  Since the beginning of the COVID-19 spreading, the number of studies on the
epidemic models increased dramatically. It is important for policymakers to
know how the disease will spread and what are the effects of the policies and
environment on the spreading. In this paper, we propose two extensions to the
standard SIR model: (a) we consider the prevention measures adopted based on
the current severity of the infection. Those measures are adaptive and change
over time; (b) multiple cities and regions are considered, with population
movements between those cities and regions, while taking into account that each
region may have different prevention measures. Although the adaptive measures
and mobility of the population were often observed during the pandemic, these
effects are rarely explicitly modeled and studied in the classical epidemic
models. The model we propose gives rise to a plateau phenomenon: the number of
people infected by the disease stays at the same level during an extended
period of time. We show what are conditions need to be met in order for the
spreading to exhibit a plateau period in a single city. In addition, this
phenomenon is interdependent when considering multiple cities. We verify from
the real-world data that the plateau phenomenon does exist in many regions of
the world in the current COVID-19 development. Finally, we provide theoretical
analysis on the plateau phenomenon for the single-city model and derive a
series of results on the emergence and the ending of the plateau, as well as on
the height and length of the plateau. Our theoretical results match well with
our experimental findings.
