Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reproduction numbers for epidemic models with households and other
  social structures II: comparisons and implications for vaccination   In this paper we consider epidemic models of directly transmissible SIR
(susceptible $\to$ infective $\to$ 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 $R_0$ 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 $R_r$, which is loosely
defined as the estimate of $R_0$ 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 $R_r \geq R_0$
when $R_0 \ge 1$ and $R_r \leq R_0$ when $R_0 \le 1$. We show that, in contrast
to models without social structure, vaccination of a fraction $1-1/R_0$ 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.

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The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
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The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph