An SVIQR model with vaccination-age, general nonlinear incidence rate and relapse: Dynamics and simulations

This work is concerned with the global dynamics of a Susceptible-Vaccinated-Infected-Isolated-Recovered model, denoted by SVIQR, with vaccination-age. Moreover, the considered model contains a relapse term and a general form of the incidence function. This model is formulated to show the effect of sanitary isolation and vaccination on the disease prevalence when the relapse phenomena occurs. First, we show that the model is mathematically well posed by using the integrated semigroup theory. Second, we prove the existence of equilibrium points based on the basic reproduction number Script capital R-0(omega,xi). Moreover, by developing appropriate Lyapunov functionals and applying the LaSalles invariance principle, we established the global dynamics of the model, especially, we show that if Script capital R-0(omega,xi) <= 1 the the disease-free equilibrium is globally asymptotically stable and, if Script capital R-0(omega,xi) > 1 the endemic equilibrium is globally asymptotically stable. Finally, using the finite difference method, numerical simulations are made to reinforce the theoretical findings and to prove the contribution of the vaccination and the isolation on the disease disappearing.