  We study the SIR epidemiological model, with a variable contagion rate,
applied to the evolution of COVID19 in Cuba. It is highlighted that an increase
in the predictive character depends on understanding the dynamics for the
temporal evolution of the rate of contagion $\beta^*$. A semi-empirical model
for this dynamics is formulated, where reaching $\beta^*\approx0$ due to
isolation is achieved after the mean duration of the disease $\tau=1/\gamma$,
in which the number of infected in the confined families has decreased. It is
considered that $\beta^*(t)$ should have an abrupt decrease on the day of
initiation of confinement and decrease until canceling at the end of the
interval $\tau$. The analysis describes appropriately the infection curve for
Germany. The model is applied to predict an infection curve for Cuba, which
estimates a maximum number of infected as less than 2000 in the middle of May,
depending on the rigor of the isolation. This is suggested by the ratio between
the daily detected cases and the total. We consider the ratio between the
observed and real infected cases (k) less than unity. The low value of k
decreases the maximum obtained when $\beta^*-\gamma>0$. The observed evolution
is independent of k in the linear region. The value of $\beta^*$ is also
studied by time intervals, adjusting to the data of Cuba, Germany and South
Korea. We compare the extrapolation of the evolution of Cuba with the contagion
rate until 16.04.20 with that obtained by a strict quarantine at the end of
April. This model with variable $\beta^*$ correctly describes the observed
infected evolution curves. We emphasize that the desired maximum of the SIR
infected curve is not the maximum standard with constant $\beta^*$, but one
achieved due to quarantine when $\tilde R_0=\beta^*/\gamma<1$. For the
countries controlling the epidemic the maxima are in the region in which SIR
equations are linear.
