Dynamics Analysis of an 11-Dimensional Multiscale COVID-19 Model with Interval Parameters

Abstract

This paper investigates an 11-dimensional slow–fast system of multiscale COVID-19 model with interval parameters. For the slow subsystem, the local dynamics of disease-free equilibrium (DFE) and endemic equilibrium (EE) are studied by using the fast–slow theory. Two criteria of the existence of forward and backward bifurcations are further obtained. When the basic reproduction number [Formula: see text] is less than unity, we show that bistabilities of DFE and EE for [Formula: see text] can be caused by backward bifurcation. Thus, controlling [Formula: see text] below critical value [Formula: see text] is effective to eliminate endemic diseases. Meanwhile, the slow subsystem undergoes saddle-node bifurcation at [Formula: see text] and undergoes pitchfork bifurcation at [Formula: see text] for EE. Moreover, the stability and bifurcation of the multiscale full system are established. As an application, the numerical simulations of real data of COVID-19 in Hong Kong are used to verify these results, which show that increasing vaccination rate, improving vaccine effectiveness and decreasing the fraction of individuals in risky state 2 are necessary to control the COVID-19.