Dynamics of vaccination in a time-delayed epidemic model with awareness

TL;DR

This paper models how awareness and vaccination, including delays and waning immunity, influence infectious disease dynamics, revealing conditions for stability and oscillations through analytical and numerical methods.

Contribution

It introduces a time-delayed epidemic model incorporating awareness, vaccination, and waning immunity, providing new insights into disease control strategies.

Findings

Conditions for disease-free equilibrium stability

Identification of Hopf bifurcation points

Impact of delays on oscillatory dynamics

Abstract

This paper investigates the effects of vaccination on the dynamics of infectious disease, which is spreading in a population concurrently with awareness. The model considers contributions to the overall awareness from a global information campaign, direct contacts between unaware and aware individuals, and reported cases of infection. It is assumed that there is some time delay between individuals becoming aware and modifying their behaviour. Vaccination is administered to newborns, as well as to aware individuals, and it is further assumed that vaccine-induced immunity may wane with time. Feasibility and stability of the disease-free and endemic equilibria are studied analytically, and conditions for the Hopf bifurcation of the endemic steady state are found in terms of system parameters and the time delay. Analytical results are supported by numerical continuation of the Hopf bifurcation and numerical simulations of the model to illustrate different types of dynamical behaviour.