  We use the logistic function to estimate the number of individuals infected
by a virus in a period of time as a function of social isolation level in the
previous period of the infection occurrences. Each period is composed by a
fixed date range in days which the social isolation is supposed to take effect
over the virus spread in the next date range. The sample is the COVID-19 cases
and social isolation level data from S\~ao Paulo State, Brazil. The proposed
method is divided into two stages: 1) The logistic function is fitted against
COVID-19 empirical data to obtain the function parameters; 2) the function
parameters, except for the overall growth rate, and the mean of social
isolation level for all periods of time are used to calculate a constant called
$\lambda$. The logistic growth rate for each period of time is calculated using
$\lambda$ and the isolation level for that period. The number of cases in a
period is estimated using the logistic function and the growth rate from
previous period of time to obtain the effect of social isolation during the
elapsed time. The period of time that produces a better correlation between
empirical and estimated data was 5 days. We conclude the method performs a data
estimation with high correlation with the empirical data.
