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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. [ABSTRACT FROM AUTHOR]

In 1960, Science published a paper by Heinz von Foerster predicting that on Friday, 13 November 2026, the “human population will approach infinity if it grows as it has grown in the last two millennia.” Just a few years after this preposterous doomsday alarm, the annual growth of global population peaked at about 2.1 percent and immediately began to decline. By 2020 the growth rate stood at just a bit more than 1 percent, the result of the steadily declining total fertility rate (TFR), the number of children born to a woman during her reproductive period. [ABSTRACT FROM AUTHOR]