Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and bifurcation analysis of a SIR model with saturated
  incidence rate and saturated treatment   We study the dynamics of a SIR epidemic model with nonlinear incidence rate,
vertical transmission vaccination for the newborns and the capacity of
treatment, that takes into account the limitedness of the medical resources and
the efficiency of the supply of available medical resources. Under some
conditions we prove the existence of backward bifurcation, the stability and
the direction of Hopf bifurcation. We also explore how the mechanism of
backward bifurcation affects the control of the infectious disease. Numerical
simulations are presented to illustrate the theoretical findings.

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The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio