Conventional malaria surveys based on the microscopic examination of blood do not always detect chronic, low-grade infections caused by immunity. A model incorporating differences in detectability within the host population shows how the false negative tests caused by poor detectability confound measures of prevalence and the rates of infection and recovery. The model can also use multiple surveys on one group of individuals to estimate roughly the true prevalence. The form of data required is the number of times parasites are detected for each person; simply noting the cumulative proportion of individuals who show positive tests, as often reported in the literature, yields little information. Improved estimation of epidemiological variables awaits additional work on how best to analyse chronic malarial infection.