Free-living Naegleria fowleri amoebae cause primary amoebic meningoencephalitis (PAM). Because of the apparent conflict between their ubiquity and the rarity of cases observed, we sought to develop a model characterizing the risk of PAM after swimming as a function of the concentration of N. fowleri. The probability of death from PAM as a function of the number of amoebae inhaled is modeled according to results obtained from animals infected with amoeba strains. The calculation of the probability of inhaling one or more amoebae while swimming is based on a double hypothesis: that the distribution of amoebae in the water follows a Poisson distribution and that the mean quantity of water inhaled while swimming is 10 ml. The risk of PAM for a given concentration of amoebae is then obtained by summing the following products: the probability of inhaling n amoebae × the probability of PAM associated with inhaling these n amoebae. We chose the lognormal model to assess the risk of PAM because it yielded the best analysis of the studentized residuals. Nonetheless, the levels of risk thereby obtained cannot be applied to humans without correction, because they are substantially greater than those indicated by available epidemiologic data. The curve was thus adjusted by a factor calculated with the least-squares method. This provides the PAM risk in humans as a function of the N. fowleri concentration in the river. For example, the risk is 8.5 × 10⁸ at a concentration of 10 N. fowleri amoebae per liter.