Applied Mathematics and Nonlinear Sciences,
Journal Year:
2022,
Volume and Issue:
8(2), P. 169 - 180
Published: Dec. 23, 2022
Abstract
As
the
scale
of
data
becomes
larger
and
larger,
clustering
processing,
a
key
step
in
mining,
has
important
practical
significance.
Aiming
at
problems
time
consumption
high
errors
when
current
algorithms
deal
with
massive
dynamic
big
data,
an
incremental
algorithm
is
proposed
by
taking
as
research
object.
By
exploring
attribute
characteristics
four
such
scale,
diversity,
speed
value
are
summarised.
For
large-scale
streams
that
have
multiple
attributes
acquired
one
one,
optimise
setting
method
K-means
category
centre
point,
combine
Kalman
filter
measure
distance
between
point
pairs.
Instead
Mahalanobis
distance,
suitable
for
constructed.
Five
sets
selected
to
carry
out
example
analysis.
The
results
verified
algorithm.
obvious
advantages
effect
data.
At
same
time,
it
also
efficient
stable
computing
performance,
which
meets
expected
design
requirements
goals.
Computational and Mathematical Methods in Medicine,
Journal Year:
2023,
Volume and Issue:
2023(1)
Published: Jan. 1, 2023
Coinfection
of
hepatitis
B
virus
(HBV)
and
COVID‐19
is
a
common
public
health
problem
throughout
some
nations
in
the
world.
In
this
study,
mathematical
model
for
coinfection
constructed
to
investigate
effect
protection
treatment
mechanisms
on
its
spread
community.
Necessary
conditions
proposed
nonnegativity
boundedness
solutions
are
analyzed.
We
calculated
reproduction
numbers
carried
out
local
stabilities
disease‐free
equilibrium
points
whenever
associated
number
less
than
unity.
Using
well‐known
Castillo‐Chavez
criteria,
shown
be
globally
asymptotically
stable
Sensitivity
analysis
proved
that
most
influential
parameters
transmission
rates.
Moreover,
we
numerical
simulation
results:
have
high
spreading
disease
transmission,
single
infections
great
impact
using
protections
treatments
simultaneously
effective
strategy
minimize
also
eradicate
HBV
It
concluded
control
both
diseases
population,
efforts
must
geared
towards
preventing
incident
infection
with
either
or
diseases.
Journal of the Egyptian Mathematical Society,
Journal Year:
2022,
Volume and Issue:
30(1)
Published: March 7, 2022
Abstract
A
mathematical
model
has
been
utilized
to
examine
the
interaction
between
tumor
cells
and
immune
cells.
In
this
model,
include
natural
killer
cells,
circulating
lymphocytes,
CD8
+
T
CD4
cytokines.
The
not
only
represents
traditional
role
of
in
activating
but
also
illustrates
its
killing
via
secretion
Besides,
treatments
with
both
chemotherapy
immunotherapy
are
considered.
However,
since
was
fitted
experimental
data
before,
parameter
estimation
is
performed
fit
data,
first.
validated
verify
correctness
using
for
growth.
Second,
numerical
experiments
a
set
human
data.
Results
show
mutual
relations
body
absence
presence
therapy.
that
could
play
crucial
immunotherapy.
Third,
sensitivity
analysis
by
calculating
normalized
coefficients
identify
relative
influence
parameters
on
cell
population.
obtained
results
provide
tool
which
should
be
increased
or
decreased
before
treatment
get
optimal
response.
Applied Sciences,
Journal Year:
2023,
Volume and Issue:
13(2), P. 1136 - 1136
Published: Jan. 14, 2023
The
equilibrium
state
of
a
dynamical
system
can
be
divided
into
the
point
and
limit
cycle.
In
this
paper,
stability
analysis
cycle
systems
are
presented
through
different
all
possible
approaches,
those
approaches
compared
as
well.
particular,
author
phase
plane
approach,
Lyapunov–LaSalle
energy-based
linearization
respectively,
for
two-dimensional
nonlinear
system,
while
is
analyzed
by
using
LaSalle
local
invariant
set
theorem
Poincaré–Bendixson
theorem,
which
only
valid
in
systems.
Different
case
studies
used
to
demonstrate
Mathematical Methods in the Applied Sciences,
Journal Year:
2024,
Volume and Issue:
unknown
Published: July 25, 2024
The
interference
of
direct‐acting
antiviral
agents
(DAAs)
within
various
steps
the
life
cycle
hepatitis
C
virus
(HCV)
results
in
a
high
cure
rate
for
chronic
HCV
infection.
To
accurately
quantify
effect
DAAs
on
treatment
and
to
achieve
an
optimal
drug
combination
treatment,
we
formulate
age‐structured
multiscale
model.
This
model
incorporates
intracellular
RNA
replication
process
corresponding
mechanism
action,
two
modes
extracellular
transmission
(virus‐to‐cell
infection
cell‐to‐cell
infection),
antibody
immune
response.
We
prove
that
threshold
dynamics
pre‐treatment
is
completely
determined
by
basic
reproduction
number
.
Under
reasonable
assumptions,
obtain
long‐term
short‐term
approximations
post‐treatment
viral
loads
identify
which
approximation
performs
better
under
scenarios.
Numerical
simulations
show
mode
cells
mainly
affects
reduction
load
third
stage,
while
response
manifested
clearance
particles
first
stage
decrease.
With
effective
treatments,
blocking
enhancing
can
effectively
reduce
short
time
period
achieving
eradication
Our
findings
suggest
highly
dynamic
post‐DAAs
early
monitoring
decline
contributes
implementation
subsequent
regimens.
Biomedical engineering,
Journal Year:
2024,
Volume and Issue:
unknown
Published: July 31, 2024
This
chapter
provides
an
overview
of
multiscale
mathematical
modeling
techniques
used
for
analyzing
complex
biological
systems
in
the
fields
bioinformatics
and
medical
informatics.
It
emphasizes
significance
gaining
insights
into
processes
understanding
their
underlying
mechanisms.
The
discusses
several
techniques,
such
as
stochastic
simulations,
continuum
models,
molecular
dynamics
explores
applications
context
Additionally,
highlights
challenges
associated
with
modeling,
need
precise
parameter
estimation
computational
efficiency.
overall
message
is
to
stress
importance
developing
refining
advance
our
comprehension
ultimately
improve
human
health.
Journal of Biological Dynamics,
Journal Year:
2024,
Volume and Issue:
18(1)
Published: Nov. 13, 2024
In
a
recent
study,
mathematically
identical
ODE
model
is
derived
from
multiscale
PDE
of
hepatitis
C
virus
infection,
which
helps
to
overcome
the
limitations
in
analysis.
Here,
an
extended
proposed
formulated
for
this
transformed
by
including
hepatocyte
proliferation
both
uninfected
and
infected
cells.
Unlike
model,
can
predict
triphasic
viral
decline
level
after
therapy
cessation
without
oscillations.
Numerical
simulations
are
performed
investigate
effect
with
direct-acting
antivirals
agents
(DAAs).
The
basic
reproduction
number
obtained,
equilibrium
points
specified,
their
stability
analysed.
A
bifurcation
analysis
specify
study
varying
system
parameters.
Various
load
profiles
generated
confirmed
fit
reported
data
literature.
