Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unifying incidence and prevalence under a time-varying general branching
  process   Renewal equations are a popular approach used in modelling the number of new
infections, i.e., incidence, in an outbreak. We develop a stochastic model of
an outbreak based on a time-varying variant of the Crump-Mode-Jagers branching
process. This model accommodates a time-varying reproduction number and a
time-varying distribution for the generation interval. We then derive
renewal-like integral equations for incidence, cumulative incidence and
prevalence under this model. We show that the equations for incidence and
prevalence are consistent with the so-called back-calculation relationship. We
analyse two particular cases of these integral equations, one that arises from
a Bellman-Harris process and one that arises from an inhomogeneous Poisson
process model of transmission. We outline an argument to show that the
incidence integral equations that arise from both of these specific models
agree with the renewal equation used ubiquitously in infectious disease
modelling. We present a numerical discretisation scheme to solve these
equations, and use this scheme to estimate rates of transmission from
serological prevalence of SARS-CoV-2 in the UK and historical incidence data on
Influenza, Measles, SARS and Smallpox.

21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat