Threshold conditions for infection persistence in complex host-vectors interactions.

2002 
Abstract As classically defined by Macdonald in the early 1950s, for the case of diseases with one vector and one host, the Basic Reproduction Number, R 0 , is defined as the number of secondary infections caused by a single infective of the same type (vector or host) during its infectiousness period in an entirely susceptible population. In the case of a disease which has one vector and one host, it is easy to show that R 0 coincides with the threshold for the establishment of an endemic state: if R 0 >1 , the disease can invade (cannot invade) the host population. In this paper we examine various epidemic situations in which there are more than one vector and/or host. We show that in those more complex systems it is not possible to deduce a single R 0 but rather a threshold for infection persistence which is a composite of several quantities closely related to the classical expression of R 0 . Another definition of R 0 given by Diekmann, Heesterbeek and Metz, and denoted in this paper R NGO 0 is discussed and applied as an alternative to calculate the thresholds for infection establishment.
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