Abstract
Vaccine-induced protection is substantial to control, prevent, and reduce the spread of infectious diseases and to get rid of infectious diseases. In this paper, we propose an SVEIR epidemic model with age-dependent vaccination, latency, and infection. The model also considers that the waning vaccine-induced immunity depends on vaccination age and the vaccinated individuals fall back to the susceptible class after losing immunity. The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. The global dynamics of the model is established through construction of appropriate Lyapunov functionals and application of Lasalle’s invariance principle. As a result, the global stability of the infection-free equilibrium and endemic equilibrium is obtained and is fully determined by the basic reproduction number R0.
Highlights
Protection induced by vaccines plays a significant role in preventing and reducing the transmission of infectious diseases
Motivated by [14, 20], we propose a new SVEIR epidemic model originated from an existing SVEIR formulated in [1], by considering continuous age-structure in latency and infection in addition to age-dependence vaccination and vaccine-age-dependence waning vaccine-induced immunity
We suppose that there exists an endemic equilibrium for system (4) denoted by E∗ = (S∗, V∗, e∗, i∗, R∗)
Summary
Protection induced by vaccines plays a significant role in preventing and reducing the transmission of infectious diseases. In [1] a multigroup SVEIR epidemic model with latent class and vaccination age was formulated to study global stability of equilibria, after assuming that vaccine-induced immunity decays with time after vaccination and likewise in [17,18,19]. To the best of our knowledge, the global dynamics of an SVEIR epidemic model with continuous age-structure in latency, infection, vaccination, and vaccine-age-dependence waning vaccineinduced immunity has not yet been neither considered nor investigated using the approach of Lyapunov functionals. Motivated by [14, 20], we propose a new SVEIR epidemic model originated from an existing SVEIR formulated in [1], by considering continuous age-structure in latency and infection in addition to age-dependence vaccination and vaccine-age-dependence waning vaccine-induced immunity (which the authors took into account in [1]).
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