Nonlinear Dynamics,
Journal Year:
2023,
Volume and Issue:
111(13), P. 12657 - 12670
Published: May 6, 2023
The
interplay
between
disease
spreading
and
personal
risk
perception
is
of
key
importance
for
modelling
the
spread
infectious
diseases.
We
propose
a
planar
system
ordinary
differential
equations
(ODEs)
to
describe
co-evolution
phenomenon
average
link
density
in
contact
network.
Contrary
standard
epidemic
models,we
assume
that
network
changes
based
on
current
prevalence
population,
i.e.\
it
adapts
state
epidemic.
described
using
two
functional
responses:
one
link-breaking
link-creation.
focus
applying
model
epidemics,
but
we
highlight
other
possible
fields
application.
derive
an
explicit
form
basic
reproduction
number
guarantee
existence
at
least
endemic
equilibrium,
all
responses.
Moreover,
show
responses,
limit
cycles
do
not
exist.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2021,
Volume and Issue:
31(5)
Published: May 1, 2021
Mathematical
epidemiology
that
describes
the
complex
dynamics
on
social
networks
has
become
increasingly
popular.
However,
a
few
methods
have
tackled
problem
of
coupling
network
topology
with
incidence
mechanisms.
Here,
we
propose
simplicial
susceptible-infected-recovered-susceptible
(SIRS)
model
to
investigate
epidemic
spreading
via
combining
higher-order
structure
nonlinear
rate.
A
network-based
system
is
reshaped
complex,
in
which
or
infection
occurs
reinforcement
characterized
by
simplex
dimensions.
Compared
previous
susceptible-infected-susceptible
(SIS)
models,
proposed
SIRS
can
not
only
capture
discontinuous
transition
and
bistability
but
also
periodic
phenomenon
outbreaks.
More
significantly,
two
thresholds
associated
bistable
region
critical
value
factor
are
derived.
We
further
analyze
stability
equilibrium
points
obtain
condition
existence
states
limit
cycles.
This
work
expands
SIS
models
sheds
light
novel
perspective
systems
rates.
Results in Physics,
Journal Year:
2021,
Volume and Issue:
22, P. 103956 - 103956
Published: Feb. 21, 2021
It
is
of
great
curiosity
to
observe
the
effects
prevention
methods
and
magnitudes
outbreak
including
epidemic
prediction,
at
onset
an
epidemic.
To
deal
with
COVID-19
Pandemic,
SEIQR
model
has
been
designed.
Analytical
study
consists
calculation
basic
reproduction
number
constant
level
disease
absent
present
equilibrium.
The
also
explores
cases
predicted
outcomes
are
in
line
registered.
By
parameters
calibration,
new
Pakistan
predicted.
patients
current
permanent
calculated
analytically
through
simulations.
future
situation
discussed,
which
could
happen
if
precautionary
restrictions
adopted.
Journal of Systems Engineering and Electronics,
Journal Year:
2023,
Volume and Issue:
34(3), P. 543 - 573
Published: June 1, 2023
Complex
systems
widely
exist
in
nature
and
human
society.
There
are
complex
interactions
between
system
elements
a
system,
show
features
at
the
macro
level,
such
as
emergence,
self-organization,
uncertainty,
dynamics.
These
make
it
difficult
to
understand
internal
operation
mechanism
of
systems.
Networked
modeling
is
favorable
means
understanding
It
not
only
represents
but
also
reflects
essential
attributes
This
paper
summarizes
research
progress
analysis
from
perspective
network
science,
including
networked
modeling,
vital
node
analysis,
invulnerability
disintegration
resilience
link
prediction,
attacker-defender
game
networks.
In
addition,
this
presents
some
points
view
on
trend
focus
future
SIAM Journal on Applied Mathematics,
Journal Year:
2024,
Volume and Issue:
84(2), P. 661 - 686
Published: April 9, 2024
We
propose
a
compartmental
model
for
disease
with
temporary
immunity
and
secondary
infections.From
our
assumptions
on
the
parameters
involved
in
model,
system
naturally
evolves
three
time
scales.We
characterize
equilibria
of
analyze
their
stability.We
find
conditions
existence
two
endemic
equilibria,
some
cases
which
R0
<
1.Then,
we
unravel
interplay
scales,
providing
to
foresee
whether
all
or
only
fast
intermediate
ones.We
conclude
numerical
simulations
bifurcation
analysis,
complement
analytical
results.
PLoS ONE,
Journal Year:
2020,
Volume and Issue:
15(7), P. e0236386 - e0236386
Published: July 31, 2020
This
paper
proposes
a
dynamic
model
to
describe
and
forecast
the
dynamics
of
coronavirus
disease
COVID-19
transmission.
The
is
based
on
an
approach
previously
used
Middle
East
Respiratory
Syndrome
(MERS)
epidemic.
methodology
in
six
countries
where
pandemic
widely
spread,
namely
China,
Italy,
Spain,
France,
Germany,
USA.
For
this
purpose,
data
from
European
Centre
for
Disease
Prevention
Control
(ECDC)
are
adopted.
It
shown
how
can
be
new
infection
cases
deceased
uncertainties
associated
prediction
quantified.
has
advantage
being
relatively
simple,
grouping
few
mathematical
parameters
many
conditions
which
affect
spreading
disease.
On
other
hand,
it
requires
previous
transmission
country,
better
suited
regions
epidemic
not
at
very
early
stage.
With
estimated
one
use
predict
evolution
disease,
turn
enables
authorities
plan
their
actions.
Moreover,
key
straightforward
interpretation
these
influence
over
altering
some
them,
so
that
evaluate
effect
public
policy,
such
as
social
distancing.
results
presented
selected
confirm
accuracy
perform
predictions.
Bollettino dell Unione Matematica Italiana,
Journal Year:
2023,
Volume and Issue:
17(2), P. 241 - 257
Published: June 6, 2023
In
this
survey,
we
propose
an
overview
on
Lyapunov
functions
for
a
variety
of
compartmental
models
in
epidemiology.
We
exhibit
the
most
widely
employed
functions,
and
provide
commentary
their
use.
Our
aim
is
to
comprehensive
starting
point
readers
who
are
attempting
prove
global
stability
systems
ODEs.
The
focus
mathematical
epidemiology,
however
some
strategies
presented
paper
can
be
adapted
wider
models,
such
as
prey-predator
or
rumor
spreading.
Journal of Mathematical Biology,
Journal Year:
2021,
Volume and Issue:
83(4)
Published: Sept. 22, 2021
We
study
a
fast-slow
version
of
an
SIRS
epidemiological
model
on
homogeneous
graphs,
obtained
through
the
application
moment
closure
method.
use
GSPT
to
model,
taking
into
account
that
infection
period
is
much
shorter
than
average
duration
immunity.
show
dynamics
occurs
sequence
fast
and
slow
flows,
can
be
described
2-dimensional
maps
that,
under
some
assumptions,
approximated
as
1-dimensional
maps.
Using
this
method,
together
with
numerical
bifurcation
tools,
we
give
rise
periodic
solutions,
differently
from
corresponding
based
mixing.
Journal of Dynamics and Differential Equations,
Journal Year:
2023,
Volume and Issue:
unknown
Published: June 3, 2023
Abstract
We
study
delayed
loss
of
stability
in
a
class
fast–slow
systems
with
two
fast
variables
and
one
slow
one,
where
the
linearisation
vector
field
along
one-dimensional
critical
manifold
has
real
eigenvalues
which
intersect
before
accumulated
contraction
expansion
are
balanced
any
individual
eigendirection.
That
interplay
between
eigendirections
renders
use
known
entry–exit
relations
unsuitable
for
calculating
point
at
trajectories
exit
neighbourhoods
given
manifold.
illustrate
various
qualitative
scenarios
that
possible
considered
here,
we
propose
novel
formulae
functions
underlie
phenomenon
therein.
