scholarly journals Modelling immune system dynamics: the interaction of HIV and recombinant virus

2015 ◽  
Vol 56 ◽  
pp. 30-35
Author(s):  
Ugnė Jankauskaitė ◽  
Olga Štikonienė
Keyword(s):  
Mathematical Model ◽  
Immune System ◽  
Numerical Simulations ◽  
Recombinant Virus ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Hopf Bifurcations ◽  
Stability Switches ◽  
Discrete Delays ◽  
Theoretical Results

We investigate the dynamical behavior of a mathematical model of HIV and recombinant rabies virus (RV), designed to infect only the lymphocytes previously infected by HIV. This model is described by five ordinary differential equations with two discrete delays. The effect of two time delays on stability of the equilibria of the system has been studied. Stability switches and Hopf bifurcations when time delays cross through some critical values are found. Numerical simulations are performed to illustrate the theoretical results.

Time delays in proliferation process for solid avascular tumor under the action of external inhibitors

2015 ◽  
Vol 08 (02) ◽  
pp. 1550018
Author(s):  
Shihe Xu ◽  
Meng Bai
Keyword(s):  
Mathematical Model ◽  
Immune System ◽  
Tumor Growth ◽  
Medical Treatment ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Stationary Solutions ◽  
The Body ◽  
Parameter Values ◽  
Avascular Tumor

In this paper a delayed mathematical model for tumor growth under the action of external inhibitors is studied. The delay represents the time taken for cells to undergo mitosis. External inhibitor means that an inhibitor is either developed from the immune system of the body or administered by medical treatment to distinguish with that secreted by tumor itself. Non-negativity of solutions is studied. Local and global stabilities of the stationary solutions are proved for some parameter values. The analysis of the effect of inhibitor's parameters on tumor's growth is presented. The results show that dynamical behavior of solutions of this model is similar to that of solutions for corresponding nondelayed model for some parameter values.

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.

scholarly journals General fractional financial models of awareness with Caputo–Fabrizio derivative

2020 ◽  
Vol 12 (11) ◽  
pp. 168781402097552
Author(s):  
Amr MS Mahdy ◽  
Yasser Abd Elaziz Amer ◽  
Mohamed S Mohamed ◽  
Eslam Sobhy
Keyword(s):  
Mathematical Model ◽  
Fixed Point ◽  
Numerical Simulations ◽  
Caputo Derivative ◽  
Existence And Uniqueness ◽  
Financial Models ◽  
Whole Number ◽  
Fractional System ◽  
Set Up ◽  
Theoretical Results

A Caputo–Fabrizio (CF) form a fractional-system mathematical model for the fractional financial models of awareness is suggested. The fundamental attributes of the model are explored. The existence and uniqueness of the suggest fractional financial models of awareness solutions are given through the fixed point hypothesis. The non-number request subordinate gives progressively adaptable and more profound data about the multifaceted nature of the elements of the proposed partial budgetary models of mindfulness model than the whole number request models set up previously. In order to confirm the theoretical results and numerical simulations studies with Caputo derivative are offered.

INTERLEUKIN MATHEMATICAL MODEL OF AN IMMUNE SYSTEM

1995 ◽  
Vol 03 (03) ◽  
pp. 889-902 ◽  
Author(s):  
URSULA FORYS
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Immune System ◽  
Numerical Simulations ◽  
Basic Properties

Some generalizations of Marchuk's model of an infectious disease with respect to the role of interleukins are presented in this paper. Basic properties of the models are studied. Results of numerical simulations with different coefficients corresponding to the different forms of the disease are shown.

scholarly journals Bifurcation of a Cohen-Grossberg Neural Network with Discrete Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Qiming Liu ◽  
Wang Zheng
Keyword(s):  
Neural Network ◽  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Hopf Bifurcations ◽  
Bifurcation Parameter ◽  
Explicit Formulas ◽  
Global Hopf Bifurcation ◽  
Discrete Delays ◽  
Bifurcation And Stability

A simple Cohen-Grossberg neural network with discrete delays is investigated in this paper. The existence of local Hopf bifurcations is first considered by choosing the appropriate bifurcation parameter, and then explicit formulas are given to determine the direction of Hopf bifurcation and stability of the periodic solutions. Moreover, a set of sufficient conditions are given to guarantee the global Hopf bifurcation. Numerical simulations are given to illustrate the obtained results.

scholarly journals Hopf Bifurcation of a Mathematical Model for Growth of Tumors with an Action of Inhibitor and Two Time Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Bao Shi ◽  
Fangwei Zhang ◽  
Shihe Xu
Keyword(s):  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Time Delays ◽  
Cell Loss ◽  
Bifurcation Parameter ◽  
Discrete Delays

A mathematical model for growth of tumors with two discrete delays is studied. The delays, respectively, represent the time taken for cells to undergo mitosis and the time taken for the cell to modify the rate of cell loss due to apoptosis and kill of cells by the inhibitor. We show the influence of time delays on the Hopf bifurcation when one of delays is used as a bifurcation parameter.

Modeling Colorectal Cancer

2013 ◽  
pp. 53-75 ◽  
Author(s):  
Svetoslav Nikolov ◽  
Mukhtar Ullah ◽  
Momchil Nenov ◽  
Julio Vera Gonzalez ◽  
Peter Raasch ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Colorectal Cancer ◽  
Mathematical Model ◽  
Systems Biology ◽  
Numerical Simulations ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Extended Version ◽  
Necessary And Sufficient ◽  
The Mathematical Model

Mathematical modeling is increasingly used to improve our understanding of colorectal cancer. In the first part of this chapter, the authors give a review of systems biology approaches to investigate colorectal cancer. In the second part, the mathematical model proposed by Johnston et al. (2007) is expanded to include time delays and analysed for its stability. For both models, the original and the extended version, the authors obtain the necessary and sufficient conditions for stability. This is confirmed by numerical simulations. Thus, some new mathematical and biological results are obtained.

scholarly journals Dynamical Behavior of a Stochastic SIRC Model for Influenza A

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 745 ◽  
Author(s):  
Tongqian Zhang ◽  
Tingting Ding ◽  
Ning Gao ◽  
Yi Song
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Influenza A ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Stochastic Lyapunov Function

In this paper, a stochastic SIRC epidemic model for Influenza A is proposed and investigated. First, we prove that the system exists a unique global positive solution. Second, the extinction of the disease is explored and the sufficient conditions for extinction of the disease are derived. And then the existence of a unique ergodic stationary distribution of the positive solutions for the system is discussed by constructing stochastic Lyapunov function. Furthermore, numerical simulations are employed to illustrate the theoretical results. Finally, we give some further discussions about the system.

scholarly journals Analysis of a Stochastic Competitive Model with Distributed Time Delays and Jumps in a Polluted Environment

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Taolin Zhang ◽  
Yuanfu Shao ◽  
Xiaowan She
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Time Delays ◽  
Polluted Environment ◽  
Persistence In Mean ◽  
Distributed Time Delays ◽  
Competitive Model ◽  
Stability In Distribution ◽  
Lévy Jumps ◽  
Theoretical Results

In this paper, a stochastic competitive model with distributed time delays and Lévy jumps is formulated. With or without a polluted environment, the model is denoted by (M) or (M0), respectively. The existence of positive solution, persistence in mean, and extinction of species for (M) and (M0) are both studied. The sufficient criteria of stability in distribution for model (M) is obtained. Finally, some numerical simulations are given to illustrate our theoretical results.

Chaotic Dynamical Behavior of Coupled One-Dimensional Wave Equations

2021 ◽  
Vol 31 (06) ◽  
pp. 2150115
Author(s):  
Fei Wang ◽  
Junmin Wang ◽  
Zhaosheng Feng
Keyword(s):  
Numerical Simulations ◽  
Wave Equations ◽  
Dynamical Behavior ◽  
Chaotic Oscillation ◽  
Van Der Pol ◽  
Velocity Feedback ◽  
One Dimensional ◽  
Theoretical Results ◽  
Dimensional Wave

In this paper, we consider the chaotic oscillation of coupled one-dimensional wave equations. The symmetric nonlinearities of van der Pol type are proposed at the two boundary endpoints, which can cause the energy of the system to rise and fall within certain bounds. At the interconnected point of the wave equations, the energy is injected into the system through an anti-damping velocity feedback. We prove the existence of the snapback repeller when the parameters enter a certain regime, which causes the system to be chaotic. Numerical simulations are presented to illustrate our theoretical results.

Sign in / Sign up

Export Citation Format

Share Document