32 research outputs found
Stability of a mathematical model of tumour-induced angiogenesis
A model consisting of three differential equations to simulate the interactions between cancer cells, the angiogenic factors and endothelial progenitor cells in tumor growth is developed. Firstly, the global existence, nonnegativity and boundedness of the solutions are discussed. Secondly, by analyzing the corresponding characteristic equations, the local stability of three boundary equilibria and the angiogenesis equilibrium of the model is discussed, respectively. We further consider global asymptotic stability of the boundary equilibria and the angiogenesis equilibrium by using the well-known Liapunov–LaSalle invariance principal. Finally, some numerical simulations are given to support the theoretical results
Dynamics of COVID-19 models with asymptomatic infections and quarantine measures
Considering the propagation characteristics of COVID-19 in different regions,
the dynamics analysis and numerical demonstration of long-term and short-term
models of COVID-19 are carried out, respectively. The long-term model is
devoted to investigate the global stability of COVID-19 model with asymptomatic
infections and quarantine measures. By using the limit system of the model and
Lyapunov function method, it is shown that the COVID-19-free equilibrium
is globally asymptotically stable if the control reproduction number
and globally attractive if , which means
that COVID-19 will die out; the COVID-19 equilibrium is globally
asymptotically stable if , which means that COVID-19 will be
persistent. In particular, to obtain the local stability of , we use
proof by contradiction and the properties of complex modulus with some novel
details, and we prove the weak persistence of the system to obtain the global
attractivity of . Moreover, the final size of the corresponding
short-term model is calculated and the stability of its multiple equilibria is
analyzed. Numerical simulations of COVID-19 cases show that quarantine measures
and asymptomatic infections have a non-negligible impact on the transmission of
COVID-19
Necessary and Sufficient Conditions of Oscillation in First Order Neutral Delay Differential Equations
We are concerned with oscillation of the first order neutral delay differential equation [x(t)−px(t−τ)]′+qx(t−σ)=0 with constant coefficients, and we obtain some necessary and sufficient conditions of oscillation for all the solutions in respective cases 01
Analysis of the current status of tuberculosis transmission in China based on a heterogeneity model
Tuberculosis (TB) is an infectious disease transmitted through the
respiratory system. China is one of the countries with a high burden of TB.
Since 2004, an average of more than 800,000 cases of active TB have been
reported each year in China. Analyzing the case data from 2004-2018, we find
significant differences in TB incidence by age group. Therefore, the effect of
age heterogeneous structure on TB transmission needs further study. We develop
a model of TB to explore the role of age heterogeneity as a factor in TB
transmission. The model is fitted numerically using the nonlinear least squares
method to obtain the key parameters in the model, and the basic reproduction
number Rv 0.8017 is calculated and the sensitivity anal-ysis of Rv to the
parameters is given. The simulation results show that reducing the number of
new infections in the elderly population and increasing the recovery rate of
elderly patients with the disease could significantly reduce the transmission
of tuberculosis. Furthermore the feasibility of achieving the goals of the WHO
End TB Strategy in China is assessed, and we obtain that with existing TB
control measures it will take another 30 years for China to reach the WHO goal
to reduce 90% of the number of new cases by year 2049. However, in theoretical
it is feasible to reach the WHO strategic goal of ending tuberculosis by 2035
if the group contact rate in the elderly population can be reduced though it is
difficulty to reduce the contact rate.Comment: We think this is a very interesting work that gives a good
understanding of the current TB transmission in China and assesses the
possibility of China achieving the 2035 TB control target and also explores
possible ways for how to prevent and control the TB in Chin
Blank peak current-suppressed electrochemical aptameric sensing platform for highly sensitive signal-on detection of small molecule
In this contribution, an electrochemical aptameric sensing scheme for the sensitive detection of small molecules is proposed using adenosine as a target model. A ferrocene (Fc)-functionalized thiolated aptamer probe is adapted and immobilized onto an electrode surface. Introducing a recognition site for EcoRI into the aptamer sequence not only suppresses the peak current corresponding to blank sample but also provides a signal-on response mechanism. In the absence of adenosine, the aptamer can fold into a hairpin structure and form a cleavable double-stranded region. Fc is capable of being removed from electrode surface by treatment with endonuclease, and almost no peak current is observed. The adenosine/aptamer binding induces the conformational transition of designed aptamer, dissociating the cleavable double-stranded segment. Therefore, the integrated aptamer sequence is maintained when exposing to endonuclease, generating a peak current of Fc. Utilizing the present sensing scheme, adenosine even at a low concentration can give a detectable current signal. Thus, a detection limit of 10−10 M and a linear response range from 3.74 × 10−9 to 3.74 × 10−5 M are achieved. The proposed proof-of-principle of a novel electrochemical sensing is expected to extend to establish various aptameric platforms for the analysis of a broad range of target molecules of interest
Dark energy model with higher derivative of Hubble parameter
In this letter we consider a dark energy model in which the energy density is
a function of the Hubble parameter and its derivative with respect to time
. The behavior of
the dark energy and the expansion history of the Universe depend heavily on the
parameters of the model , and . It is very interesting
that the age problem of the well-known three old objects can be alleviated in
this models.Comment: 11 pages, 6 figures, the correct version accepted for publication in
PL
A novel analysis approach of uniform persistence for a COVID-19 model with quarantine and standard incidence rate
A coronavirus disease 2019 (COVID-19) model with quarantine and standard
incidence rate is first developed, then a novel analysis approach for finding
the ultimate lower bound of COVID-19 infectious individuals is proposed, which
means that the COVID-19 pandemic is uniformly persistent if the control
reproduction number . This approach can be applied to other
related biomathematical models, and some existing works can be improved by
using it. In addition, the COVID-19-free equilibrium is locally
asymptotically stable (LAS) if and linearly stable if
, respectively; while is unstable if
.Comment: 13 pages, 1 figur
The surface geometry and shadow of a Schwarzschild black hole with halo
We have studied the surface geometry and shadows of Schwarzschild black hole
with a halo containing quadrupolar and octopolar terms. We found the event
horizon is prolate for the quadrupole strength , and it becomes
oblate for . The event horizon stretches downward for
. But for the case of , the event horizon
stretches upward. We found the radius of light rings in the space-time
of Schwarzschild black hole with halo only depends on the quadrupole strength
. The black hole shadow is oblate when the quadrupole strength
is larger than zero, and it is prolate when is less
than zero. Black hole shadow shifts upward when the octopolar strength
is less than zero, and shifts downward when is
larger than zero. From the observable width , height , oblateness and
distortion parameter of black hole shadow, one can determine the
quadrupole strength and the octopolar strength of
Schwarzschild black hole with halo. Black hole shadow is always a circle for
the observers with the inclination angle , and becomes bigger
with the increase of or . Our results show that the
quadrupolar and octopolar terms yield a series of interesting patterns for the
shadow of a Schwarzschild black hole with halo.Comment: 18 pages,11 figure
Necessary and sufficient conditions for oscillation of neutral delay differential equations
In this article, we concerned with oscillation of the neutral delay
differential equation with constant
coefficients. By constructing several suitable auxiliary functions,
we obtained some necessary and sufficient conditions for oscillation
of all the solutions of the aforementioned equation for the cases
and