Conditional herd immunity threshold in the southern cone

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Resumo: The main question we try to answer is: "When we begin to see the effect of the large vaccination program in certain country?" In epidemiological terms it consists in finding the Herd Immunity Threshold - HIT, i.e. the protected proportion of population needed to revert the increasing of contagious. One one side, this HIT depends (within other factors) on social contacts (measured by social mobility) and main circulating variants (with different contagiousness capabilities). On the other, it depends on the proportion of fully vaccinated population, including the type of vaccine, and natural immunizations. To determine when the HIT is achieved, a predictor based on social mobility is produced. The demographic structure of the country is also included in the computation. A statistical descriptive approach is applied, describing the evolution of the main quantities involved. Data from the countries of the southern cone are included in the study (Argentina, Brasil, Chile, Paraguay and Uruguay). For the sake of reference, similar computations are carried out in the case of Israel and Italy. Our main finding is the estimate a HIT with a corresponding confidence interval, and the determination of a date when this HIT is achieved for each of the countries. Due to large uncertainty in different involved quantities, the intervals are excessively large. Nevertheless, all intervals share the common sub-interval (39-5\%,39+5\%), that constitutes the main finding of the paper.