scholarly journals State-Dependent Pulse Vaccination and Therapeutic Strategy in an SI Epidemic Model with Nonlinear Incidence Rate

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Kaiyuan Liu ◽  
Tongqian Zhang ◽  
Lansun Chen
Keyword(s):  
Therapeutic Strategy ◽  
Equation Model ◽  
Pulse System ◽  
Pulse Vaccination ◽  
Stable Order ◽  
State Dependent ◽  
Asymptotical Stable ◽  
Homoclinic Cycle ◽  
Theoretical Results

In this paper, the state-dependent pulse vaccination and therapeutic strategy are considered in the control of the disease. A pulse system is built to model this process based on an SI ordinary differential equation model. At first, for the system neglecting the impulse effect, we give the classification of singular points. Then for the pulse system, by using the theory of the semicontinuous dynamic system, the dynamics is analyzed. Our analysis shows that the pulse system exhibits rich dynamics and the system has a unique order-1 homoclinic cycle, and by choosing p as the control parameter, the order-1 homoclinic cycle disappears and bifurcates an orbitally asymptotical stable order-1 periodic solution when p changes. Numerical simulations by maple 18 are carried out to illustrate the theoretical results.

scholarly journals A Delay Differential Equation Model of HIV Infection, with Therapy and CTL Response

2014 ◽  
Vol 9 ◽  
pp. 53-68 ◽  
Author(s):  
B. El Boukari ◽  
N. Yousfi
Keyword(s):  
Reproduction Number ◽  
Equation Model ◽  
Asymptotically Stable ◽  
Differential Equation Model ◽  
Globally Asymptotically Stable ◽  
Intracellular Delay ◽  
Immunodeficiency Virus ◽  
Delay Differential ◽  
Theoretical Results ◽  
Disease Free

In this work we investigate a new mathematical model that describes the interactions betweenCD4+ T cells, human immunodeficiency virus (HIV), immune response and therapy with two drugs.Also an intracellular delay is incorporated into the model to express the lag between the time thevirus contacts a target cell and the time the cell becomes actively infected. The model dynamicsis completely defined by the basic reproduction number R0. If R0 ≤ 1 the disease-free equilibriumis globally asymptotically stable, and if R0 > 1, two endemic steady states exist, and their localstability depends on value of R0. We show that the intracellular delay affects on value of R0 becausea larger intracellular delay can reduce the value of R0 to below one. Finally, numerical simulationsare presented to illustrate our theoretical results.

DYNAMICS OF A PREY-DEPENDENT DIGESTIVE MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL

2012 ◽  
Vol 22 (04) ◽  
pp. 1250092 ◽  
Author(s):  
LINNING QIAN ◽  
QISHAO LU ◽  
JIARU BAI ◽  
ZHAOSHENG FENG
Keyword(s):  
Numerical Simulations ◽  
Analytical Method ◽  
Impulsive Control ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Period Doubling ◽  
Lambert W Function ◽  
Impulsive Effect ◽  
State Dependent ◽  
Theoretical Results

In this paper, we study the dynamical behavior of a prey-dependent digestive model with a state-dependent impulsive effect. Using the Poincaré map and the Lambert W-function, we find the analytical expression of discrete mapping. Sufficient conditions are established for transcritical bifurcation and period-doubling bifurcation through an analytical method. Exact locations of these bifurcations are explored. Numerical simulations of an example are illustrated which agree well with our theoretical results.

Bioheat Transfer in a Branching Countercurrent Network During Hyperthermia

1989 ◽  
Vol 111 (4) ◽  
pp. 263-270 ◽  
Author(s):  
C. K. Charny ◽  
R. L. Levin
Keyword(s):  
Muscle Blood Flow ◽  
Equation Model ◽  
Bioheat Transfer ◽  
Tissue Temperature ◽  
Transfer Model ◽  
Temperature Profiles ◽  
The Mean ◽  
Pennes Model ◽  
Theoretical Results ◽  
Two Parameter

A bioheat transfer model which computes the spatial variations in the arteriole, venule, and muscle temperatures in a human extremity under both resting and hyperthermic conditions is presented. This model uses the two-parameter model first proposed by Baish et al. [2] to account for the heat exchange between tissue and the paired arterioles and venules that comprise the microcirculation. Thermoregulation of the muscle blood flow during hyperthermia is also incorporated into the model. Results show that even when the paired arteriole and venule are assumed to have equal radii, the mean temperature under both steady and transient conditions is not equal to the mean of the arteriole and venule blood temperatures. Tissue temperature profiles during hyperthermia computed with the three-equation model presented in this study are similar in shape and magnitude to those predicted by the traditional one-equation Pennes bioheat transfer model [1]. This is due primarily to the influence of thermoregulatory mechanism in the heated muscle. The unexpected agreement is significant given the inherent relative simplicity of the traditional Pennes model. An “experimental” thermal conductivity is presented to relate the theoretical results to experimental procedures that are widely used to estimate the enhancement of conductivity by perfusion.

scholarly journals Existence of Center for Planar Differential Systems with Impulsive Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Dengguo Xu
Keyword(s):  
Computing Methods ◽  
Impulsive Systems ◽  
Differential Systems ◽  
Numerical Examples ◽  
State Dependent ◽  
Planar Systems ◽  
Linear And Nonlinear ◽  
Impulsive Perturbations ◽  
The Stability ◽  
Theoretical Results

We present a method that uses successor functions in ordinary differential systems to address the “center-focus” problem of a class of planar systems that have an impulsive perturbation. By deriving solution formulae for impulsive systems, several interesting criteria for distinguishing between the center and the focus of linear and nonlinear planar systems with state-dependent impulsions are established. The conditions describing the stability of the focus of the considered models are also given. The computing methods presented here are more convenient for determining the center of impulsive systems than those in the literature. Numerical examples are given to show the effectiveness of the theoretical results.

scholarly journals Complete Periodic Synchronization of Memristor-Based Neural Networks with Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Huaiqin Wu ◽  
Luying Zhang ◽  
Sanbo Ding ◽  
Xueqing Guo ◽  
Lingling Wang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Matrix Theory ◽  
Adaptive Controller ◽  
Network System ◽  
Time Varying ◽  
State Dependent ◽  
Coincidence Theorem ◽  
Error System ◽  
Theoretical Results

This paper investigates the complete periodic synchronization of memristor-based neural networks with time-varying delays. Firstly, under the framework of Filippov solutions, by usingM-matrix theory and the Mawhin-like coincidence theorem in set-valued analysis, the existence of the periodic solution for the network system is proved. Secondly, complete periodic synchronization is considered for memristor-based neural networks. According to the state-dependent switching feature of the memristor, the error system is divided into four cases. Adaptive controller is designed such that the considered model can realize global asymptotical synchronization. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.

scholarly journals Dynamics of the Stochastic Belousov-Zhabotinskii Chemical Reaction Model

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 663
Author(s):  
Ying Yang ◽  
Daqing Jiang ◽  
Donal O’Regan ◽  
Ahmed Alsaedi
Keyword(s):  
Chemical Reaction ◽  
Existence And Uniqueness ◽  
Reaction Model ◽  
Equation Model ◽  
Asymptotically Stable ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Globally Asymptotically Stable ◽  
Chemical Reaction Model ◽  
Theoretical Results

In this paper, we discuss the dynamic behavior of the stochastic Belousov-Zhabotinskii chemical reaction model. First, the existence and uniqueness of the stochastic model’s positive solution is proved. Then we show the stochastic Belousov-Zhabotinskii system has ergodicity and a stationary distribution. Finally, we present some simulations to illustrate our theoretical results. We note that the unique equilibrium of the original ordinary differential equation model is globally asymptotically stable under appropriate conditions of the parameter value f, while the stochastic model is ergodic regardless of the value of f.

Ejector Refrigeration Cycles

2015 ◽  
pp. 1-35 ◽  
Author(s):  
Marek J Bergander
Keyword(s):  
Research Funding ◽  
Heat Pumps ◽  
Two Phase ◽  
Private Companies ◽  
Thermodynamic Cycles ◽  
The Us ◽  
Us Government ◽  
Air Conditioning Systems ◽  
Theoretical Results

This chapter describes a collaborative effort of US private companies and various departments of the US Government to investigate the possibility of improving the efficiency of HVAC systems by use of one and two-phase ejectors. It is anticipated that this technology, when fully developed will result in attractive, energy saving products that significantly improve the performance of commercial and residential chiller/air-conditioning systems, refrigeration plants, and heat pumps (geothermal and air-source). Although the literature describing ejector applications in refrigeration dates back to the year of 1900, the ejector use was always considered as controversial, because the previous research had resulted with only theoretical results and without visible, commercial products. The research on the ejector application is consistent with present directions in the HVAC industry and it will attract more attention and research funding in the future. A classification of thermodynamic cycles where ejectors can be applied composed by three distinctive “categories” is suggested.

Recognition of singularities of rectifying worldsheets generated by framed worldlines

2021 ◽  
Vol 36 (23) ◽  
pp. 2150172
Author(s):  
Hongyu Guo ◽  
Siyao Liu ◽  
Zhigang Wang ◽  
Haiming Liu
Keyword(s):  
Finite Type ◽  
Topological Structures ◽  
Detailed Classification ◽  
Cuspidal Edge ◽  
Theoretical Results

In this paper, we consider the local topological structures of a class of new worldsheets, call it the rectifying worldsheets, which are generated by a class of singular worldlines. Using the classification approaches of the finite type on the tangent developables and defining the extended striction curve, this paper gives the detailed classification of the rectifying worldsheets of singular worldlines. It is demonstrated that the rectifying worldsheets of singular worldlines will appear not only in cuspidal edge and swallowtail, but cuspidal beaks under suitable conditions. Especially the singularities of rectifying worldsheets of singular worldlines are associated with curvature functions such that the singularities can be characterized by these functions. Two examples are provided to put the theoretical results into the practice of computation and classification.

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