SVLIAR age-of-infection and -immunity structured epidemic model of COVID-19 dynamics

Abstract

Stability analysis of nonlinear age-of-infection and -immunity structured SVLIAR-type model of susceptible, vaccinated, latent, COVID-19 infected, asymptomatic and recovered sub-classes of population dynamics is carried out in this paper. The SVLIAR model uses five age variables - age of vaccine immunity of vaccinated individuals, age of virus infection in organism during incubation period of latent individuals, “age” of infectious disease treatment of infected individuals, age of asymptomatic infectious dis-ease of asymptomatic individuals, “age” of immunity of organism after recovering of recovered individuals. Individuals can move from one subclass to another when these age variables take some fixed values, that is the processes in sub-classes are adjusted and synchronized by age variables. The conditions for the existence of disease-free and unique endemic equilibria and their local asymptotic stability were obtained. The local asymptotic stability/instability of endemic equilibrium of SVLIAR model is defined by criterion, which relates the demographic characteristics of population, infection disease characteristics (disease-induced death rate, death rate induced by the complications after disease), characteristics of vaccination (fraction of fully vaccinated susceptibles per unit of time, vaccination efficacy) and characteristics of age variables (their maximum values) of sub-classes. These theoretical results help understand better the conditions of transmission dynamics of the COVID-19 induced disease.