The differential infectivity and staged progression models for the transmission of HIV

Hyman, James M.; Li, Jia; Stanley, E. Ann

doi:10.1016/s0025-5564(98)10057-3

Cited by 254 publications

(170 citation statements)

References 35 publications

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“…, then R 0 gives the basic reproduction number for the standard incidence as in [11,20,22], while if α = 0, R 0 gives the basic reproduction number for the bilinear incidence. We note that the basic reproduction number for a class of finite-stage SP models with a general distribution function for the infectious periods was derived in [4].…”

Section: Impacts Of Amelioration On the Basic Reproduction Numbermentioning

confidence: 99%

“…Staged-progression (SP) models have been formulated in the literature to investigate variability of infectivity during the progression of HIV infection [1,4,6,8,9,11,12,18,19,20,21]. In [11], SP models using ordinary differential equations were derived.…”

Section: Introductionmentioning

confidence: 99%

“…In [11], SP models using ordinary differential equations were derived. In [4], SP models with general distribution functions were formulated, and the models are described by systems of differentialintegral equations.…”

Section: Introductionmentioning

confidence: 99%

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Global dynamics of a staged-progression model with amelioration for infectious diseases

Guo

Li²

2008

Journal of Biological Dynamics

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We analyze the global dynamics of a mathematical model for infectious diseases that progress through distinct stages within infected hosts with possibility of amelioration. An example of such diseases is HIV/AIDS that progresses through several stages with varying degrees of infectivity; amelioration can result from a host's immune action or more commonly from antiretroviral therapies, such as highly active antiretroviral therapy. For a general n-stage model with constant recruitment and bilinear incidence that incorporates amelioration, we prove that the global dynamics are completely determined by the basic reproduction number R 0 . If R 0 ≤ 1, then the disease-free equilibrium P 0 is globally asymptotically stable, and the disease always dies out. If R 0 > 1, P 0 is unstable, a unique endemic equilibrium P * is globally asymptotically stable, and the disease persists at the endemic equilibrium. Impacts of amelioration on the basic reproduction number are also investigated.

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Section: Impacts Of Amelioration On the Basic Reproduction Numbermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Global dynamics of a staged-progression model with amelioration for infectious diseases

Guo

Li²

2008

Journal of Biological Dynamics

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“…An SIAS model in a population of constant size considered by Cooke and the sharp threshold was found in [4]. Hyman et al [9] introduced a DI model with dissimilar groups of infective individuals. There are some models which combine DI and susceptibility [8].…”

Section: Introductionmentioning

confidence: 99%

Global analysis of an SAIS model

Razvan

Yasaman

2012

Journal of Biological Dynamics

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This paper is concerned with global analysis of an SAIS epidemiological model in a population of varying size introduced by Busenberg and van den Driessche. In this model the population is divided into three subgroups of susceptible, asymptomatic and infective individuals. It has been shown that this system has no periodic solutions and all its trajectories tend to the equilibria of the system. We use the Poincaré Index theorem to determine the number of the equilibria and their stability properties. We have shown that bistability occurs for suitable values of parameters and found a set of examples of all possible dynamics of the system.

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“…The dynamics of infectious diseases in a closed population is a well known topic in the literature [1][2][3][4][5]. These models are commonly classified using the prefixes SIR and SEIR.…”

Section: Introductionmentioning

confidence: 99%

Time delay in non-lethal infectious diseases

2012

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The effects of the incubation period q on the dynamics of non-lethal infectious diseases in a fixed-size population are studied by means of a delay differential equation model. It is noted that the ratio between the quantity q and the time τ for recovering from the illness plays an important role in the onset of the epidemic breakthrough. An approximate analytic expression for the solution of the delay differential equation governing the dynamics of the system is proposed and a comparison is made with the classical SEIR model.

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The differential infectivity and staged progression models for the transmission of HIV

Cited by 254 publications

References 35 publications

Global dynamics of a staged-progression model with amelioration for infectious diseases

Global dynamics of a staged-progression model with amelioration for infectious diseases

Global analysis of an SAIS model

Time delay in non-lethal infectious diseases

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