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Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
The type-reproduction number T in models for infectious disease control
J A P Heesterbeek1, M G Roberts
1Faculty of Veterinary Medicine, University of Utrecht, Yalelaan 7, 3584 CL, Utrecht, The Netherlands. j.a.p.heesterbeek@vet.uu.nl
Abstract:
A ubiquitous quantity in epidemic modelling is the basic reproduction number R(0). This became so popular in the 1990s that 'All you need know is R(0)!' became a familiar catch-phrase. The value of R(0) defines, among other things, the control effort needed to eliminate the infection from a homogeneous host population, but can be misleading when applied to a heterogeneous population for the same purpose. We have defined the type-reproduction number T for an infectious disease, and shown that this not only has the required threshold behaviour, but also correctly determines the critical control effort for heterogeneous populations. The two quantities coincide for homogeneous populations. In this paper we further develop the new threshold quantity as an indicator of control effort required in a system where multiple types of individuals are recognised when control targets a specific type.
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