Prof. Jacek Banasiak, University of Pretoria

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Title: Life cycle of mosquitoes and malaria – a journey through asymptotic analysis and monotone systems
Authors: J. Banasiak, S. Y. Tchoumi and M. Bime Ghakanyuy, University of Pretoria

Abstract:

Due to the presence of populations with widely different vital rates, such as mosquitoes and humans, malaria dynamics offers rewarding examples of multiscale models represented by regularly and singularly perturbed systems of differential equations [3,5,6]. Recent improvements in their analysis [1,2] allow for significantly simplifying such models without losing salient features and their original long-term dynamics. Moreover, in many cases, the application of the singular perturbation theory leads to simplified models that are monotone and thus allow for an even more comprehensive analysis. We illustrate the theoretical results with concrete models describing the spreading of malaria [3] and the gonotrophic cycle of mosquitoes [4,7].

Literature
[1] F.C. Hoppensteadt, Singular perturbations on the infinite interval, Trans. Amer. Math. Soc. 123 (1966) 521–535.
[2] J. Banasiak, A note on the Tikhonov theorem on an infinite interval, Vietnam J. Math. 49 (2021), no. 1, 69–86.
[3] J. Banasiak, S.Y. Tchoumi, Multiscale malaria models and their uniform in-time asymptotic analysis, Mathematics and Computers in Simulation, 221 (2024), 1 – 18.
[4] G.A. Ngwa, M.I. Teboh-Ewungkem, Y. Dumont, R. Ouifki, J. Banasiak, On a three-stage structured model for the dynamics of malaria transmission with human treatment, adult vector demographics and one aquatic stage, J. Theoret. Biol. 481 (2019) 202–222.
[5] P. Rashkov, B.W. Kooi, Complexity of host-vector dynamics in a two-strain dengue model, J. Biol. Dyn. 15 (1) (2021) 35–72.
[6] P. Rashkov, E. Venturino, M. Aguiar, N. Stollenwerk, B.W. Kooi, On the role of vector modeling in a minimalistic epidemic model, Math. Biosci. Eng. 16 (5) (2019) 4314–4338.
[7] J. Banasiak, G. Ngwa, M. Bime, The Impact of Mating on Modeling Mosquito Dynamics: A Mathematical Investigation, in preparation.