Mathematical Methods in the Applied Sciences,
Journal Year:
2025,
Volume and Issue:
unknown
Published: Feb. 17, 2025
ABSTRACT
In
the
present
investigation,
a
mathematical
model
with
vaccination,
treatment,
and
environmental
impact
under
real
data
is
presented.
Initially,
we
without
any
interventions,
followed
by
an
examination
of
its
equilibrium
points.
The
stability
analysis
indicates
confirmation
local
asymptotical
disease‐free
(DFE),
,
whenever
.
Moreover,
demonstrate
global
for
We
also
investigate
endemic
equilibria
show
that
there
exists
unique
equilibrium,
which
confirms
does
not
exhibit
backward
bifurcation.
Utilizing
TB
from
Pakistan
(Khyber
Pakhtunkhwa)
over
specific
timeframe,
parameterize
accordingly.
perform
sensitivity
to
assess
parameters
on
results
depicted
graphically.
Subsequently,
extend
include
vaccination
optimal
control
framework,
deriving
relevant
outcomes.
numerical
solutions
are
presented
various
strategies,
demonstrating
simultaneous
activation
all
four
controls
yields
effective
in
managing
TB.
strategies
management
through
framework
shown.
reveal
controls,
awareness,
screening,
pathogens
clearance,
simultaneously
yield
most
reduction
both
exposed
infected
cases,
highlighting
necessity
integrated
approach
prevention
control.
Proceedings of the Institution of Mechanical Engineers Part N Journal of Nanomaterials Nanoengineering and Nanosystems,
Journal Year:
2025,
Volume and Issue:
unknown
Published: Jan. 19, 2025
This
article
investigates
the
bioconvection
flow
of
Oldroyd-B
nanomaterial
toward
an
exponentially
stretched
surface
considering
effect
Darcy-Brinkman-Forchheimer,
nonlinear
thermal
radiation,
buoyancy
driven
forces,
and
Arrhenius
chemical
reaction.
Features
heat
transport
are
presented
in
presence
activation
energy
distinction.
The
variations
thermophoretic
Brownian
motion
taken
into
account
concentration
distribution.
Nonlinear
partial
differential
equations
(PDEs)
transformed
set
ordinary
(ODEs)
by
utilizing
appropriate
variables.
expression
implemented
through
homotopy
approach.
effects
numerous
associated
variables
on
velocity,
thermal,
concentration,
motile
microorganisms,
Nusselt
number
explained
graphically.
It
is
illustrated
that
velocity
curve
decays
for
dimensionless
relaxation
time
while
opposite
behavior
noticed
porosity
factor.
Thermal
mass
rate
escalated
motion.
outcomes
also
revealed
microorganism’s
density
declined
with
Lewis
variable.
