A STOCHASTIC MULTI-SCALE COVID-19 MODEL WITH INTERVAL PARAMETERS

A stochastic multi-scale COVID-19 model that coupling within-host and between-host dynamics with interval parameters is established. The model is composed of a within-host fast model and a between-host slow stochastic model. The dynamics of fast model can be governed by basic reproduction number R-0w. The uninfected equilibrium E-0w is globally asymptotically stable (g.a.s) when R-0w < 1, but infected equilibrium E-fast(& lowast;) is g.a.s when R-0w > 1. The dynamics of the coupling slow stochastic model can be governed by stochastic threshold R-s. The disease will die out when R-s < 1 and will persistent in mean when R-s > 1. One finds that R-s is an increasing function of R0w. Further, some numerical simulations are presented to demonstrate the results and reveal that the dynamics of the slow stochastic model are approximate to the stochastic multi-scale model. It provides us a method to investigate the stochastic multi-scale model. Furthermore, some effective measures are given to control the COVID-19. Moreover, our work contributes basic understandings of coupling within-host and between-host models with interval parameters and environmental noises.