scholarly journals Global Stability of an HIV-1 Infection Model with General Incidence Rate and Distributed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Abdoul Samba Ndongo ◽  
Hamad Talibi Alaoui
Keyword(s):  
Incidence Rate ◽  
Viral Entry ◽  
Disease Transmission ◽  
Transmission Function ◽  
Infection Model ◽  
Global Dynamics ◽  
General Incidence Rate ◽  
Delay Differential ◽  
Hiv 1 ◽  
Intracellular Delays

In this work an HIV-1 infection model with nonlinear incidence rate and distributed intracellular delays and with humoral immunity is investigated. The disease transmission function is assumed to be governed by general incidence rate f(T,V)V. The intracellular delays describe the time between viral entry into a target cell and the production of new virus particles and the time between infection of a cell and the emission of viral particle. Lyapunov functionals are constructed and LaSalle invariant principle for delay differential equation is used to establish the global asymptotic stability of the infection-free equilibrium, infected equilibrium without B cells response, and infected equilibrium with B cells response. The results obtained show that the global dynamics of the system depend on both the properties of the general incidence function and the value of certain threshold parameters R0 and R1 which depends on the delays.

GLOBAL DYNAMICS OF A DELAYED HIV-1 INFECTION MODEL WITH ABSORPTION AND SATURATION INFECTION

2012 ◽  
Vol 05 (03) ◽  
pp. 1260012 ◽  
Author(s):  
RUI XU
Keyword(s):  
Viral Entry ◽  
Chronic Infection ◽  
Infection Model ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Basic Reproduction Ratio ◽  
Globally Asymptotically Stable ◽  
Reproduction Ratio ◽  
Virus Particles ◽  
Hiv 1

In this paper, an HIV-1 infection model with absorption, saturation infection and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is investigated. By analyzing the characteristic equations, the local stability of an infection-free equilibrium and a chronic-infection equilibrium of the model is established. By using suitable Lyapunov functionals and LaSalle's invariance principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable; and if the basic reproduction ratio is greater than unity, sufficient condition is derived for the global stability of the chronic-infection equilibrium.

scholarly journals Global Stability of HIV-1 Infection Model with Two Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hui Miao ◽  
Xamxinur Abdurahman ◽  
Ahmadjan Muhammadhaji
Keyword(s):  
Immune Response ◽  
Delay Differential Equations ◽  
Time Delays ◽  
Infection Model ◽  
Global Dynamics ◽  
Response Model ◽  
Delay Differential ◽  
Ctl Immune Response ◽  
Hiv 1

We investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. The model has two time delays describing time needed for infection of cell and CTLs generation. Our model admits three possible equilibria: infection-free equilibrium, CTL-absent infection equilibrium, and CTL-present infection equilibrium. The effect of time delay on stability of the equilibria of the CTL immune response model has been studied.

GLOBAL DYNAMICS OF AN IN-HOST HIV-1 INFECTION MODEL WITH THE LONG-LIVED INFECTED CELLS AND FOUR INTRACELLULAR DELAYS

2012 ◽  
Vol 05 (06) ◽  
pp. 1250058 ◽  
Author(s):  
SHIFEI WANG ◽  
YICANG ZHOU
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Infection Model ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Infected Cells ◽  
Hiv 1 ◽  
Intracellular Delays ◽  
The Basic Reproduction Number

In this paper, we investigate global dynamics for an in-host HIV-1 infection model with the long-lived infected cells and four intracellular delays. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. We derive that the global dynamics are completely determined by the values of the basic reproduction number: if the basic reproduction number is less than one, the uninfected equilibrium is globally asymptotically stable, and the virus is cleared; if the basic reproduction number is larger than one, then the infection persists, and the infected equilibrium is globally asymptotically stable.

scholarly journals Global dynamics and bifurcation analysis of a fractional-order SEIR epidemic model with saturation incidence rate

2021 ◽  
Author(s):  
Parvaiz Ahmad Naik ◽  
Muhammad Bilal Ghori ◽  
Jian Zu ◽  
Zohre Eskandari ◽  
Mehraj-ud-din Naik
Keyword(s):  
Incidence Rate ◽  
Fractional Order ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Disease Status ◽  
Host Population ◽  
Sensitivity Analyses ◽  
Feasible Region ◽  
Global Dynamics ◽  
Globally Stable

The present paper studies a fractional-order SEIR epidemic model for the transmission dynamics of infectious diseases such as HIV and HBV that spreads in the host population. The total host population is considered bounded, and Holling type-II saturation incidence rate is involved as the infection term. Using the proposed SEIR epidemic model, the threshold quantity, namely basic reproduction number R0, is obtained that determines the status of the disease, whether it dies out or persists in the whole population. The model’s analysis shows that two equilibria exist, namely, disease-free equilibrium (DFE) and endemic equilibrium (EE). The global stability of the equilibria is determined using a Lyapunov functional approach. The disease status can be verified based on obtained threshold quantity R0. If R0 < 1, then DFE is globally stable, leading to eradicating the population’s disease. If R0 > 1, a unique EE exists, and that is globally stable under certain conditions in the feasible region. The Caputo type fractional derivative is taken as the fractional operator. The bifurcation and sensitivity analyses are also performed for the proposed model that determines the relative importance of the parameters into disease transmission. The numerical solution of the model is obtained by the generalized Adams- Bashforth-Moulton method. Finally, numerical simulations are performed to illustrate and verify the analytical results.

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