Although anti-severe acute respiratory syndrome-coronavirus 2 antibody kinetics have been described in large populations of vaccinated individuals, we still poorly understand how they evolve during a natural infection and how this impacts viral clearance. For that purpose, we analyzed the kinetics of both viral load and neutralizing antibody levels in a prospective cohort of individuals during acute infection with alpha variant. Using a mathematical model, we show that the progressive increase in neutralizing antibodies leads to a shortening of the half-life of both infected cells and infectious viral particles. We estimated that the neutralizing activity reached 90% of its maximal level within 11 days after symptom onset and could reduce the half-life of both infected cells and circulating virus by a 6-fold factor, thus playing a key role to achieve rapid viral clearance. Using this model, we conducted a simulation study to predict in a more general context the protection conferred by pre-existing neutralization titers, due to either vaccination or prior infection. We predicted that a neutralizing activity, as measured by 50% effective dose > 103 , could reduce by 46% the risk of having viral load detectable by standard polymerase chain reaction assays and by 98% the risk of having viral load above the threshold of infectiousness. Our model shows that neutralizing activity could be used to define correlates of protection against infection and transmission.