Modelling pandemics of quarantine pests and diseases: problems and perspectives

Abstract

To develop a general framework for a mathematical theory of pandemics, known facts about pandemics of plant diseases are reconsidered. A pandemic is thought to consist of three parts called zero-order, first-order and second-order epidemics. The zero-order epidemic is the spread of a disease within the boundaries of a single crop field; it includes the establishment of an initial focus and of daughter foci. The first-order epidemic is the spread of a disease over an area with many fields during a single growing season of the host crop. The second-order epidemic is the spread of a disease over a large area during consecutive growing seasons of the host crop. The mathematical description of a second-order epidemic is supposed to lead to a travelling wave solution, the wave travelling at its highest and constant speed during the middle part of the second-order epidemic. Selected empirical evidence supports this hypothesis. Whereas the zero-order and first-order epidemics can be described as continuous processes, the second-order epidemic cannot because of crop seasonality. Comparisons are drawn between botanical and medical epidemiology. The approach taken is deterministic; stochasticity of epidemiological processes is disregarded in this paper.