, and productivity losses. Mosquito-borne diseases are transmitted through the bite of female mosquitoes, which acquire the pathogen from an infected human and then pass it on to others. These mosquitoes exhibit specific behaviours, including questing for blood by seeking out human habitats, and resting in or near these habitats after feeding to digest the blood and develop eggs. Mosquitoes often return to breeding sites to lay their eggs, completing the reproductive or gonotrophic cycle. This behaviour allows mosquitoes to effectively transmit diseases like mosquito-borne disease between humans.

Insecticide-treated nets (ITNs) are a cornerstone of mosquito-borne disease control, acting as both a physical barrier and a means to kill or repel mosquitoes through the insecticide coating. By reducing mosquito bites and lowering mosquito populations, ITNs significantly reduce mosquito-borne disease transmission. Additionally, breeding site removal, which targets mosquito habitats, further decreases mosquito numbers and transmission potential. Together, these interventions are crucial in reducing mosquito-borne disease's burden.

The goal of this project is to develop and apply a mathematical model to understand the combined impact of ITNs and breeding site removal on long-term Mosquito-borne disease control. The model will aim to identify the minimum intervention level needed to achieve a decline in mosquito populations, specifically targeting breeding site, questing, and resting mosquitoes.

Research Question. What is the minimum level of combined ITN use and breeding site removal required to achieve a sustainable reduction in mosquito populations and long-term mosquito-borne disease control?

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 repro-ductive stage-structured model for the population dynamics of the malaria vector, Bulletin of Mathema-tical 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 bed-net 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 (2016)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.

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Presenter: Professor Neville Fowkes, School of Mathematics and Applied Mathematics, University of Western Australia

 Problem Statement

 Penguins need sardines and other sea food  to survive,  and fishermen need sardines `to live'.  They compete (unfairly).  The South African Little Penguin is critically endangered. Governments   can  regulate   the fishermen’s  catch in various ways  and penguins just do what they naturally do.  

• Explore the possible outcomes if various regulations are introduced.
• Check out available information about the African Penguin in this context.
• One way of improving the outcome is to exclude fishing in regions near penguin colonies. How much area should be `reserved' to ensure survival?

This problem relates to the MISG penguin problem which is concerned with the effect of climate change on the survivability of the penguin. The penguin population is critically endangered even without climate change with many  factors playing a role (predators, tourists, oil spill,...), however sardine biomass is thought to be the most critical factor. I  am  not  an expert and there has been much work on the problem so  we all will need to inform ourselves.

 For a start we might extend/modify  the standard predator/prey model to deal with   two competing (sardine)   predators. This may enable us to understand what  parameter combinations are important. 

足球竞彩app排名s should be able to handle ODE solution methods analytically and numerically using  any of the available packages.   We will introduce students to predator/prey and species competition modelling if necessary.

References

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Presenter:

Professor Graeme Hocking, School  of Mathematics and Statistics, Murdoch University, Perth, Australia.

Problem Statement

Th onset of the effects of climate change have motivated the development of wind farms throughout the world. Many of these are in the sea and now many more are being built on land.  The design of wind turbines is to be optimised so that they generate the maximum amount of energy in the most efficient manner.  Barotrauma is damage caused to organs by variations in pressure.

In planning for a wind farm, the developers must consider the environmental impact of their construction and the ongoing effect on the environment and seek approval from the appropriate Government Authorities. There is a lot of evidence now that these wind turbines can have a significant impact on birds through possible collisions with the blades and this has been the focus of many studies.  However, there are other environmental factors that have not been studied, one of which is the impact of the wind turbines on bats.

There is evidence that although it is unlikely that bats fly high enough to be struck by the turbines, there do appear to be many casualties due to their co-location.  It is theorised that this may be due to the low pressure developed by the so-called wing-tip vortices that are shed from the downstream edge of the turbine blades.  The blades of the turbine are aerodynamic objects much like aircraft wings and are designed to generate sideways lift causing the rotor to spin most effectively.  Bats have weak lungs and if they are “struck” by a low pressure region from the blades of the turbine, it is possible that their lung tissue may rupture.

In this project, you would consider the basics of wind turbine blade design and the aerodynamics associated with this in order to examine the flow of air over the blades and how that can form into a vortex sheet that rolls into a spiral.   This spiral can create a very low pressure patch that may impact on bats.  There are some general theories for these aerodynamic features that do not rely on complex simulations and so these should be considered.  If time permits, design of the turbine blades to minimise the intensity of the “wing-tip” vortices might be considered.

References

Supporting Material

First-day Presentation

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