scholarly journals Threshold dynamics of a time-delayed hantavirus infection model in periodic environments

2019 ◽  
Vol 16 (5) ◽  
pp. 4758-4776
Author(s):  
Junli Liu ◽  
Keyword(s):  
Hantavirus Infection ◽  
Infection Model ◽  
Threshold Dynamics ◽  
Periodic Environments

scholarly journals Threshold dynamics and threshold analysis of HIV infection model with treatment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Zhimin Chen ◽  
Xiuxiang Liu ◽  
Liling Zeng
Keyword(s):  
Hiv Infection ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Threshold Dynamics ◽  
Positive Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Immunodeficiency Virus ◽  
Hiv Infection Model

Abstract In this paper, a human immunodeficiency virus (HIV) infection model that includes a protease inhibitor (PI), two intracellular delays, and a general incidence function is derived from biologically natural assumptions. The global dynamical behavior of the model in terms of the basic reproduction number $\mathcal{R}_{0}$ R 0 is investigated by the methods of Lyapunov functional and limiting system. The infection-free equilibrium is globally asymptotically stable if $\mathcal{R}_{0}\leq 1$ R 0 ≤ 1 . If $\mathcal{R}_{0}>1$ R 0 > 1 , then the positive equilibrium is globally asymptotically stable. Finally, numerical simulations are performed to illustrate the main results and to analyze thre effects of time delays and the efficacy of the PI on $\mathcal{R}_{0}$ R 0 .

DYNAMICS OF A NON-AUTONOMOUS HIV-1 INFECTION MODEL WITH DELAYS

2013 ◽  
Vol 06 (05) ◽  
pp. 1350030 ◽  
Author(s):  
XIA WANG ◽  
SHENGQIANG LIU ◽  
XINYU SONG
Keyword(s):  
Time Delays ◽  
Oscillation Theory ◽  
Threshold Value ◽  
Infection Model ◽  
Threshold Dynamics ◽  
Homeostatic Proliferation ◽  
Varying Coefficients ◽  
Analysis Theory ◽  
Constant Coefficients ◽  
Hiv 1

In this paper, following a previous paper ([32] Permanence and extinction of a non-autonomous HIV-1 model with two time delays, preprint) on the permanence and extinction of a delayed non-autonomous HIV-1 within-host model, we introduce and investigate a delayed HIV-1 model including maximum homeostatic proliferation rate of CD4+T-cells and varying coefficients. By applying the asymptotic analysis theory and oscillation theory, we show: (i) the system will be permanent when the threshold value R*> 1, and for this case we also obtain the explicit estimate of the eventual lower bound of the HIV-1 virus load; (ii) the threshold value R* < 1 implies the extinction of the virus. Furthermore, we obtain that the threshold dynamics is in agreement with that of the corresponding autonomous system, which extends the classic results for the system with constant coefficients. Numerical simulations are also given to illustrate our main results, and in particular, some sensitivity test of R*is established.

Shifted Boubaker Lagrangian approach for solving biological systems

2018 ◽  
Vol 11 (03) ◽  
pp. 1850039 ◽  
Author(s):  
Kourosh Parand ◽  
Hossein Yousefi ◽  
Mina Fotouhifar ◽  
Mehdi Delkhosh ◽  
Mehdi Hosseinzadeh
Keyword(s):  
Mathematical Models ◽  
Hantavirus Infection ◽  
Infection Model ◽  
Algebraic Equations ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Immunodeficiency Virus ◽  
Nonlinear Algebraic Equations ◽  
Newton Iteration Method ◽  
Hiv Infection Model

Mathematical models and computer simulations are useful experimental tools for building and testing theories. Many mathematical models in biology can be formulated by a nonlinear system of ordinary differential equations. This work deals with the numerical solution of the hantavirus infection model, the human immunodeficiency virus (HIV) infection model of CD4[Formula: see text]T cells and the susceptible–infected–removed (SIR) epidemic model using a new reliable algorithm based on shifted Boubaker Lagrangian (SBL) method. This method reduces the solution of such system to a system of linear or nonlinear algebraic equations which are solved using the Newton iteration method. The obtained results of the proposed method show highly accurate and valid for an arbitrary finite interval. Also, those are compared with fourth-order Runge–Kutta (RK4) method and with the solutions obtained by some other methods in the literature.

scholarly journals Global dynamics of a stage-structured hantavirus infection model with seasonality

2021 ◽  
Vol 26 (1) ◽  
pp. 21-40
Author(s):  
Junli Liu ◽  
Tailei Zhang
Keyword(s):  
Periodic Solution ◽  
Control Strategies ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Clethrionomys Glareolus ◽  
Hantavirus Infection ◽  
Infection Model ◽  
Global Dynamics ◽  
Periodic Model ◽  
Globally Attractive

In this paper, we study a time-periodic model, which incorporates seasonality and host stage-structure. This model describes the propagation of Puumala hantavirus within the bank vole population of Clethrionomys glareolus. The basic reproduction number R0 is obtained. By appealing to the theory of monotone dynamical systems and chain transitive sets, we establish a threshold-type result on the global dynamics in terms of R0, that is, the virus-free periodic solution is globally attractive, and the virus dies out if R0 ≤ 1, while there exists a unique positive periodic solution, which is globally attractive, and the virus persists if R0 > 1. Numerical simulations are given to confirm our theoretical results and to show that cleaning environment and controlling the grow of mice population are essential control strategies to reduce hantavirus infection.

Dynamical Analysis of a Fractional-Order Hantavirus Infection Model

2020 ◽  
Vol 21 (2) ◽  
pp. 171-181 ◽  
Author(s):  
Mahmoud Moustafa ◽  
Mohd Hafiz Mohd ◽  
Ahmad Izani Ismail ◽  
Farah Aini Abdullah
Keyword(s):  
Fractional Order ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Fractional Order System ◽  
Order System ◽  
Logistic Growth ◽  
Hantavirus Infection ◽  
Infection Model ◽  
The Impact

AbstractThis paper considers a Hantavirus infection model consisting of a system of fractional-order ordinary differential equations with logistic growth. The fractional-order model describes the spread of Hantavirus infection in a system consisting of a population of susceptible and infected mice. The existence, uniqueness, non-negativity and boundedness of the solutions are established. In addition, the local and global asymptotic stability of the equilibrium points of the fractional order system and the basic reproduction number are studied. The impact of basic reproduction number and carrying capacity on the stability of the fractional order system are also theoretically and numerically investigated.

scholarly journals Threshold Dynamics of an HIV-TB Co-infection Model with Multiple Time Delays

2021 ◽  
Vol 53 ◽  
Author(s):  
M. Pitchaimani ◽  
A. Saranya Devi
Keyword(s):  
Basic Reproduction Number ◽  
Time Delays ◽  
Reproduction Number ◽  
Numerical Study ◽  
Single Infection ◽  
Infection Model ◽  
Threshold Dynamics ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
The Basic Reproduction Number

In this article, a mathematical model to study the dynamics ofHIV-TB co-infection with two time delays is proposed and analyzed.We compute the basic reproduction number for each disease (HIV andTB) which acts as a threshold parameters. The disease dies out whenthe basic reproduction number of both diseases are less than unityand persists when the basic reproduction number of atleast one of thedisease is greater than unity. A numerical study on the model is alsoperformed to investigate the influence of certain key parameters on thespread of the disease. Mathematical analysis of our model shows thatswitching co-infection (HIV and TB) to single infection (HIV) can beachieved by imposing treatment for both the disease simultaneouslyas TB eradication is made possible with effective treatment.

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