Monitoring a population for a disease requires the hosts to be sampled and tested for the pathogen. This results in sampling series from which we may estimate the disease incidence, i.e. the proportion of hosts infected. Existing estimation methods assume that disease incidence does not change between monitoring rounds, resulting in an underestimation of the disease incidence. In this paper, we develop an incidence estimation model accounting for epidemic growth with monitoring rounds that sample varying incidence. We also show how to accommodate the asymptomatic period that is the characteristic of most diseases. For practical use, we produce an approximation of the model, which is subsequently shown to be accurate for relevant epidemic and sampling parameters. Both the approximation and the full model are applied to stochastic spatial simulations of epidemics. The results prove their consistency for a very wide range of situations. The estimation model is made available as an online application. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’. This theme issue is linked with the earlier issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’.