Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extinction and permanence in a stochastic SIRS model in regime-switching
  with general incidence rate   In this paper, we consider a stochastic SIRS model with general incidence
rate and perturbed by both white noise and color noise. We determine the
threshold $\lambda$ that is used to classify the extinction and permanence of
the disease. In particular, $\lambda<0$ implies that the disease-free $(K, 0,
0)$ is globally asymptotic stable, i.e., the disease will eventually disappear.
If $\lambda>0$ the epidemic is strongly stochastically permanent. Our result is
considered as a significant generalization and improvement over the results in
\cite{HZ1, GLM1, LOK1, SLJJ1, ZJ1}.

31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th