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?.
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)
susceptible transmission routes
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