trigram

This is a table of type trigram and their frequencies. Use it to search & browse the list to learn more about your study carrel.

trigram	frequency
the number of	318
the spread of	188
in order to	125
of the covid	122
of the disease	121
the dynamics of	115
basic reproduction number	109
of the epidemic	107
in this paper	100
based on the	100
the impact of	94
spread of the	93
of the model	92
the basic reproduction	91
spread of covid	91
the effect of	85
due to the	84
number of infected	81
as well as	76
it can be	75
dynamics of the	75
of novel coronavirus	74
total number of	73
of the virus	70
the novel coronavirus	67
the rate of	67
the proposed model	61
is given by	59
of infectious diseases	59
one of the	58
solitons fractals doi	58
chaos solitons fractals	58
analysis of the	58
the evolution of	57
the sir model	57
number of infections	56
the total number	56
on the other	55
the other hand	54
in terms of	53
the value of	52
transmission dynamics of	52
in this section	51
a mathematical model	51
the existence of	50
dynamics of covid	49
to predict the	49
the transmission dynamics	46
the case of	45
reproduction number r	45
number of cases	44
with respect to	44
number of confirmed	44
estimation of the	44
in the population	44
evolution of the	44
the model is	43
the end of	43
there is no	43
can be seen	43
of the system	43
shown in fig	43
there is a	42
fractional differential equations	42
of the novel	42
of confirmed cases	42
of infected individuals	41
model for the	41
of the infected	41
world health organization	41
in this work	40
in this study	40
the authors declare	39
in this case	39
locally asymptotically stable	38
number of deaths	38
to study the	38
of coronavirus disease	38
the total population	38
of the population	38
epidemic model with	38
we assume that	37
according to the	37
that they have	36
the beginning of	36
shown in figure	36
as shown in	36
authors declare that	36
of the outbreak	35
they have no	35
solution of the	35
the use of	35
in the following	34
the optimal control	34
related to the	34
in the number	34
acute respiratory syndrome	34
of the number	34
we consider the	33
is locally asymptotically	33
in cryptocurrency markets	33
declare that they	33
value of the	33
of new cases	33
of the infection	33
the transmission of	32
severe acute respiratory	32
of the pandemic	32
by using the	32
of the proposed	32
we have the	31
that could have	31
increase in the	31
to reduce the	31
and control of	31
reported in this	31
the epidemic spreading	31
the outbreak of	31
of fractional order	30
the fractional order	30
ordinary differential equations	30
relationships that could	30
are given in	29
such as the	29
virus in the	29
appeared to influence	29
personal relationships that	29
the rest of	29
could have appeared	29
given by the	29
have appeared to	29
or personal relationships	29
influence the work	29
interests or personal	29
to influence the	29
in the case	29
financial interests or	29
competing financial interests	29
the role of	28
known competing financial	28
globally asymptotically stable	28
in the model	28
work reported in	28
shows that the	28
the work reported	28
no known competing	28
have no known	28
is shown in	28
mathematical model for	28
the influence of	27
be used to	27
rate of new	27
of infected people	27
the fact that	27
the model parameters	27
most of the	27
the effectiveness of	27
the endemic equilibrium	27
in stock markets	27
the susceptible population	27
show that the	26
models have been	26
assume that the	26
model can be	26
to model the	26
the effects of	26
the epidemic peak	26
the risk of	26
growth rate of	26
number of new	26
in the environment	26
numerical solution of	26
of this paper	26
is given as	26
to control the	25
that there is	25
the coronavirus disease	25
of the coronavirus	25
transmission of the	25
it should be	25
large number of	25
have the following	25
optimal control problem	25
cumulative number of	25
which can be	25
a novel coronavirus	24
on the dynamics	24
of the spread	24
the solution of	24
with the help	24
the help of	24
to find the	24
the basis of	24
to understand the	24
the infected population	24
in which the	24
beginning of the	24
well as the	24
we use the	24
the peak of	24
the presence of	24
markets during pandemic	24
can be used	24
it has been	24
is globally asymptotically	24
individuals in the	24
markets before pandemic	24
a case study	23
the analysis of	23
fractional optimal control	23
the development of	23
the probability of	23
of the parameters	23
differential equations with	23
prediction of the	23
the seir model	22
cases of covid	22
on the basis	22
of the total	22
compared to the	22
during the pandemic	22
optimal control of	22
sir epidemic model	22
control of covid	22
the state of	22
is given in	22
depends on the	22
a large number	22
of the basic	22
at time t	22
around the world	22
transmission of covid	22
parameters of the	21
vaccine failure rate	21
associated with the	21
the absence of	21
of the fractional	21
next generation matrix	21
of disease transmission	21
in the world	21
public health interventions	21
mathematical theory of	21
depending on the	21
model of covid	21
a modelling study	21
stability of the	21
daily new cases	21
is based on	21
is defined as	21
be seen that	21
of susceptible individuals	20
the mathematical theory	20
at the beginning	20
is used to	20
respiratory syndrome coronavirus	20
the proof of	20
in the system	20
by the following	20
to estimate the	20
to analyze the	20
used in the	20
the next generation	20
rest of the	20
at a rate	20
are shown in	20
different values of	20
of the country	20
period of time	20
that the model	20
assumed to be	20
to minimize the	19
impact of the	19
of this virus	19
the numerical solution	19
in the host	19
on the spread	19
as a result	19
around the globe	19
the incubation period	19
rate of infection	19
in the first	19
number of susceptible	19
we propose a	19
model for covid	19
strict social distancing	19
behavior of the	19
disease free equilibrium	18
given in table	18
the virus in	18
in the early	18
fractional white noise	18
and it is	18
be noted that	18
a function of	18
to be the	18
the fraction of	18
this paper is	18
the cumulative number	18
model has been	18
dynamics of transmission	18
we obtain the	18
are presented in	18
and forecasting the	18
of the transmission	18
to describe the	18
the spreading of	18
to assess the	18
reduction in the	18
results of the	18
the onset of	18
we observe that	18
number of covid	18
in the same	18
end of the	18
a number of	17
in the absence	17
has a unique	17
to determine the	17
described by the	17
in the country	17
free equilibrium is	17
have been proposed	17
theory of epidemics	17
we have that	17
of this study	17
dynamics of novel	17
control of the	17
analysis of a	17
that can be	17
the level of	17
to the mathematical	17
on the number	17
the implementation of	17
the infected individuals	17
asymptotically stable if	17
the context of	17
caputo fractional derivative	17
the world health	17
of the sars	17
the values of	17
mathematical model of	17
of differential equations	16
stock markets before	16
in addition to	16
the early phase	16
the behavior of	16
to account for	16
the amount of	16
each of the	16
to evaluate the	16
we can obtain	16
there are no	16
international spread of	16
of the sir	16
an epidemic model	16
it follows that	16
a mathematical modelling	16
of an epidemic	16
solutions of the	16
an introduction to	16
infection in the	16
impact on the	16
and the number	16
be considered as	16
size of the	16
the nature of	16
in the future	16
be seen in	16
model based on	16
in case of	16
of transmission and	16
to fit the	16
of the most	16
when r b	16
sir model is	16
of epidemic spreading	16
the recovery rate	16
study of the	15
of transmission of	15
the transmission rate	15
peak of the	15
can be described	15
of the world	15
be applied to	15
the appearance of	15
and international spread	15
early dynamics of	15
is less than	15
based on a	15
shown that the	15
the ministry of	15
to solve the	15
is assumed to	15
the real data	15
ncov outbreak originating	15
in the next	15
potential domestic and	15
fractional derivative order	15
strategies for covid	15
originating in wuhan	15
the topic of	15
with fractional derivative	15
for the covid	15
assumed that the	15
at the end	15
to investigate the	15
a backward bifurcation	15
nature of the	15
the high risk	15
the third equation	15
mathematical modeling of	15
in the table	15
completes the proof	15
domestic and international	15
for the spread	15
respect to the	15
which is a	15
in the context	15
the potential domestic	15
the city of	15
cryptocurrency markets before	15
study on the	15
reproduction number of	15
the caputo fractional	15
is one of	15
shown in table	15
of the data	15
existence of the	15
early phase of	15
has been used	15
forecasting the potential	15
the control measures	15
of infected population	15
nowcasting and forecasting	15
outbreak originating in	15
values of the	15
the parameters of	14
as a function	14
are used to	14
is organized as	14
the disease is	14
the disease free	14
confirmed cases of	14
asymptotic stability of	14
the mitigation strategies	14
organized as follows	14
phase of the	14
stock markets during	14
should be noted	14
for the numerical	14
data from the	14
growth of the	14
of asymptomatic infectives	14
the possibility of	14
this study is	14
this completes the	14
global stability of	14
daily growth rate	14
of individuals in	14
for different values	14
epidemic spreading and	14
the results of	14
international stock markets	14
in heilongjiang province	14
fractional order differential	14
effect of the	14
total population of	14
the reproduction number	14
has not been	14
the system is	14
the daily growth	14
of a novel	14
conflict of interest	14
into account the	14
is the most	14
the disease in	14
of the new	14
people in the	14
case of covid	14
is divided into	14
numerical solutions of	14
number of active	14
in the susceptible	14
function of time	14
high risk group	14
two types of	14
the second equation	14
can be written	14
the initial conditions	14
cryptocurrency markets during	14
the disease to	14
effectiveness of the	14
to obtain the	14
it is assumed	14
the whole population	14
is that the	14
of fractional derivative	14
of the quarantine	14
the virus and	14
some of the	14
used in this	14
stable if r	14
modeling the dynamics	14
mathematical modelling study	14
that there are	14
transmission and control	14
can be obtained	14
and recovered cases	14
in the form	14
consider the following	14
the low risk	13
of social distancing	13
a fractional order	13
the reproductive number	13
seen that the	13
asymptotically infected people	13
is applied to	13
to prevent the	13
the stability of	13
to forecast the	13
the data from	13
is the average	13
dynamics and control	13
the united states	13
if r b	13
is assumed that	13
order differential equations	13
which may be	13
see that the	13
asymptomatic infectious individuals	13
we take the	13
mitigation strategies for	13
the jacobian matrix	13
of infectious disease	13
to the model	13
duration of the	13
and so on	13
of fractional differential	13
to get the	13
an infectious disease	13
from the first	13
sir model with	13
of the asymptomatic	13
global sensitivity analysis	13
can be found	13
it is a	13
apen variance in	13
for the fractional	13
the disease and	13
the growth rate	13
by the government	13
variance in cryptocurrency	13
is defined by	13
note that the	13
part of the	13
than that of	13
in the time	13
characteristics of the	13
number of days	13
of the mitigation	13
low risk group	13
the epidemic threshold	13
that it is	13
second wave of	13
may be considered	13
impact of non	13
it is observed	13
incubation period of	13
estimated to be	13
the susceptible individuals	13
less than unity	13
no conflict of	13
which is the	13
of cases and	13
ministry of health	13
has become a	13
we set the	12
due to covid	12
sensitivity analysis of	12
to deal with	12
epidemic in china	12
the most important	12
rate of the	12
case study of	12
figure shows the	12
we can see	12
are given by	12
in the second	12
web of science	12
from the environment	12
and in the	12
of the current	12
applied to the	12
fabrizio fractional derivative	12
a set of	12
of an infectious	12
conditions for the	12
the mutation rate	12
be written as	12
considered as potential	12
analysis of an	12
is presented in	12
slow down the	12
number of novel	12
the increase in	12
it follows from	12
is possible to	12
of infected cases	12
the epidemic dynamics	12
from the disease	12
the social distancing	12
with recurrent mobility	12
apen mean in	12
that the covid	12
obtained from the	12
of the lockdown	12
mean in cryptocurrency	12
the application of	12
the study of	12
the fractional derivative	12
fractional brownian motion	12
the form of	12
novel coronavirus in	12
of being infected	12
description of the	12
and the uk	12
prevention and control	12
rate of detection	12
observed that the	12
time series forecasting	12
would like to	12
epidemic spreading in	12
on the covid	12
inter zone mobilization	12
found that the	12
mathematical models have	12
the duration of	12
the time interval	12
development of the	12
mathematical modelling of	12
transmission dynamics in	12
fractional order sidarthe	12
model and the	12
found to be	12
lle variance in	12
leads to the	12
an outbreak of	12
mean in stock	12
a second wave	12
of backward bifurcation	12
we see that	12
the isolation room	12
the asymptomatic infectious	12
that the number	12
confirmed cases and	12
the local stability	12
move to the	12
model of the	12
proof of theorem	12
to the following	12
host and between	12
cases and deaths	12
to have a	12
in other words	12
the pandemic is	12
it is not	12
influence of the	12
the characteristic equation	12
the importance of	12
it is clear	12
in this way	12
it is possible	12
on the disease	12
in the last	12
application of the	12
in the present	12
second equation of	12
variance in stock	12
peak number of	12
epidemic model for	12
cases in the	12
lle mean in	12
to the best	12
equation of system	11
contribution to the	11
the function f	11
the eigenvalues of	11
on the one	11
in this model	11
the sensitivity analysis	11
across the globe	11
in the field	11
the lancet infectious	11
disease information diffusion	11
the course of	11
been proposed to	11
and then the	11
proposed model is	11
social distancing and	11
confirmed cases in	11
we present a	11
recurrent mobility pattern	11
distribution of the	11
coronavirus disease in	11
the time of	11
the average number	11
novel coronavirus outbreak	11
less than one	11
the time series	11
li et al	11
in a population	11
of the time	11
best of our	11
in different countries	11
data for the	11
table and table	11
a total of	11
in the literature	11
contact with the	11
is carried out	11
this can be	11
time evolution of	11
optimal control problems	11
with the following	11
of the season	11
our model is	11
stochastic differential equations	11
the epidemic and	11
state of the	11
average number of	11
is equal to	11
control the spread	11
the infection rate	11
number of daily	11
outbreak of covid	11
paper is organized	11
this paper we	11
reported in the	11
are based on	11
reproduction number is	11
is the rate	11
so that the	11
the diffusion of	11
the daily new	11
the paper is	11
may not be	11
classic sir model	11
the solutions of	11
for simulating the	11
the data of	11
of our knowledge	11
taken into account	11
is estimated to	11
third equation of	11
lancet infectious diseases	11
and stock markets	11
compared with the	11
in the class	11
the mean value	11
caused by the	11
changes in the	11
to explore the	11
the best of	11
risk of the	11
the same as	11
we present the	11
the recorded data	11
dynamics of hiv	11
the epidemic in	11
can also be	11
the classic sir	11
a time series	11
the time evolution	11
the model to	11
the disease information	11
a model based	11
it is also	11
since the first	11
p r a	11
the following theorem	11
the model and	11
results show that	11
the infectious disease	11
states of india	11
mean time between	11
which means that	11
in the usa	11
using machine learning	11
control measures v	11
the set of	11
the mean of	11
this is not	11
coupled slow system	11
number of people	10
structure of the	10
was used to	10
of the first	10
the virus is	10
been applied to	10
and predict the	10
time series data	10
predict the covid	10
q s q	10
a new fractional	10
cryptocurrency and stock	10
we know that	10
represents the number	10
outbreak of the	10
the population of	10
will not be	10
in this context	10
infectious diseases of	10
we study the	10
such that the	10
social distancing is	10
during this period	10
of the parameter	10
model on the	10
countries around the	10
the parameter values	10
data of the	10
can be observed	10
an increase in	10
the state variables	10
and prediction of	10
the following result	10
with fractional order	10
financial interests personal	10
the definition of	10
endemic equilibrium point	10
onset of symptoms	10
without singular kernel	10
that the disease	10
of fractional calculus	10
interests personal relationships	10
model for simulating	10
of the risk	10
r in the	10
sarii q s	10
the pairwise approach	10
is clear that	10
the growth of	10
means that the	10
was carried out	10
the following financial	10
definition of fractional	10
in the covid	10
of pandemic covid	10
spreading of the	10
can be applied	10
taking into account	10
isolated slow system	10
myopic update rule	10
for the next	10
asymptomatic infected individuals	10
personal relationships which	10
have been applied	10
can be easily	10
is related to	10
following financial interests	10
a result of	10
is described by	10
declare the following	10
outbreak in china	10
it is important	10
we confirm that	10
spreading in china	10
this leads to	10
the one hand	10
this section we	10
model based study	10
relative cost of	10
of health of	10
contributions to the	10
results in a	10
that the virus	10
analysis and forecast	10
the population is	10
stability analysis of	10
of public health	10
time of the	10
is expected to	10
relationships which may	10
take into account	10
is considered as	10
transmission risk of	10
follows from the	10
and forecast of	10
the infected people	10
the existence and	10
each of these	10
health of morocco	10
we found that	10
there will be	10
number of the	10
in a given	10
w is locally	10
number of swabs	10
fractional order model	10
forecasts of the	10
to characterize the	10
all over the	10
the epidemic is	10
mathematical analysis of	10
of infected players	10
the dynamics and	10
in the state	10
spread of infectious	10
and of the	10
we want to	10
operational matrix of	10
is able to	10
of the three	10
in the current	10
hiv aids epidemic	10
the propagation of	10
assessment of the	10
for public health	10
models of disease	10
equations of the	10
the published data	10
leads to a	10
during the covid	10
the disease transmission	10
corresponds to the	10
indicates that the	10
is important to	10
model to the	10
at the same	10
new infection cases	10
tests per day	9
dynamics in wuhan	9
to that of	9
the transmission risk	9
the probability that	9
the characteristics of	9
that number of	9
infected and recovered	9
depend on the	9
trend of covid	9
female sex workers	9
the same way	9
number of recovered	9
during the outbreak	9
princess cruise ship	9
risk assessment of	9
the mild cases	9
sei i r	9
authors declare the	9
this is the	9
of control strategies	9
for the same	9
as potential competing	9
the same time	9
been used to	9
optimal control is	9
basic reproductive number	9
outbreak in wuhan	9
is the time	9
the mathematics of	9
a long time	9
the diamond princess	9
equilibrium w is	9
to the disease	9
the trend of	9
is a constant	9
of the infectious	9
when compared to	9
by the end	9
integrated moving average	9
early detection of	9
autoregressive integrated moving	9
we consider a	9
we show the	9
cost of vaccination	9
is not the	9
shown in the	9
and information diffusion	9
the latent period	9
over the world	9
rate at which	9
the spectral radius	9
local and global	9
there exists a	9
has been considered	9
the sensitivity of	9
and the initial	9
we have considered	9
we have used	9
of virus in	9
number of individuals	9
number of tests	9
the length of	9
assessment of novel	9
for the disease	9
is the same	9
the infected density	9
is depicted in	9
the mean time	9
study is to	9
controlling the spread	9
of social media	9
for the transmission	9
for each country	9
of the state	9
given in fig	9
number r b	9
existence and uniqueness	9
to the number	9
we do not	9
natural death rate	9
the infected person	9
model with a	9
the epidemic topic	9
see for example	9
has been shown	9
cases and the	9
the infection is	9
the data and	9
seir model with	9
the sum of	9
forecast of covid	9
as soon as	9
of the epidemics	9
optimal control strategies	9
the control of	9
an infected person	9
middle east respiratory	9
and uniqueness of	9
analysis in the	9
to identify the	9
the prediction of	9
is said to	9
case of the	9
is easy to	9
local stability of	9
reduce the number	9
more than one	9
obtain the following	9
ncov and its	9
due to a	9
has been proposed	9
with novel coronavirus	9
of the paper	9
likely due to	9
needs to be	9
point of view	9
potential competing interests	9
by solving the	9
attention to the	9
disease in the	9
corona virus disease	9
the simulation results	9
the initial condition	9
with a case	9
at any time	9
matrix of fractional	9
implication for public	9
existence of a	9
is necessary to	9
of infection is	9
convolutional neural network	9
to tackle the	9
can be defined	9
we investigate the	9
the first equation	9
for the model	9
many of the	9
in controlling the	9
data becomes available	9
the arima model	9
been carried out	9
for the infected	9
the class of	9
presented in section	9
its implication for	9
parameter values are	9
r a ft	9
the basic reproductive	9
the disease spread	9
at the point	9
the final size	9
the average time	9
ml and ai	9
it is worth	9
with saturated incidence	9
mathematics of infectious	9
model with the	9
given in the	9
transmission dynamics with	9
this shows that	9
is observed that	9
and optimal control	9
that of the	9
mobility and contact	9
and its implication	9
the following form	9
and disease information	9
values of fractional	9
networked population with	9
maximum number of	9
of the optimal	9
for the first	9
novel corona virus	9
expected number of	9
on epidemic spreading	9
with each other	9
at the rate	9
pharmaceutical interventions on	9
to show that	9
spreading and information	9
for the number	9
the purpose of	9
we note that	9
prediction of covid	9
infected with novel	9
and the existence	9
fact that the	9
of the exposed	9
covidmaroc the ministry	9
free equilibrium point	9
new fractional derivative	9
it is shown	9
s q model	9
of the control	9
detected infected population	9
start of the	9
with a large	9
observe that the	9
of confirmed covid	9
east respiratory syndrome	9
insights into the	9
from january to	9
amount of virus	9
higher than the	8
the lockdown rate	8
mathematical model to	8
virus infection in	8
the model can	8
it is easy	8
forecasting of the	8
in the community	8
it is necessary	8
and forecasting of	8
understanding of the	8
of our model	8
clinical characteristics of	8
is greater than	8
study the dynamics	8
for more details	8
at the dfe	8
the contribution of	8
performance of the	8
the world and	8
infectious diseases in	8
similar to the	8
have been infected	8
for all t	8
because of the	8
kermack and mckendrick	8
first of all	8
the proposed fractional	8
model to study	8
of control measures	8
method for the	8
we analyze the	8
that the epidemic	8
are reported in	8
to mitigate the	8
the field of	8
model parameters are	8
the social distance	8
condition for the	8
was used for	8
by means of	8
the inflection point	8
the size of	8
sir model can	8
estimate of the	8
it is found	8
the fractional optimal	8
in the initial	8
this implies that	8
which implies that	8
allows us to	8
d is the	8
this means that	8
first equation of	8
system of differential	8
by the same	8
to the data	8
time forecasts and	8
of hiv aids	8
diamond princess cruise	8
to show the	8
we conclude that	8
infected population and	8
by the time	8
the global stability	8
for compartmental models	8
and social distancing	8
time a new	8
detected and quarantined	8
is the first	8
based transmissibility of	8
of vaccination c	8
the infected and	8
epidemic models with	8
a unique solution	8
this virus is	8
the following system	8
day of the	8
be found in	8
time markov chain	8
infected cases and	8
the structure of	8
a recovered person	8
asymptotically stable when	8
to the covid	8
analysis of covid	8
of new infection	8
models for the	8
determined by the	8
of the dynamics	8
the performance of	8
infection from the	8
from the third	8
to prove the	8
new infected cases	8
compartmental models of	8
describe the dynamics	8
effective reproduction number	8
the estimated parameters	8
signifies the rate	8
the new fractional	8
can be explained	8
mutation rate is	8
of asymptomatic infected	8
and analysis of	8
early transmission dynamics	8
in more detail	8
health care facilities	8
rate due to	8
the peak number	8
the vaccine failure	8
the nucleotide mutation	8
against the covid	8
to the fact	8
a and b	8
respect to time	8
function of the	8
initial conditions are	8
endemic equilibria for	8
equation in the	8
the contact rate	8
in such a	8
prediction and control	8
the pandemic period	8
social distancing measures	8
seen in fig	8
of the network	8
equilibria for compartmental	8
reproduction numbers and	8
the results are	8
of active cases	8
the coupled slow	8
in view of	8
of new infections	8
considered to be	8
at the time	8
transmissibility of a	8
of patients infected	8
in the dynamics	8
we discuss the	8
to calculate the	8
time between infections	8
population due to	8
each time step	8
the numerical simulation	8
soon as possible	8
have been used	8
that the total	8
of all the	8
of the next	8
which leads to	8
deep convolutional neural	8
a deep learning	8
in each of	8
of the cumulative	8
forecasts and risk	8
spread of disease	8
the turning point	8
supplementary material fig	8
order sidarthe model	8
global asymptotic stability	8
the containment rate	8
a susceptible individual	8
by applying the	8
the model was	8
for fractional order	8
with different fractional	8
diseases of humans	8
corresponding to the	8
depicted in figure	8
have not been	8
of days between	8
the control strategies	8
for the sir	8
and dynamics of	8
the system of	8
have been reported	8
is close to	8
in the figure	8
of fractional differentiation	8
the infection and	8
equilibrium is globally	8
approach for the	8
mean square error	8
numerical simulation of	8
mean value function	8
the disease burden	8
of the hiv	8
the proposed hybrid	8
model to predict	8
we can observe	8
together with the	8
with real data	8
the above equation	8
t is the	8
subject to the	8
rate of recovery	8
has also been	8
the start of	8
has been observed	8
be defined as	8
a machine learning	8
on the data	8
wave of infection	8
due to its	8
it could be	8
different types of	8
across the world	8
in this article	8
the equilibrium points	8
and can be	8
a contribution to	8
will have a	8
a numerical scheme	8
in the appendix	8
at least one	8
the brownian motion	8
dynamics of a	8
be able to	8
which in turn	8
control of a	8
individuals and the	8
driven adaptive process	8
the proposed method	8
coronavirus in wuhan	8
the pandemic in	8
isolation of cases	8
the control u	8
spreading of pandemic	8
across the country	8
preliminary estimation of	8
an infected individual	8
a class of	8
infected population due	8
modeling of the	8
infected individuals and	8
population with recurrent	8
the numerical results	8
at which the	8
equilibrium point is	8
necessary conditions for	8
a lot of	8
sir model and	8
is the number	8
number of secondary	8
presented in the	8
the sirsi model	7
concluded that the	7
it difficult to	7
the present study	7
risk of transmission	7
and move to	7
and found that	7
for the seir	7
trend of the	7
the epidemic prevalence	7
of susceptible people	7
is independent of	7
fractional order derivative	7
we give a	7
following system of	7
the ongoing covid	7
the outbreak is	7
necessary optimality conditions	7
given in section	7
as compared to	7
before the pandemic	7
the recovered individuals	7
to the reported	7
the epidemic will	7
of ordinary differential	7
be described by	7
of the models	7
with pneumonia in	7
supported by the	7
all individuals are	7
case projection using	7
in supplementary material	7
is to say	7
the most effective	7
of the theorem	7
has been developed	7
sir model in	7
and during the	7
and contact tracing	7
affected by the	7
surges in the	7
and the control	7
and control the	7
the epidemic spread	7
science foundation of	7
that when the	7
the final state	7
that is to	7
is the total	7
with optimal control	7
disease caused by	7
at each time	7
in this manuscript	7
the model in	7
the success of	7
the asymptomatic class	7
the process of	7
infected individual is	7
of this epidemic	7
the exposed individuals	7
the other countries	7
as a pandemic	7
infections generated by	7
agreement with the	7
if it is	7
on the epidemic	7
order model for	7
the state and	7
in the hospital	7
of the following	7
the relative cost	7
the aim of	7
patients with pneumonia	7
we have seen	7
number of asymptomatic	7
deal with the	7
person to be	7
fractional derivative without	7
the new coronavirus	7
are listed in	7
exposed to the	7
of the function	7
we define the	7
is no conflict	7
the range of	7
that our model	7
applied over the	7
we compute the	7
accumulated number of	7
case of a	7
to be a	7
r epidemic model	7
been shown in	7
a given time	7
the maximum number	7
there has been	7
of hiv infection	7
outbreaks by isolation	7
the interplay between	7
caputo fractional derivatives	7
nucleotide mutation rate	7
definition of the	7
presented in figure	7
differential equations and	7
patients infected with	7
science and engineering	7
about of the	7
the assumption that	7
of the solution	7
that the spread	7
to the new	7
a total population	7
spread the disease	7
the proposed approach	7
in china and	7
we derive the	7
is determined by	7
of the above	7
an updated estimation	7
and the epidemic	7
natural science foundation	7
appearance of symptoms	7
is to be	7
we need to	7
as we can	7
the infected individual	7
in the presence	7
machine learning approach	7
of the impact	7
the variance of	7
cases of the	7
feasibility of controlling	7
of time series	7
measures such as	7
cases and contacts	7
that the mean	7
model with saturated	7
epidemic in india	7
in recent years	7
in the network	7
the formulation of	7
onset of the	7
can be reduced	7
the lockdown period	7
in a similar	7
stochastic epidemic model	7
to capture the	7
within the population	7
individuals who have	7
in this regard	7
of the mild	7
and machine learning	7
models can be	7
we can write	7
spread in the	7
city of wuhan	7
a variety of	7
equal to zero	7
the observed daily	7
unique solution of	7
of the daily	7
two positive equilibria	7
detection of covid	7
characteristic equation of	7
the system has	7
of these models	7
into the environment	7
is obvious that	7
governed by the	7
cases in china	7
the necessary conditions	7
have also been	7
the estimated value	7
infected with covid	7
was supported by	7
we apply the	7
let us consider	7
prediction for the	7
where is the	7
the infectious rate	7
course of the	7
control strategies to	7
model that can	7
the increase of	7
in the sir	7
fractional derivative is	7
mutation rate of	7
the environment by	7
unique endemic equilibrium	7
there are many	7
confirmed infected cases	7
the control is	7
has a disease	7
has been carried	7
i and j	7
city of jakarta	7
lower than the	7
the need to	7
it is obvious	7
as in the	7
and more than	7
reproductive number of	7
the first case	7
of daily new	7
the best fit	7
of a large	7
is an important	7
the first days	7
in the sense	7
stereographic projection coordinates	7
a period of	7
state of texas	7
epidemic in wuhan	7
given in figure	7
can observe that	7
and inter zone	7
of vaccinated individuals	7
and the state	7
considered as a	7
the rate at	7
basis of the	7
clinical features of	7
are depicted in	7
cumulative confirmed cases	7
i r epidemic	7
decrease in the	7
approach based on	7
in the previous	7
is lower than	7
all of the	7
case fatality rate	7
asymptotically stable whenever	7
seir epidemic model	7
on the topic	7
data up to	7
infected individuals from	7
novel coronavirus from	7
a unique positive	7
number of patients	7
then the system	7
the real world	7
lead to a	7
transition rate from	7
it is expected	7
of stability in	7
before and during	7
view of the	7
and implementation of	7
to become cure	7
infected people increases	7
for the country	7
used for the	7
that the peak	7
is higher than	7
intra and inter	7
among the population	7
implementation of population	7
decay of the	7
based study on	7
deep transfer learning	7
government of india	7
partial rank correlation	7
fractional differential equation	7
to the spread	7
spread of coronavirus	7
the first day	7
epidemic and implementation	7
then we have	7
sensitivity analysis is	7
the mortality rate	7
parts of the	7
brownian motion on	7
the following equation	7
the infection rates	7
and control measures	7
for a long	7
presence of a	7
derivative without singular	7
host dynamics in	7
system of ordinary	7
used to model	7
r b and	7
the model with	7
driven analysis in	7
from the model	7
the efficiency of	7
of this pandemic	7
can see that	7
for the rest	7
fx t dg	7
conflicts of interest	7
and effectiveness of	7
estimated value of	7
an overview of	7
by isolation of	7
the observed data	7
in the city	7
updated estimation of	7
spread of hiv	7
the total cumulative	7
the sign of	7
time series analysis	7
smaller than the	7
epidemiology of infectious	7
proof of the	7
total population n	7
of cd t	7
estimated from the	7
the distribution of	7
is associated with	7
as it can	7
to do this	7
for the optimal	7
as far as	7
with a total	7
and using the	7
using lstm networks	7
population in the	7
of asymptomatic patients	7
illustrated in fig	7
a reduction in	7
is denoted by	7
values for the	7
sensitive to the	7
of the work	7
w is unstable	7
free and endemic	7
the effective reproduction	7
the delay between	7
the unique solution	7
reproduction number and	7
the case fatality	7
global financial crisis	7
has been a	7
simulating the phase	7
n is the	7
which makes it	7
features of patients	7
parameters and the	7
and risk assessment	7
confirm that the	7
of the isolation	7
predictions of the	7
the model from	7
the present paper	7
of a stochastic	7
who do not	7
be described as	7
given time t	7
the population and	7
between individuals and	7
novel coronavirus disease	7
the initial value	7
in our model	7
between infection and	6
province in china	6
it does not	6
of caputo fractional	6
the epidemic of	6
that the data	6
the coronavirus outbreak	6
a major role	6
at the disease	6
they can be	6
of both the	6
to the system	6
existence of equilibria	6
epidemic in italy	6
in mainland china	6
the positive equilibrium	6
from the data	6
the normalized forward	6
no more than	6
infected individuals in	6
model using the	6
a stochastic epidemic	6
dynamics of epidemic	6
pandemic in the	6
cases for the	6
the severe acute	6
in networked population	6
zhang et al	6
country or region	6
to stop the	6
stable when r	6
interventions on the	6
but it is	6
given by where	6
the following results	6
with a new	6
to the asymptomatic	6
fractional order derivatives	6
new cases is	6
more than countries	6
incubation period and	6
to compare the	6
what are the	6
control the disease	6
that have been	6
the government to	6
equilibrium of system	6
that we have	6
and forecast the	6
adjusted estimation of	6
always has a	6
days since the	6
baleanu fractional derivative	6
support vector regression	6
model to analyze	6
as one of	6
similar to that	6
the numerical solutions	6
a report of	6
in the transmission	6
a boundary arc	6
model with fractional	6
find out the	6
different fractional derivative	6
and is the	6
is considered to	6
consistent with the	6
that the system	6
known as the	6
from the above	6
infection of the	6
the novel covid	6
a constant rate	6
is smaller than	6
to improve the	6
the strength of	6
is plotted in	6
for infectious diseases	6
more than of	6
due to spreading	6
period of the	6
the following fractional	6
deep learning model	6
is governed by	6
will be used	6
carried out to	6
of the pathogen	6
as of april	6
the incubation time	6
to real data	6
all the eigenvalues	6
driven receding horizon	6
saturated incidence rate	6
for the time	6
the expectation of	6
the second wave	6
in modeling the	6
and that the	6
the objective functional	6
a stochastic model	6
this indicates that	6
to contain the	6
we observed that	6
results in the	6
and we have	6
the myopic update	6
of this disease	6
it is evident	6
model of hiv	6
the following two	6
the transition from	6
to derive the	6
parameter values and	6
negative real parts	6
the results found	6
change of the	6
is similar to	6
model in the	6
of chest ct	6
in india is	6
the raw data	6
is known that	6
the epidemic peaks	6
been observed that	6
the higher the	6
the standard sir	6
with applications to	6
to spreading of	6
of the main	6
for the other	6
the actual data	6
free equilibrium w	6
peaks of the	6
of continuously evolving	6
of a fractional	6
a numerical solution	6
the previous section	6
is obtained as	6
noted that the	6
and r score	6
isolation and quarantine	6
the center manifold	6
and deep learning	6
symptomatic infectious individuals	6
to the basic	6
transmission dynamics and	6
due to their	6
and reported in	6
to be used	6
role in the	6
we can say	6
can be estimated	6
the reduction of	6
of hubei province	6
has been performed	6
is found that	6
the overall number	6
to the other	6
the yule process	6
spread of this	6
a global pandemic	6
topic discussion rate	6
the exposed class	6
the memory effect	6
sk shahid nadim	6
and global stability	6
proposed fractional order	6
the accumulated number	6
to find out	6
disease model with	6
optimal control analysis	6
the positivity and	6
dynamics with a	6
partial differential equations	6
daily new covid	6
implies that the	6
data set is	6
and application to	6
on social media	6
during pandemic apen	6
the time window	6
to be more	6
and the effects	6
this is a	6
is in the	6
model is the	6
the information diffusion	6
account for the	6
caused by a	6
a generalization of	6
to be in	6
national natural science	6
and on the	6
a ft t	6
our proposed model	6
before pandemic apen	6
takes the form	6
we give the	6
from patients with	6
the disease with	6
symptoms of the	6
infected population i	6
final size and	6
study of a	6
for predicting the	6
in this research	6
the new data	6
defined by the	6
number of coronavirus	6
on the time	6
can say that	6
the model predictions	6
as seen in	6
can be controlled	6
the pandemic and	6
we can get	6
the acquired immunity	6
the first time	6
the relationship between	6
of the class	6
machine learning techniques	6
an optimal control	6
the asymptomatic duration	6
a comparative study	6
during a match	6
boundedness of solutions	6
the immune system	6
the degree of	6
fourth equation of	6
projection using reduction	6
a sir model	6
stability of disease	6
induced death rate	6
addition to the	6
to validate the	6
to be zero	6
the advantage of	6
at least of	6
have been taken	6
deep learning techniques	6
days from the	6
the corresponding author	6
point t n	6
with the same	6
of this work	6
this study are	6
model and its	6
behavioral change for	6
new mathematical model	6
numerical method for	6
of people in	6
the day of	6
to perform the	6
pandemic in pakistan	6
study on covid	6
characteristics of coronavirus	6
it is the	6
this is shown	6
the current covid	6
new training data	6
symptomatic and asymptomatic	6
of the key	6
estimates of the	6
suggested that the	6
be interpreted as	6
of health care	6
available in the	6
the disease has	6
for the three	6
to the fractional	6
taken from the	6
before pandemic lle	6
and recovered individuals	6
using reduction in	6
social distancing rule	6
to the infection	6
any of the	6
mathematical models in	6
spreading of covid	6
to flatten the	6
numerical scheme for	6
to quantify the	6
sir model to	6
in real time	6
pandemic apen variance	6
listed in table	6
in complex networks	6
the emergence of	6
mean of the	6
networks and the	6
depicted in fig	6
that represents the	6
the lipschitz condition	6
in each country	6
the construction of	6
satisfies the following	6
as an example	6
dynamics of infectious	6
reduction of the	6
considered as the	6
south africa and	6
flattening the curve	6
based on our	6
arima model is	6
disease in china	6
deaths and recovered	6
of mathematical modeling	6
the covid epidemic	6
will be applied	6
we show that	6
for all the	6
normalized forward sensitivity	6
disease transmission model	6
to curtail the	6
any time t	6
positive for all	6
fractional order sei	6
of severe acute	6
at a given	6
on th january	6
in india and	6
and references therein	6
the strict social	6
with the total	6
we have a	6
the infection in	6
for which the	6
it is known	6
italy and france	6
to fight against	6
deaths in the	6
of controlling covid	6
are detected and	6
of the caputo	6
in the infected	6
r for the	6
days between matches	6
there are two	6
is shown that	6
during pandemic lle	6
from chest x	6
the sarii q	6
so as to	6
of changing the	6
and the disease	6
public health measures	6
which is an	6
the solution is	6
the government of	6
in the estimated	6
the lack of	6
the disease persists	6
control in the	6
and asymptotically infected	6
as can be	6
order sei i	6
continuously evolving training	6
the change of	6
exponential growth of	6
that for the	6
has been applied	6
and governmental action	6
the order of	6
observed daily new	6
interventions such as	6
population of the	6
of infections and	6
used to predict	6
pandemic lle mean	6
focus on the	6
pandemic apen mean	6
infectious disease dynamics	6
in good agreement	6
pandemic lle variance	6
have shown that	6
the confirmed cases	6
of the whole	6
a new approach	6
pure birth process	6
for the development	6
individual reaction and	6
the fractional model	6
pandemic in india	6
appears to be	6
fight against the	6
the model are	6
of a delayed	6
from infection to	6
model from scratch	6
publicly available data	6
when r w	6
diagnosis of covid	6
first day of	6
endemic equilibrium is	6
the epidemics trend	6
johns hopkins university	6
disease transmission rate	6
fit to the	6
this is because	6
the null hypothesis	6
and its applications	6
individuals can be	6
the human body	6
causal variables that	6
of the manuscript	6
the efficacy of	6
interventions in italy	6
people increases with	6
for the parameters	6
birth and death	6
properties of the	6
forecasting of covid	6
from to a	6
the laplace transform	6
that the infection	6
the disease can	6
in a hospital	6
have the greatest	6
behaviour of the	6
and the effectiveness	6
individuals who are	6
on the transmission	6
has caused a	6
to protect themselves	6
the following expression	6
with the aim	6
susceptible population s	6
to carry out	6
and therefore the	6
in patients with	6
based forecasting model	6
algorithm for the	6
lle and apen	6
when the basic	6
differential equations of	6
modeling of covid	6
rate of change	6
the attack rate	6
overall number of	6
for the prediction	6
fractional derivative with	6
a system of	6
with the real	6
in the battle	6
like to thank	6
the magnitude of	6
the severity of	6
study of wuhan	6
approximate solution of	6
set is received	6
and recovery rate	6
that we can	6
we calculate the	6
epidemics trend of	6
wide interventions in	6
of the second	6
of epidemic diseases	6
the concept of	6
network model for	6
described in section	6
the point t	6
can be adjusted	6
reaction and governmental	6
weeks after the	6
local asymptotic stability	6
for the above	6
for the coronavirus	6
severity of the	6
we used the	6
mortality rate of	6
down the epidemic	6
of the countries	6
for time series	6
showed that the	6
integrating the second	6
the early stage	6
induced optimization problem	6
the proportion of	6
the infected class	6
the current pandemic	6
the estimated parameter	6
to be determined	6
various operating procedures	6
available data from	6
lead to an	6
are found to	6
infected individuals are	6
battle against the	6
the battle against	6
even if the	6
evolving training data	6
not consider the	5
the work of	5
there are some	5
purpose of this	5
better understanding of	5
consequence of the	5
model to explore	5
presented in fig	5
asymptomatic infectious to	5
for fractional differential	5
under the myopic	5
the idea of	5
the actual number	5
the fractional calculus	5
while the other	5
seir and ai	5
it possible to	5
global dynamics of	5
which an infected	5
fractional order epidemic	5
a fractional optimal	5
in the united	5
which is shown	5
prompt isolation of	5
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a model for	5
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short period of	5
infection of cd	5
segmented poisson model	5
persists in the	5
the problem of	5
we get the	5
the outbreaks of	5
liouville fractional derivative	5
beltrami operator of	5
for the period	5
responses are reported	5
backward bifurcation phenomenon	5
as the basic	5
communicated by the	5
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our model could	5
us consider the	5
contact with a	5
attack rate of	5
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the isolated slow	5
strategies to reduce	5
of infection and	5
complexity of the	5
be seen from	5
from scratch every	5
takes into account	5
on the nature	5
the model shows	5
output of the	5
masks in public	5
study the transmission	5
network in the	5
of these two	5
early stages of	5
machine learning and	5
endemic equilibrium w	5
of the solutions	5
of confirmed infected	5
of isolated individuals	5
population has been	5
on the mathematical	5
transmission of this	5
as the number	5
the virus has	5
dynamic model of	5
indicating that the	5
for the whole	5
transition density function	5
the public health	5
between the hosts	5
backward bifurcation in	5
we did not	5
let us denote	5
the per capita	5
of cases of	5
and the mean	5
and when r	5
the enhancement of	5
in this area	5
a model with	5
have a great	5
differential equations in	5
that the state	5
a new study	5
context of covid	5
model to forecast	5
to prove that	5
distancing rule is	5
coronavirus outbreak in	5
the most influential	5
the greatest potential	5
results are shown	5
higher compared to	5
the epidemic starts	5
using deep learning	5
the initial phase	5
techniques have been	5
countries and territories	5
of parameters in	5
should be done	5
longer period of	5
sum of the	5
overview of the	5
free equilibrium e	5
and only if	5
that increasing the	5
of the study	5
this strategy is	5
model is described	5
day by day	5
models in the	5
and the usa	5
have been developed	5
fractional differentiation on	5
to the pandemic	5
the curve of	5
pathogen from the	5
not be as	5
set to be	5
effective way of	5
the interaction radius	5
when the value	5
riesz wavelet systems	5
for this purpose	5
using the proposed	5
only way to	5
will eventually be	5
of more than	5
number of publications	5
is a new	5
during the first	5
presence of the	5
as there is	5
the rapid dissemination	5
vaccination and treatment	5
this is an	5
the lockdown effect	5
a deterministic model	5
can be achieved	5
are displayed in	5
fractional derivatives with	5
to sars coronavirus	5
under public health	5
editorial submission system	5
developed a mathematical	5
the informed individuals	5
the jacobian of	5
will reduce r	5
the spreading dynamics	5
comparison of the	5
is obtained from	5
probability of disease	5
evolution of covid	5
peak in the	5
to reduce social	5
was reported on	5
pneumonia of unknown	5
facilitates the rapid	5
infected population is	5
the genomic sequence	5
using mathematical models	5
differential equation model	5
the incidence data	5
is higher compared	5
where the number	5
from the outbreak	5
new cases of	5
with that of	5
reported in fig	5
parameters for the	5
sir model for	5
wuhan novel coronavirus	5
individuals which is	5
obtain this way	5
and capacity constraints	5
of reported cases	5
after implementing control	5
and sensitivity analysis	5
some of them	5
stability results of	5
the global asymptotic	5
infectious diseases and	5
with individual reaction	5
number of infectious	5
since there is	5
of the slow	5
that social distancing	5
for the simulation	5
infected country or	5
on complex networks	5
model is then	5
a plethora of	5
modelling the spread	5
of the two	5
wang et al	5
this model can	5
disease and to	5
equation of the	5
if and only	5
of vaccine failure	5
rise in the	5
as it is	5
manuscript has been	5
the host will	5
conclude that the	5
unquarantined asymptomatic infectious	5
or the other	5
critical model parameters	5
the mathematical modelling	5
motion on s	5
for the local	5
and reduce the	5
the treatment of	5
information diffusion and	5
in most of	5
economic and social	5
boundary value problem	5
existence of backward	5
of spread of	5
social distancing in	5
dynamics on the	5
than one sentence	5
it seems that	5
if r c	5
proposed sirsi model	5
fractional derivative of	5
covid epidemic in	5
class of asymptomatic	5
the vaccination behavior	5
set of asymptomatic	5
public health authorities	5
mathematical models for	5
been used in	5
and has been	5
infections and deaths	5
control strategies for	5
the epidemic duration	5
cases generated by	5
carried out by	5
the manuscript has	5
generation matrix method	5
the disease dynamics	5
solution to the	5
for different countries	5
mathematical model that	5
epidemic spreading process	5
this work is	5
the health system	5
likely to be	5
of the endemic	5
the virus will	5
will lead to	5
mean of apen	5
system of the	5
recovery rate of	5
details of the	5
clusters distributed as	5
used for this	5
the eigenvalues are	5
exponential increase in	5
convolutional neural networks	5
with the lockdown	5
of newly infected	5