  Stellar evolution calculations were carried out from the main sequence to the
final AGB stage of stars with initial masses from 1 to $2M_\odot$ and
metallicity $Z=0.01$. Selected models of evolutionary sequences were used as
initial conditions for solution of the equations of radiation hydrodynamics and
time-dependent convection describing radial stellar pulsations. The study was
aimed to construct the hydrodynamic models of Mira-type stars that show the
secular decrease in the pulsation period commenced in 1970--th at $\Pi=315$
day. We show that such a condition for the period change is satisfied with
evolutionary sequences from 1 to $1.2M_\odot$ and the best agreement with
observations is obtained for models with initial mass $1.2M_\odot$. The
pulsation period reduction is due to both the stellar radius decrease during
the thermal pulse of the helium burning shell and mode switch from the
fundamental mode to the first overtone. Theoretical estimates of the
fundamental parameters of the star at the onset of pulsation period reduction
are as follows: the mass is $M=0.93M_\odot$, the luminosity is $L =
4080L_\odot$, and the radius is $R=220R_\odot$. The mode switch occurs 35 years
after the onset of period reduction.
