  We consider the SEIRS compartment epidemiology model suitable for predicting
the evolution of the COVID-19 pandemy in the extreme limiting case of no
acquired immunity. The disease-free and endemic fixed points are found and
their stability is analysed. The expression for the basic reproduction ratio is
obtained and discussed, emphasizing on its dependence on the model parameters.
The threshold contact ratio is found which determines the possibility for a
stable disease-free fixed point existence. Numeric solution for the pandemy
evolution is also undertaken together with the approximate analytic solutions
for the early stage of the disease spread as well as as for its decay after the
rapid measures are undertaken. We analysed several possible scenarios for
introducing and relaxing the quarantine measures. The cyclic "quarantine on"
and "quarantine off" strategy at fixed identification and isolation ratios fail
to reduce the lowering of the second and the consecutive waves, whereas this
goal is possible to achieve if the flexible increase of the identification and
isolation ratios is also involved.
