| Abstract: | Theoretical and practical purposes of mathematical modelling are discussed. Of these, special attention is given to large scale simulation models and regression models. It is pointed out that, for proper use of simulation models for predictive purposes, it is necessary to realize the uncertainties associated with such model predictions. These uncertainties are mainly due to insufficient knowledge of parameter values included in the simulation model. As these model predictions are made iteratively (i.e. by short time steps), biases in parameter estimates have, with increasing length of simulated time, an accumulating effect on the biases in the output variables. Regression models are described and methods for finding the best mathematical model are discussed. Assumptions regarding statistical properties of the data from which the regression model is constructed are discussed. It is pointe out that valid predictions are made only within the domain defined by the data Examples of regression models for forecasting rodent outbreaks are discussed. Some further developments are proposed. Results from a model emphasizing spatio-temporal heterogeneity in a heterogeneous region are discussed. Based on this model conclusions regarding what type of landscapes are likely to cause rodent outbreaks are deduced. Furthermore, proposed control treatments are suggested by analyzing the model. It is concluded that larger regions should be composed of suitable and non-suitable rodent habitats interminded with each other. It is suggested that treatments for increasing the local extinction rate be applied uniformly over the whole region, but varyjng in time as much as possible and not correlated with the density in local habitats nor in the entire region. Within these limits, treatments should be applied during periods of low mobility and low reproduction. |
