Threshold parameters for epidemics in different community settings.

Threshold parameters of epidemic models play a central role in the assessment of proposed control strategies for infectious diseases. They have been determined for numerous standard epidemic models. This paper points out, with several examples, that threshold parameters depend on the social setting of the community and the variations in the behavior of the members of the community. Specifically, communities are considered in which individuals have fixed patterns of behavior or random patterns of behavior as well as communities of households with fixed or random patterns of behavior. A threshold parameter is computed for each of the different settings. Some comparisons are made to provide insights into the effects that social settings and behavior changes have on the threshold parameters.

[1]  K Dietz,et al.  The basic reproduction ratio for sexually transmitted diseases: I. Theoretical considerations. , 1991, Mathematical biosciences.

[2]  G Scalia-Tomba The effect of structural behavior change on the spread of HIV in a one-sex population. , 1991, Mathematical biosciences.

[3]  N. Ling The Mathematical Theory of Infectious Diseases and its applications , 1978 .

[4]  J. Heesterbeek,et al.  The basic reproduction ratio for sexually transmitted diseases. Part 2. Effects of variable HIV infectivity. , 1993, Mathematical biosciences.

[5]  A. Langworthy,et al.  An influenza simulation model for immunization studies. , 1976, American journal of epidemiology.

[6]  K. Dietz The estimation of the basic reproduction number for infectious diseases , 1993, Statistical methods in medical research.

[7]  O. Diekmann,et al.  On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations , 1990, Journal of mathematical biology.

[8]  Herbert W. Hethcote,et al.  Epidemiological models for heterogeneous populations: proportionate mixing, parameter estimation, and immunization programs , 1987 .

[9]  Denis Mollison,et al.  The Analysis of Infectious Disease Data. , 1989 .

[10]  R. Bartoszynski On a certain model of an epidemic , 1972 .

[11]  L Sattenspiel Epidemics in nonrandomly mixing populations: a simulation. , 1987, American journal of physical anthropology.

[12]  E Ackerman,et al.  Stochastic two-agent epidemic simulation models for a community of families. , 1971, American journal of epidemiology.

[13]  Ian C. Marschner,et al.  The effect of heterogeneity on the spread of disease , 1990 .

[14]  N. Becker,et al.  Estimation for discrete time branching processes with application to epidemics. , 1977, Biometrics.