Models in the epidemiology of air-borne viruses of Poaceae

A model is a simplified representation of a real (physical, biological, etc.. .) system. A mathematical model is an equation (or a set of equations) containing variables, meant to be analogous to physical entities, related to each other by mathematical expressions including parameters. In plant virology, as in many other fields, mathematical models are used mainly for two purposes, i.e. to develop predictive tools and control strategies, and to elucidate mechanisms of biological responses by description and simulation; the two aims are often representative also of two (extreme) approaches to model-building: empirical functions statistically correlating variables and analytic models deriving from the mathematical formalization of knowledge about a system. Mathematical models of the two types, plus the variants in between, including simulators of various origin, have been used for analysing, describing, simulating, forecasting, and managing epidemics caused by air-borne viruses. Vector-borne viruses are traditionally classified as: 1) non-persistently transmitted (non-persistent viruses), 2) semi-persistently transmitted, and 3) persistently transmitted, either circulative or replicative. From the point of view of the relationshipswith their vectors, the non-persistent viruses are characterised by: the short time needed for both acquisition and inoculation (seconds to minutes), the relatively short time of retention of infectivity (hours), the lack of a latent time (i.e. the time between the end of the acquisition and the beginning of infectivity), and the loss of infectivity with the vector moult. The semi-persistent viruses need longer times of both acquisition and inoculation (minutes to hours), retain infectivity for longer times (days), do not have a latency. The persistent viruses, both circulating and multiplying in the vector, have a measurable latent time in the vector, retain infectivity for days or for the life of the vector, and through the moult. In this chapter models used for air-borne viruses of Poaceae are reviewed, divided for convenience in the classical modes of transmission: non-persistent, semi-persistent, and persistent, both circulative and replicative, with mathematical details given in the Appendices.