International Journal of Mathematics and Computer in Engineering,
Год журнала:
2024,
Номер
3(1), С. 35 - 46
Опубликована: Июнь 1, 2024
Abstract
This
study
presents
a
mathematical
model
to
investigate
the
dynamics
of
Human
Immunodeficiency
Virus
infection
and
Acquired
Syndrome
(HIV/AIDS)
transmission.
Employing
analysis,
non-negativity,
boundedness,
basic
reproduction
number
ℛ
0
,
stability
both
disease-free
endemic
equilibrium
proposed
were
derived.
Normalized
forward
sensitivity
techniques
are
used
determine
significance
importance
sensitive
parameters
associated
with
.
To
gain
insights
into
dynamical
behavior
each
compartment,
an
effective
numerical
scheme
was
utilized,
results
obtained
suggest
that
there
is
need,
even
if
individuals
infected
virus,
use
non-pharmaceutical
interventions
as
control
strategies.
Scientific Reports,
Год журнала:
2024,
Номер
14(1)
Опубликована: Март 4, 2024
Abstract
Different
cross-sectional
and
clinical
research
studies
investigated
that
chronic
HBV
infected
individuals’
co-epidemic
with
COVID-19
infection
will
have
more
complicated
liver
than
individuals
in
the
absence
of
infection.
The
main
objective
this
study
is
to
investigate
optimal
impacts
four
time
dependent
control
strategies
on
transmission
using
compartmental
modeling
approach.
qualitative
analyses
model
solutions
non-negativity
boundedness,
calculated
all
models
effective
reproduction
numbers
by
applying
next
generation
operator
approach,
computed
disease-free
equilibrium
point
(s)
endemic
proved
their
local
stability,
shown
phenomenon
backward
bifurcation
Center
Manifold
criteria.
By
applied
Pontryagin’s
Maximum
principle,
re-formulated
analyzed
problem
incorporating
controlling
variables.
also
carried
out
numerical
simulations
verify
results
proposed
strategies.
finding
reveals
implementation
protections,
vaccine,
treatment
simultaneously
most
strategy
tackle
spreading
community.
Healthcare Analytics,
Год журнала:
2023,
Номер
3, С. 100151 - 100151
Опубликована: Фев. 24, 2023
This
paper
aims
to
study
the
impacts
of
COVID-19
and
dengue
vaccinations
on
dynamics
zika
transmission
by
developing
a
vaccination
model
with
incorporation
saturated
incidence
rates.
Analyses
are
performed
assess
qualitative
behavior
model.
Carrying
out
bifurcation
analysis
model,
it
was
concluded
that
co-infection,
super-infection
also
re-infection
same
or
different
disease
could
trigger
backward
bifurcation.
Employing
well-formulated
Lyapunov
functions,
model's
equilibria
shown
be
globally
stable
for
certain
scenario.
Moreover,
global
sensitivity
analyses
impact
dominant
parameters
drive
each
disease's
its
co-infection.
Model
fitting
is
actual
data
state
Amazonas
in
Brazil.
The
fittings
reveal
our
behaves
very
well
data.
significance
rates
three
diseases
highlighted.
Based
numerical
investigation
observed
increased
efforts
against
positively
co-spread
triple
infections.
PLoS ONE,
Год журнала:
2023,
Номер
18(5), С. e0284759 - e0284759
Опубликована: Май 5, 2023
HIV/AIDS
and
COVID-19
co-infection
is
a
common
global
health
socio-economic
problem.
In
this
paper,
mathematical
model
for
the
transmission
dynamics
of
that
incorporates
protection
treatment
infected
(and
infectious)
groups
formulated
analyzed.
Firstly,
we
proved
non-negativity
boundedness
solutions,
analyzed
single
infection
models
steady
states,
calculated
basic
reproduction
numbers
using
next
generation
matrix
approach
then
investigated
existence
local
stabilities
equilibriums
Routh-Hurwiz
stability
criteria.
Then
Center
Manifold
criteria
to
investigate
proposed
exhibited
phenomenon
backward
bifurcation
whenever
its
effective
number
less
than
unity.
Secondly,
incorporate
time
dependent
optimal
control
strategies,
Pontryagin's
Maximum
Principle
derive
necessary
conditions
disease.
Finally,
carried
out
numerical
simulations
both
deterministic
incorporating
controls
found
results
solutions
are
converging
endemic
equilibrium
point
greater
unity,
also
from
problem
applying
combinations
all
possible
strategies
together
most
strategy
drastically
minimizing
in
community
under
consideration
study.
Journal of Biological Dynamics,
Год журнала:
2023,
Номер
18(1)
Опубликована: Дек. 22, 2023
In
this
paper,
a
compartmental
model
on
the
co-infection
of
pneumonia
and
HIV/AIDS
with
optimal
control
strategies
was
formulated
using
system
ordinary
differential
equations.
Using
qualitative
methods,
we
have
analysed
mono-infection
models.
We
computed
effective
reproduction
numbers
by
applying
next-generation
matrix
method,
Castillo
Chavez
criteria
models
disease-free
equilibrium
points
global
stabilities
were
shown,
while
used
Centre
manifold
to
determine
that
infection
exhibit
phenomenon
backward
bifurcation
whenever
corresponding
number
is
less
than
unity.
carried
out
numerical
simulations
investigate
behaviour
solutions.
Furthermore,
investigated
various
predict
best
strategy
minimize
possibly
eradicate
from
community.
Scientific Reports,
Год журнала:
2024,
Номер
14(1)
Опубликована: Июль 23, 2024
Abstract
In
this
article,
we
considered
a
nonlinear
compartmental
mathematical
model
that
assesses
the
effect
of
treatment
on
dynamics
HIV/AIDS
and
pneumonia
(H/A-P)
co-infection
in
human
population
at
different
infection
stages.
Understanding
complexities
co-dynamics
is
now
critically
necessary
as
consequence.
The
aim
research
to
construct
H/A-P
context
fractional
calculus
operators,
white
noise
probability
density
functions,
employing
rigorous
biological
investigation.
By
exhibiting
system
possesses
non-negative
bounded
global
outcomes,
it
shown
approach
both
mathematically
biologically
practicable.
required
conditions
are
derived,
guaranteeing
eradication
infection.
Furthermore,
adequate
prerequisites
established,
configuration
tested
for
existence
an
ergodic
stationary
distribution.
For
discovering
system’s
long-term
behavior,
deterministic-probabilistic
technique
modeling
designed
operated
MATLAB.
extensive
review,
hope
previously
mentioned
improves
leads
mitigating
two
diseases
their
co-infections
by
examining
variety
behavioral
trends,
such
transitions
unpredictable
procedures.
addition,
piecewise
differential
strategies
being
outlined
having
promising
potential
scholars
range
contexts
because
they
empower
them
include
particular
characteristics
across
multiple
time
frame
phases.
Such
formulas
can
be
strengthened
via
classical
techniques,
power
law,
exponential
decay,
generalized
Mittag-Leffler
kernels,
functions
random
get
accurate
description
function
encircling
quasi-equilibrium
point
if
minimizes
propagation
co-dynamics.
Consequently,
obtain
better
outcomes
when
analyzing
facts
using
perturbations
implementing
these
challenging
issues.
Random
crucial
controlling
spread
epidemic
whenever
suggested
circulation
steady
amount
eliminated
closely
correlated
with
perturbation
level.
Scientific Reports,
Год журнала:
2025,
Номер
15(1)
Опубликована: Фев. 14, 2025
HIV/AIDS
is
among
the
major
viral
infectious
diseases
that
are
traits
with
high
human
morbidity
and
mortality
impacts
it
has
detrimental
effects
on
economies
health
of
nations
worldwide.
In
current
study,
we
formulated
analyzed
an
compartmental
epidemic
model
by
dividing
entire
susceptible
population
into
two
groups,
such
as
sexually
mature
immature
stage
structure
groups
optimal
control
strategies,
since
been
a
cause
death
for
individuals
in
different
age
groups.
Qualitatively,
computed
model's
unique
disease-free
endemic
equilibrium
points,
using
next-generation
matrix
operator
approach
calculated
basic
reproduction
number,
proved
local
stabilities
both
points
applying
Routh-Hurwitz
stability
criteria,
also
global
building
suitable
representative
Lyapunov
function.
Using
Pontryagin's
Maximum
Principle,
optimality
system
which
determines
necessary
circumstances
to
improve
over
spread
disease
built
examined.
We
performed
numerical
simulations
validate
qualitative
analysis
explore
suggested
techniques
measure,
ART
treatment
measure
concurrently,
i.e.,
putting
Strategy
F
practice
essential
reducing
controlling
community.
Therefore,
urge
possible
policymakers
public
stakeholders
prioritize
implementation
F,
aims
reduce
prevalence
population.
Journal of Biological Dynamics,
Год журнала:
2023,
Номер
17(1)
Опубликована: Фев. 14, 2023
HIV/AIDS-COVID-19
co-infection
is
a
major
public
health
concern
especially
in
developing
countries
of
the
world.
This
paper
presents
to
investigate
impact
interventions
on
its
transmission
using
ordinary
differential
equation.
In
analysis
model,
solutions
are
shown
be
non-negative
and
bounded,
next-generation
matrix
approach
basic
reproduction
numbers
computed,
sufficient
conditions
for
stabilities
equilibrium
points
established.
The
sensitivity
showed
that
rates
most
sensitive
parameters
have
direct
protection
treatment
more
indirect
numbers.
Numerical
simulations
some
parameter
effects
single
infections
as
well
co-infection,
applying
effective
roles
minimize
also
eradicate
spreading
community.
