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

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.

A time-delayed SVEIR model for imperfect vaccine with a generalized nonmonotone incidence and application to measles

“…One of the most effective means of disease control and prevention is vaccination [1] . They played a major role in the eradication of many infectious diseases completely, such as smallpox, or partially, like measles [2] . Many authors in the literature have studied the dynamics of epidemics models with different types of vaccination schedules [3] , [4] , [5] , [6] , [7] .…”

“…In [19] , a disease transmission model with two delays in incubation and asymptomatic carriage periods is investigated. In addition, many authors studied time delayed epidemic models with vaccination [2] , [25] , [26] , [27] . For example, the authors in [2] study a vaccination model with a time delay to represent the time that an unaware susceptible individual takes to become aware of the infection.…”

Threshold dynamics of a time-delayed epidemic model for continuous imperfect-vaccine with a generalized nonmonotone incidence rate

“…In [7], the authors studied a time-delayed SIR model with nonlinear incidence rate and Holling functional type II treatment rate for epidemic transmission. Also, many authors studied time-delayed epidemic models with vaccination [8][9][10][11]. For example, the authors in [9] study a vaccination model with a time delay to represent the time that an unaware susceptible individual takes to become aware of the infection.…”

“…Also, many authors studied time-delayed epidemic models with vaccination [8][9][10][11]. For example, the authors in [9] study a vaccination model with a time delay to represent the time that an unaware susceptible individual takes to become aware of the infection. Due to the inherent complexity of epidemiological transmission, other works studied epidemic complex network models.…”

Mathematical Modeling of Listeriosis Incorporating Effects of Awareness Programs

“…Sensitivity analysis of their model also reveals that, the outbreak severity is more sensitive to the weight α 1 than weight α 2 . Further, mathematical models with time delay were used in [15][16][17], to investigate the effects of awareness programs on dynamics of infectious diseases.…”