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.

Supporting Material

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