Global threshold dynamics of an SVIR model with age-dependent infection and relapse

ABSTRACT

A susceptible-vaccinated-infectious-recovered epidemic model with infection age and relapse age has been formulated. We first address the asymptotic smoothness of the solution semiflow, existence of a global attractor, and uniform persistence of the model. Then by constructing suitable Volterra-type Lyapunov functionals, we establish a global threshold dynamics of the model, which is determined by the basic reproduction number. Biologically, it is confirmed that neglecting the possibility of vaccinees getting infected will over-estimate the effect of vaccination strategies. The obtained results generalize some existing ones.

KEYWORDS:

• SVIR model
• basic reproduction number
• global stability
• infection age
• relapse age

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

J. Wang was supported by the National Natural Science Foundation of China [Nos. 11401182, 11471089], Science and Technology Innovation Team in Higher Education Institutions of Heilongjiang Province [No. 2014TD005]. Y. Chen was supported partially by the Natural Sciences and Engineering Research Council (NSERC) of Canada.