Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous and discrete dynamics of a deterministic model of HIV
  infection   We will study a mathematical model of the human immunodeficiency virus (HIV)
infection in the presence of combination therapy that includes within-host
infectious dynamics. The deterministic model requires us to analyze asymptotic
stability of two distinct steady states, disease-free and endemic equilibria.
Previous results have focused on investigating the global asymptotic stability
of the trivial steady state using an implicit finite-difference method which
generates a system of difference equations. We, instead, provide analytic
solutions and long term attractive behavior for the endemic steady state using
the theory of difference equations. The dynamics of estimated model is
appropriately determined by a certain quantity threshold maintaining the immune
response to a sufficient level. The result also indicates that a forward
bifurcation in the model happens when the disease-free equilibrium loses its
stability and a stable endemic equilibrium appears as the basic reproduction
number exceeds unity. In this scenario, the classical requirement of the
reproduction number being less than unity becomes a necessary and sufficient
condition for disease mitigation. When the associated reproduction number is in
excess of unity, a stable endemic equilibrium emerges with an unstable
disease-free equilibrium (leading to the persistence and existence of HIV
within the infected individuals). The attractivity of the model reveals that
the disease-free equilibrium is globally asymptotically stable under certain
assumptions. A comparison between the continuous and estimated discrete models
is also provided to have a clear perception in understanding the behavioral
dynamics of disease modelling. Finally, we show that the associated estimation
method is very robust in the sense of numerical stability since the equilibria
and the stability conditions are independent of the time step.

35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int