Multiscale malaria models and their uniform in-time asymptotic analysis

Jacek Banasiak; Stephane Tchoumi

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arXiv · 2309.15935

Multiscale malaria models and their uniform in-time asymptotic analysis

Jacek Banasiak·Stephane Tchoumi

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Abstract

In this paper, we show that an extension of the classical Tikhonov--Fenichel asymptotic procedure applied to multiscale models of vector-borne diseases, with time scales determined by the dynamics of human and vector populations, yields a simplified model approximating the original one in a consistent, and uniform for large times, way. Furthermore, we construct a higher-order approximation based on the classical Chapman-Enskog procedure of kinetic theory and show, in particular, that it is equivalent to the dynamics on the first-order approximation of the slow manifold in the Fenichel theory.

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Jacek Banasiak, Stephane Tchoumi. 2023-09-27. Multiscale malaria models and their uniform in-time asymptotic analysis. https://arxiv.org/abs/2309.15935

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