Multiscale Analysis for a Vector-Borne Epidemic Model

TL;DR

This paper explores a multiscale approach to a vector-borne epidemic model, deriving simplified models for fast host or vector dynamics and validating these with numerical and rigorous proofs.

Contribution

It introduces a multiscale analysis framework for vector-borne disease models, deriving reduced models based on intrinsic time-scale differences and providing rigorous validation.

Findings

Fast host dynamics lead to a simplified SIR model with rational incidence rate

Fast vector dynamics result in an SI model for vectors with hosts disappearing

Numerical and rigorous proofs confirm the accuracy of the reduced models

Abstract

Traditional studies about disease dynamics have focused on global stability issues, due to their epidemiological importance. We study a classical SIR-SI model for arboviruses in two different directions: we begin by describing an alternative proof of previously known global stability results by using only a Lyapunov approach. In the sequel, we take a different view and we argue that vectors and hosts can have very distinctive intrinsic time-scales, and that such distinctiveness extends to the disease dynamics. Under these hypothesis, we show that two asymptotic regimes naturally appear: the fast host dynamics and the fast vector dynamics. The former regime yields, at leading order, a SIR model for the hosts, but with a rational incidence rate. In this case, the vector disappears from the model, and the dynamics is similar to a directly contagious disease. The latter yields a SI model for the vectors, with the hosts disappearing from the model. Numerical results show the performance of the approximation, and a rigorous proof validates the reduced models.