Dependence of epidemic and population velocities on basic parameters
This paper describes the use of linear deterministic models for examining the spread of population processes, discussing their advantages and limitations. Their main advantages are that their assumptions are relatively transparent and that they are easy to analyze, yet they generally give the same velocity as more complex linear stochastic and nonlinear deterministic models. Their simplicity, especially if we use the elegant reproduction and dispersal kernel formulation of \textit{O. Diekmann} [J. Math. Biol. 6, 109-130 (1978; Zbl 0415.92020)] and \textit{F. van den Bosch}, \textit{J. A. J. Metz} and \textit{O. Diekmann} [ibid. 28, 529- 565 (1990; Zbl 0732.92026)], allows us greater freedom to choose a biologically realistic model and greatly facilitates examination of the dependence of conclusions on model components and of how these are incorporated into the model and fitted from data. This is illustrated by consideration of a range of examples, including both diffusion and dispersal models and by discussion of their application to both epidemic and population dynamic problems.
scientific article; zbMATH DE number 33889