Epidemiology and Infection

A clarification of transmission terms in host-microparasite models: numbers, densities and areas

M.  BEGON  a1 c1, M.  BENNETT  a2, R. G.  BOWERS  a3, N. P.  FRENCH  a2, S. M.  HAZEL  a2 and J.  TURNER  a2
a1 Centre for Comparative Infectious Diseases and Population and Evolutionary Biology Research Group, School of Biological Sciences, The University of Liverpool, Liverpool, UK
a2 Faculty of Veterinary Science, The University of Liverpool, Liverpool, UK
a3 Department of Mathematical Sciences, The University of Liverpool, Liverpool, UK


Transmission is the driving force in the dynamics of any infectious disease. A crucial element in understanding disease dynamics, therefore, is the ‘transmission term’ describing the rate at which susceptible hosts are ‘converted’ into infected hosts by their contact with infectious material. Recently, the conventional form of this term has been increasingly questioned, and new terminologies and conventions have been proposed. Here, therefore, we review the derivation of transmission terms, explain the basis of confusion, and provide clarification. The root of the problem has been a failure to include explicit consideration of the area occupied by a host population, alongside both the number of infectious hosts and their density within the population. We argue that the terms ‘density-dependent transmission’ and ‘frequency-dependent transmission’ remain valid and useful (though a ‘fuller’ transmission term for the former is identified), but that the terms ‘mass action’, ‘true mass action’ and ‘pseudo mass action’ are all unhelpful and should be dropped. Also, contrary to what has often been assumed, the distinction between homogeneous and heterogeneous mixing in a host population is orthogonal to the distinction between density- and frequency-dependent transmission modes.

(Accepted March 7 2002)

c1 Author for correspondence: School of Biological Sciences, Nicholson Building, The University of Liverpool, Liverpool L69 3GS, UK.