Multiscale malaria models and their uniform in-time asymptotic analysis

TL;DR

This paper extends classical asymptotic methods to multiscale malaria models, providing uniform in-time approximations and higher-order corrections that enhance understanding of disease dynamics over large timescales.

Contribution

It introduces a novel application of Tikhonov--Fenichel and Chapman-Enskog procedures to malaria models, offering uniform asymptotic approximations and higher-order corrections.

Findings

Derived a simplified model approximating the original multiscale system.

Constructed a higher-order approximation equivalent to the first-order slow manifold.

Proved the uniform validity of the asymptotic approximations over large times.

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.