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Abstract
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 R0, 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



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1998-1999 Mathematics in Biology

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