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In this paper, we investigate the dynamics of a five-dimensional virus model with immune responses and an intracellular delay which describes the interactions of the HIV virus, CD4 cells and CTLs within host, which is an improvement of some existing models by incorporating (i) two distributed kernels reflecting the variance of time for virus to invade into… (More)

In this paper, by extending well-known Lyapunov function techniques, we establish sufficient conditions for the global stability of an endemic equilibrium of a multi-group SIRS epidemic model with varying population sizes which has cross patch infection between different groups. Our proof no longer needs such a grouping technique by graph theory commonly… (More)

>IJH=?J In this paper, we study the long-time behavior of a nonautonomous SEIRS epidemic model. We obtain new sucient conditions for the permanence (uniform persistence) and extinction of infectious population of the model. By numerical examples we show that there are cases such that our results improve the previous results obtained in [T. We discuss a… (More)

In this paper, applying Lyapunov functional approach, we establish sufficient conditions under which each equilibrium is globally asymptotically stable for a class of multi-group SIR epidemic models. The incidence rate is given by nonlinear incidence rates and distributed delays incorporating not only an exchange of individuals between patches through… (More)

Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the… (More)

In mathematical epidemiology, age-structured epidemic models have usually been formulated as the boundary-value problems of the partial differential equations. On the other hand, in engineering, the backstepping method has recently been developed and widely studied by many authors. Using the backstepping method, we obtained a boundary feedback control which… (More)

- Jinliang Wang, Ran Zhang, Toshikazu Kuniya
- 2015

In this article, we study a continuous age-structured HIV infection model. For the case of the saturation infection rate, the basic reproduction number 0 is shown to be a sharp threshold value for the global dynamics; that is, the infection-free equilibrium is globally stable if 0 < 1, while a unique infection equilibrium is so if 0 > 1. For the proof, we… (More)

In this paper, we formulate an SIR epidemic model with hybrid of multigroup and patch structures, which can be regarded as a model for the geographical spread of infectious diseases or a multi-group model with perturbation. We show that if a threshold value, which corresponds to the well-known basic reproduction number R0, is less than or equal to unity,… (More)