English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we consider epidemic models of directly transmissible SIR(susceptible $\to$ infective $\to$ recovered) and SEIR (with an additionallatent class) infections in fully-susceptible populations with a socialstructure, consisting either of households or of households and workplaces. Wereview most reproduction numbers defined in the literature for these models,including the basic reproduction number $R_0$ introduced in the companion paperof this, for which we provide a simpler, more elegant derivation. Extendingprevious work, we provide a complete overview of the inequalities among thesereproduction numbers and resolve some open questions. Special focus is put onthe exponential-growth-associated reproduction number $R_r$, which is looselydefined as the estimate of $R_0$ based on the observed exponential growth of anemerging epidemic obtained when the social structure is ignored. We show thatfor the vast majority of the models considered in the literature $R_r \geq R_0$when $R_0 \ge 1$ and $R_r \leq R_0$ when $R_0 \le 1$. We show that, in contrastto models without social structure, vaccination of a fraction $1-1/R_0$ of thepopulation, chosen uniformly at random, with a perfect vaccine is usuallyinsufficient to prevent large epidemics. In addition, we provide significantlysharper bounds than the existing ones for bracketing the critical vaccinationcoverage between two analytically tractable quantities, which we illustrate bymeans of extensive numerical examples.

Reproduction numbers for epidemic models with households and other social structures II: comparisons and implications for vaccination