On an impulsive faecal-oral model in a periodically evolving environment

TL;DR

This paper models the spread of faecal-oral diseases considering impulsive interventions and regional evolution, providing theoretical analysis and numerical simulations to inform disease control strategies.

Contribution

It introduces a novel impulsive faecal-oral model in a periodically evolving environment, analyzing eigenvalues and threshold behaviors related to disease spread.

Findings

Large impulsive intervention intensity aids disease control.

Small regional evolution rate helps prevent disease spread.

Theoretical results are confirmed by numerical simulations.

Abstract

To understand how impulsive intervention and regional evolution jointly influence the spread of faecal-oral diseases, this paper develops an impulsive faecal-oral model in a periodically evolving environment. The well-posedness of the model is first checked. Then, the existence of the principal eigenvalue dependent on impulse intensity and evolving rate is proved based on Krein-Rutman theorem. With the help of this value, the threshold dynamical behaviours of the model are explored. More importantly, this paper also derives the monotonicity of the principal eigenvalue with respect to initial region and impulse intensity and estimates the principal eigenvalue in some special cases. Finally, numerical simulations are used to verify the correctness of the theoretical results and to explore the impact of regional evolution rate on the spread of the diseases. Our research shows that large impulsive intensity $1-g'(0)$ and small evolving rate $\rho(t)$ play a positive role in the prevention and control of the diseases.