  With the prevalence of COVID-19, the modeling of epidemic propagation and its
analyses have played a significant role in controlling epidemics. However,
individual behaviors, in particular the self-protection and migration, which
have a strong influence on epidemic propagation, were always neglected in
previous studies. In this paper, we mainly propose two models from the
individual and population perspectives. In the first individual model, we
introduce the individual protection degree that effectively suppresses the
epidemic level as a stochastic variable to the SIRS model. In the alternative
population model, an open Markov queueing network is constructed to investigate
the individual number of each epidemic state, and we present an evolving
population network via the migration of people. Besides, stochastic methods are
applied to analyze both models. In various simulations, the infected
probability, the number of individuals in each state and its limited
distribution are demonstrated.
