The qualitative analysis of the impact of media delay on the control of infectious disease

TL;DR

This paper analyzes how media delay impacts infectious disease control using a delayed epidemic model, establishing stability conditions and demonstrating how media parameters influence disease spread with H1N1 data.

Contribution

It introduces a delayed SISM epidemic model incorporating media awareness and provides stability analysis and bifurcation conditions, linking media parameters to disease control.

Findings

Shortening media lag reduces disease spread

Increasing media transmission rate enhances control

Media efforts significantly impact epidemic dynamics

Abstract

In this paper, we consider the impact of time delay by media on the control of the disease. We set up a class of SISM epidemic model with the time delay and the cumulative density of awareness caused by media. The sufficient condition of global asymptotic stability of disease-free equilibrium is approved. We get the global stability of the epidemic equilibrium and the existence conditions of Hopf bifurcation. Numerical simulations are presented to illustrate the analytical results. Finally, we analyze the influence of parameters on the control of infectious disease by combining the data of H1N1. By shortening the time of media lag, increasing transmission rate of media and the implementation rate of the media project, the spread of disease will be controlled effectively.