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1.
An HIV/AIDS epidemic model with different latent stages and treatment is constructed. The model allows for the latent individuals to have the slow and fast latent compartments. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are determined by the basic reproduction number under some conditions. If R0 < 1, the disease free equilibrium is globally asymptotically stable, and if R0 > 1, the endemic equilibrium is globally asymptotically stable for a special case. Some numerical simulations are also carried out to confirm the analytical results.  相似文献   

2.
In this paper, we investigate a Vector‐Borne disease model with nonlinear incidence rate and 2 delays: One is the incubation period in the vectors and the other is the incubation period in the host. Under the biologically motivated assumptions, we show that the global dynamics are completely determined by the basic reproduction number R0. The disease‐free equilibrium is globally asymptotically stable if R0≤1; when R0>1, the system is uniformly persistent, and there exists a unique endemic equilibrium that is globally asymptotically. Numerical simulations are conducted to illustrate the theoretical results.  相似文献   

3.
In this paper, the global stability of a virus dynamics model with intracellular delay, Crowley–Martin functional response of the infection rate, and CTL immune response is studied. By constructing suitable Lyapunov functions and using LaSalles invariance principle, the global dynamics is established; it is proved that if the basic reproductive number, R0, is less than or equal to one, the infection‐free equilibrium is globally asymptotically stable; if R0 is more than one, and if immune response reproductive number, R0, is less than one, the immune‐free equilibrium is globally asymptotically stable, and if R0 is more than one, the endemic equilibrium is globally asymptotically stable. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

4.
A virus infection model with time delays and humoral immunity has been investigated. Mathematical analysis shows that the global dynamics of the model is fully determined by the basic reproduction numbers of the virus and the immune response, R0 and R1. The infection‐free equilibrium P0 is globally asymptotically stable when R0≤1. The infection equilibrium without immunity P1 is globally asymptotically stable when R1≤1 < R0. The infection equilibrium with immunity P2 is globally asymptotically stable when R1>1. The expression of the basic reproduction number of the immune response R1 implies that the immune response reduces the concentration of free virus as R1>1. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

5.
In this paper, applying Lyapunov functional techniques to nonresident computer virus models, we establish global dynamics of the model whose threshold parameter is the basic reproduction number R0 such that the virus‐free equilibrium is globally asymptotically stable when R0 ≤ 1, and the infected equilibrium is globally asymptotically stable when R0 > 1 under the same restricted condition on a parameter, which appeared in the literature on delayed susceptible‐infected‐recovered‐susceptible (SIRS) epidemic models. We use new techniques on permanence and global stability of this model for R0 > 1. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

6.
In this paper, we study a virus dynamics model with logistic mitosis, cure rate, and intracellular delay. By means of construction of a suitable Lyapunov functionals, obtained by linear combinations of Volterra—type functions, composite quadratic functions and Volterra—type functionals, we provide the global stability for this model. If R0, the basic reproductive number, satisfies R0 ≤ 1, then the infection‐free equilibrium state is globally asymptotically stable. Our system is persistent if R0 > 1. On the other hand, if R0 > 1, then infection‐free equilibrium becomes unstable and a unique infected equilibrium exists. The local stability analysis is carried out for the infected equilibrium, and it is shown that, if the parameters satisfy a condition, the infected equilibrium can be unstable and a Hopf bifurcation can occur. We also have that if R0 > 1, then the infected equilibrium state is globally asymptotically stable if a sufficient condition is satisfied. We illustrate our findings with some numerical simulations. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

7.
In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. The model has two distributed time delays describing time needed for infection of cell and virus replication. Our model admits three possible equilibria, an uninfected equilibrium and infected equilibrium with or without immune response depending on the basic reproduction number for viral infection R0 and for CTL response R1 such that R1<R0. It is shown that there always exists one equilibrium which is globally asymptotically stable by employing the method of Lyapunov functional. More specifically, the uninfected equilibrium is globally asymptotically stable if R0?1, an infected equilibrium without immune response is globally asymptotically stable if R1?1<R0 and an infected equilibrium with immune response is globally asymptotically stable if R1>1. The immune activation has a positive role in the reduction of the infection cells and the increasing of the uninfected cells if R1>1.  相似文献   

8.
We investigate a class of multi-group epidemic models with distributed delays. We establish that the global dynamics are completely determined by the basic reproduction number R0. More specifically, we prove that, if R0?1, then the disease-free equilibrium is globally asymptotically stable; if R0>1, then there exists a unique endemic equilibrium and it is globally asymptotically stable. Our proof of global stability of the endemic equilibrium utilizes a graph-theoretical approach to the method of Lyapunov functionals.  相似文献   

9.
This paper considers an epidemic model of a vector-borne disease which has direct mode of transmission in addition to the vector-mediated transmission. The incidence term is assumed to be of the bilinear mass-action form. We include both a baseline ODE version of the model, and, a differential-delay model with a discrete time delay. The ODE model shows that the dynamics is completely determined by the basic reproduction number R0. If R0?1, the disease-free equilibrium is globally stable and the disease dies out. If R0>1, a unique endemic equilibrium exists and is locally asymptotically stable in the interior of the feasible region. The delay in the differential-delay model accounts for the incubation time the vectors need to become infectious. We study the effect of that delay on the stability of the equilibria. We show that the introduction of a time delay in the host-to-vector transmission term can destabilize the system and periodic solutions can arise through Hopf bifurcation.  相似文献   

10.
Control of epidemic infections is a very urgent issue today. To develop an appropriate strategy for vaccinations and effectively prevent the disease from arising and spreading, we proposed a modified Susceptible‐Infected‐Removed model with impulsive vaccinations. For the model without vaccinations, we proved global stability of one of the steady states depending on the basic reproduction number R0. As typically in the epidemic models, the threshold value of R0 is 1. If R0 is greater than 1, then the positive steady state called endemic equilibrium exists and is globally stable, whereas for smaller values of R0, it does not exist, and the semi‐trivial steady state called disease‐free equilibrium is globally stable. Using impulsive differential equation comparison theorem, we derived sufficient conditions under which the infectious disease described by the considered model disappears ultimately. The analytical results are illustrated by numerical simulations for Hepatitis B virus infection that confirm the theoretical possibility of the infection elimination because of the proper vaccinations policy. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

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