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Effects of heterogeneity in hosts and pathogens on effectiveness of vaccination Mirjam Kretzschmar RIVM, Department of Infectious Diseases Epidemiology The Netherlands Populations are heterogeneous ... Why do we have to think about heterogeneity?
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RIVM, Department of Infectious Diseases Epidemiology
Measles outbreak (almost 3000 cases) despite coverage of 96%
number: order of diagnosis
0 index case
A.S. Klovdahl. Social networks and the spread of infectious diseases:
The AIDS example. Soc. Sci. Med. 21 (1985): 1203-1216.
People are not the same and they choose contacts with certain preferences
these choices influence the way infectious diseases spread
Equalizing strategy: Choose individuals for
vaccination sequentially from those households with largest number of susceptibles.
Minimizes the number of vaccinations needed to reduce R to below 1.
Ball, Mollison & Scalia-Tomba.Ann. Appl. Prob. 7 (1997) 46.
The expected number of secondary cases caused by one index case during his entire infectious period in a completely susceptible population.
homogeneous population: R0=cD
heterogeneous population: number of secondary cases has to be averaged in the right way.
Diekmann, Heesterbeek, Metz. J. Math. Biol. 1990; 28:365-382
Diekmann, Heesterbeek. Mathematical Epidemiology of Infectious Diseases, Wiley, 2000.
Next generation operator
Number of cases in the (n+1)-th generation of infections given the distribution of infectious individuals (with respect to population structure) in the n-th generation.
Basic reproduction number
Dominant eigenvalue of the next-generation operator
Explicit calculation of R0 for separable mixing
Contact funtion c(a,b)=f(a)g(b)
immuneModel structureWilliams et al. (1996), Epidemiol & Infect. 116: 71-89Kretzschmar et al. (2002) Epidemiol & Infect. 128: 229-244.
Individuals can be infected via two routes.
R0 is the dominant eigenvalue of next generation matrix
s sexual transmission
v vertical transmission
i transmission probability per partnership
PC(,a) has factor p(a), the probability of becoming carrier
when infected at age a
Edmunds et al. 1993:
Point estimate of parameters 1 and 2 from data
from 29 different studies
() fertility rate at age
bi transmission probabilities per offspring
R0 = 1.29
endemic prevalence, together they can
A.R. McLean. Proc R Soc Lond B (1995) 261: 389-393.
recovery + death
M. Lipsitch. Emerging Infectious Diseases (1999) 5: 336-345