Global Attractivity of a Nonlocal Delayed Diffusive Dengue Model in a Spatially Homogeneous Environment

TL;DR

This paper proves that a nonlocal delayed diffusive dengue model's disease-free state is globally attractive when the basic reproduction number exceeds one, using Lyapunov functionals to strengthen previous results.

Contribution

It introduces a Lyapunov functional approach to establish global attractivity without the previous threshold condition on , improving the understanding of disease stability in the model.

Findings

Global attractivity when  > 1

Elimination of the previous sufficient condition

Enhanced stability analysis of the dengue model

Abstract

In Xu and Zhao (2015), the global attractivity of positive constant steady state is established through the application of the fluctuation method, subject to the sufficient condition that the disease will stabilized at the unique spatially-homogeneous steady state if $\Re_0>1$ exceeds a certain threshold. The focus of this study is to eliminate the need for a sufficient condition by employing a suitable Lyapunov functional and prove that the positive constant steady state is globally attractive when $\Re_0$ is exactly greater than unity, which significantly enhancing the findings outlined in Theorem 3.3 of Xu and Zhao (2015).