Mathematical models for the spread of invading plant organisms typically utilize population growth and dispersal dynamics to predict the time-evolution of a population distribution. In this paper, we revisit a particular class of deterministic contact models obtained from a stochastic birth process for invasive organisms. These models were introduced by Mollison (J R Stat Soc 39(3):283, 1977). We derive the deterministic integro-differential equation of a more general contact model and show that the quantity of interest may be interpreted not as population size, but rather as the probability of species occurrence. We proceed to show how landscape heterogeneity can be included in the model by utilizing the concept of statistical habitat suitability models which condense diverse ecological data into a single statistic. As ecologists often deal with species presence data rather than population size, we argue that a model for probability of occurrence allows for a realistic determination of initial conditions from data. Finally, we present numerical results of our deterministic model and compare them to simulations of the underlying stochastic process.