Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The impact of network properties and mixing on control measures and
  disease-induced herd immunity in epidemic models: a mean-field model
  perspective   The contact structure of a population plays an important role in transmission
of infection. Many ``structured models'' capture aspects of the contact
structure through an underlying network or a mixing matrix. An important
observation in such models, is that once a fraction $1-1/\mathcal{R}_0$ has
been infected, the residual susceptible population can no longer sustain an
epidemic. A recent observation of some structured models is that this threshold
can be crossed with a smaller fraction of infected individuals, because the
disease acts like a targeted vaccine, preferentially immunizing higher-risk
individuals who play a greater role in transmission. Therefore, a limited
``first wave'' may leave behind a residual population that cannot support a
second wave once interventions are lifted. In this paper, we systematically
analyse a number of mean-field models for networks and other structured
populations to address issues relevant to the Covid-19 pandemic. In particular,
we consider herd-immunity under several scenarios. We confirm that, in networks
with high degree heterogeneity, the first wave confers herd-immunity with
significantly fewer infections than equivalent models with lower degree
heterogeneity. However, if modelling the intervention as a change in the
contact network, then this effect might become more subtle. Indeed, modifying
the structure can shield highly connected nodes from becoming infected during
the first wave and make the second wave more substantial. We confirm this
finding by using an age-structured compartmental model parameterised with real
data and comparing lockdown periods implemented either as a global scaling of
the mixing matrix or age-specific structural changes. We find that results
regarding herd immunity levels are strongly dependent on the model, the
duration of lockdown and how lockdown is implemented.

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The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph