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 São 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. The logistic growth rate for each period of time is calculated using the constant 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.