Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mathematical Model and Optimal Control of the Transmission Dynamics of
  Avian Spirochaetosis (TICK Fever)   Avian Spirochaetosis is an acute endemic tick-borne disease of birds, caused
by Borrelia anserins, a species of Borrelia bacteria. In this paper, we present
a compartmental Mathematical model of the disease for the bird population and
Tick population. The model so constructed was analyzed using methods from
dynamical systems theory. \tcr{The disease steady (equilibrium) state was
determined and the conditions for the disease-free steady state to be stable
were determined}. The analysis showed that the disease-free steady state is
locally stable if $d\geq \tau_B$ and $\delta \geq \tau_T$, that is, the natural
death rate of birds (d) will be greater than the per capita birth rate of birds
$\tau_B$ and the death rate of tick $\delta)$ is greater than the per capita
birth rate of tick $\tau_T$. This means that for the disease to be under
control and eradicated within a while from its outbreak, the natural death rate
of birds $d$ will be greater than the per capita birth rate of bird $\tau_B$
and the death rate of tick $\delta$ is greater than the per capita birth rate
of tick $\tau_T$. It was also proved the disease-free equilibrium (DFE) and the
endemic equilibrium (EE) are globally stable using Lyaponov method. Three
control measures were introduced into the model. The optimality system of the
three controls is characterized using optimal control theory and the existence
and uniqueness of the optimal control are established. Then, the effect of the
incorporation of the three controls is investigated by performing numerical
simulation.

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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph