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Abstract

Reflections on Epidemic Models

Reflections on Epidemic Models

**Odo Diekmann **

Mathematics Department

Utrecht University

diekmann@math.uu.nl

A key ingredient for the spread (in time and space) of an
infectious disease is the contact process, on which transmission
is superimposed. In this lecture we review various assumptions
that have been made concerning the influence of population size
and structure on contact intensity. Next we discuss some of
the known implications for various indicators of infectiousness
at the population level, such as R_{0}, r, the probability
of a minor outbreak, the size of a major outbreak and the asymptotic
speed of propagation. The ultimate goal is to deduce relevant
characteristics of epidemic spread from a statistical description
of the spatio-temporal contact patterns. As the lecture will
stress, there is still a long way to go to achieve this goal!

References:

O.Diekmann, M.C.M. de Jong, A.A. de Koeijer, P. Reijnders, The force of infection in populations of varying size:a modelling problem, J. Biol. Syst. 3 (1995) 519-529

O.Diekmann, A.A. de Koeijer, J.A.J. Metz, On the final size of epidemics within herds, Can. Appl. Math. Quart. 4 (1996) 21-30

O.Diekmann, Reflections on models for epidemics triggered
by the case of Phocine Distemper Virus among seals,

In : Case Studies in Mathematical Modelling in Biology, - Ecology,Physiology,and
Cell Biology (H.G.Othmer, F.R.Adler, M.A.Lewis & J.C. Dallon,
eds; Prentice Hall; 1997) 51-59.

A.de Koeijer, O.Diekmann, P.Reijnders, Modelling the spread of Phocine Distemper Virus (PDV) among Harbour seals, Bull.Math.Biol. 60 (1998) 585-596 O.Diekmann, M.C.M. de Jong, J.A.J. Metz, A deterministic epidemic model taking account of repeated contacts between the same individuals, J.Appl.Prob. 35 (1998) 448-462

O.Diekmann, J.A.P. Heesterbeek (in preparation)

Mathematical Epidemiology of Infectious Diseases : Model Building, Analysis and Interpretation, Wiley Series in Mathematical and Computational Biology