Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation of epidemic models by diffusion processes and their
  statistical inference   Multidimensional continuous-time Markov jump processes $(Z(t))$ on
$\mathbb{Z}^p$ form a usual set-up for modeling $SIR$-like epidemics. However,
when facing incomplete epidemic data, inference based on $(Z(t))$ is not easy
to be achieved. Here, we start building a new framework for the estimation of
key parameters of epidemic models based on statistics of diffusion processes
approximating $(Z(t))$. First, \previous results on the approximation of
density-dependent $SIR$-like models by diffusion processes with small diffusion
coefficient $\frac{1}{\sqrt{N}}$, where $N$ is the population size, are
generalized to non-autonomous systems. Second, our previous inference results
on discretely observed diffusion processes with small diffusion coefficient are
extended to time-dependent diffusions. Consistent and asymptotically Gaussian
estimates are obtained for a fixed number $n$ of observations, which
corresponds to the epidemic context, and for $N\rightarrow \infty$. A
correction term, which yields better estimates non asymptotically, is also
included. Finally, performances and robustness of our estimators with respect
to various parameters such as $R_0$ (the basic reproduction number), $N$, $n$
are investigated on simulations. Two models, $SIR$ and $SIRS$, corresponding to
single and recurrent outbreaks, respectively, are used to simulate data. The
findings indicate that our estimators have good asymptotic properties and
behave noticeably well for realistic numbers of observations and population
sizes. This study lays the foundations of a generic inference method currently
under extension to incompletely observed epidemic data. Indeed, contrary to the
majority of current inference techniques for partially observed processes,
which necessitates computer intensive simulations, our method being mostly an
analytical approach requires only the classical optimization steps.

28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess