Reproduction numbers for epidemic models with households and other social structures II: Comparisons and implications for vaccination.
Math Biosci
; 274: 108-39, 2016 Apr.
Article
in En
| MEDLINE
| ID: mdl-26845663
ABSTRACT
In this paper we consider epidemic models of directly transmissible SIR (susceptible â infective â recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting either of households or of households and workplaces. We review most reproduction numbers defined in the literature for these models, including the basic reproduction number R0 introduced in the companion paper of this, for which we provide a simpler, more elegant derivation. Extending previous work, we provide a complete overview of the inequalities among these reproduction numbers and resolve some open questions. Special focus is put on the exponential-growth-associated reproduction number Rr, which is loosely defined as the estimate of R0 based on the observed exponential growth of an emerging epidemic obtained when the social structure is ignored. We show that for the vast majority of the models considered in the literature Rr ≥ R0 when R0 ≥ 1 and Rr ≤ R0 when R0 ≤ 1. We show that, in contrast to models without social structure, vaccination of a fraction 1-1/R0 of the population, chosen uniformly at random, with a perfect vaccine is usually insufficient to prevent large epidemics. In addition, we provide significantly sharper bounds than the existing ones for bracketing the critical vaccination coverage between two analytically tractable quantities, which we illustrate by means of extensive numerical examples.
Key words
Full text:
1
Collection:
01-internacional
Database:
MEDLINE
Main subject:
Basic Reproduction Number
/
Epidemics
/
Models, Biological
Type of study:
Prognostic_studies
Limits:
Humans
Language:
En
Journal:
Math Biosci
Year:
2016
Document type:
Article
Affiliation country:
United kingdom
Publication country:
EEUU
/
ESTADOS UNIDOS
/
ESTADOS UNIDOS DA AMERICA
/
EUA
/
UNITED STATES
/
UNITED STATES OF AMERICA
/
US
/
USA