Analysis of An Age-Infection-Structured HIV Model With Impulsive Finding

2021 ◽  
Vol 67 (6) ◽  
pp. 21-26
Author(s):  
Yongle Fu
Keyword(s):  
Hiv Model

A note of a staged progression HIV model with imperfect vaccine

2014 ◽  
Vol 234 ◽  
pp. 412-416 ◽  
Author(s):  
Liming Cai ◽  
Bin Fang ◽  
Xuezhi Li
Keyword(s):  
Hiv Model

scholarly journals Modelling HIV dynamics with cell-to-cell transmission and CTL response

2021 ◽  
Author(s):  
Zirui Zhu ◽  
Ranchao Wu ◽  
Yu Yang ◽  
Yancong Xu
Keyword(s):  
Hopf Bifurcation ◽  
Cell Interaction ◽  
Backward Bifurcation ◽  
Hiv Treatment ◽  
Hiv Model ◽  
Ctl Response ◽  
Hiv Dynamics ◽  
Subcritical Hopf Bifurcation ◽  
Cell Transmission ◽  
New Type

In most HIV models, the emergence of backward bifurcation means that the control for basic reproduction number less than one is no longer effective for HIV treatment. In this paper, we study an HIV model with CTL response and cell-to-cell transmission by using the dynamical approach. The local and global stability of equilibria is investigated, the relations of subcritical Hopf bifurcation and supercritical bifurcation points are revealed, especially, the so-called new type bifurcation is also found with two Hopf bifurcation curves meeting at the same Bogdanov-Takens bifurcation point. Forward and backward bifurcation, Hopf bifurcation, saddle-node bifurcation, Bogdanov-Takens bifurcation are investigated analytically and numerically. Two limit cycles are also found numerically, which indicates that the complex behavior of HIV dynamics. Interestingly, the role of cell-to-cell interaction is fully uncovered, it may cause the oscillations to disappear and keep the so-called new type bifurcation persist. Finally, some conclusions and discussions are also given.

scholarly journals A Partial Lagrangian Approach to Mathematical Models of Epidemiology

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
R. Naz ◽  
I. Naeem ◽  
F. M. Mahomed
Keyword(s):  
Mathematical Models ◽  
Exact Solutions ◽  
Numerical Solutions ◽  
First Integrals ◽  
Order Equation ◽  
Second Order ◽  
Lagrangian Approach ◽  
Hiv Model ◽  
First Order ◽  
Partial Lagrangian

This paper analyzes the first integrals and exact solutions of mathematical models of epidemiology via the partial Lagrangian approach by replacing the three first-order nonlinear ordinary differential equations by an equivalent system containing one second-order equation and a first-order equation. The partial Lagrangian approach is then utilized for the second-order ODE to construct the first integrals of the underlying system. We investigate the SIR and HIV models. We obtain two first integrals for the SIR model with and without demographic growth. For the HIV model without demography, five first integrals are established and two first integrals are deduced for the HIV model with demography. Then we utilize the derived first integrals to construct exact solutions to the models under investigation. The dynamic properties of these models are studied too. Numerical solutions are derived for SIR models by finite difference method and are compared with exact solutions.

Sign in / Sign up

Export Citation Format

Share Document