A time delay model about AIDS-related cancer: equilibria, cycles and chaotic behavior

Lou, Jie; Ruggeri, Tommaso

doi:10.1007/s11587-007-0013-6

Cited by 18 publications

(12 citation statements)

References 14 publications

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“…The time delays are also often introduced to the systems describing the avascular tumour growth [14,15,[35][36][37][38][39][40][41] or HIV-related tumour growth models [42][43][44][45].…”

Section: Discussionmentioning

confidence: 99%

Analysis of the Hopf bifurcation for the family of angiogenesis models

Piotrowska

Foryś

2011

Journal of Mathematical Analysis and Applications

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In this paper we study a family of models with delays describing the process of angiogenesis, that is a physiological process involving the growth of new blood vessels from pre-existing ones. This family includes the well-known models of tumour angiogenesis proposed by Hahnfeldt et al. and d'Onofrio-Gandolfi and is based on the Gompertz type of the tumour growth. As a consequence we start our analysis from the influence of delay onto the Gompertz model dynamics. The family of models considered in this paper depends on two time delays and a parameter α ∈ [0, 1] which reflects how strongly the vessels dynamics depends on the ratio between tumour and vessels volume. We focus on the analysis of the model in three cases: one of the delays is equal to 0 or both delays are equal, depending on the parameter α. We study the stability switches, the Hopf bifurcation and the stability of arising periodic orbits for different α ∈ [0, 1], especially for α = 1 and α = 0 which reflects the Hahnfeldt et al. and the d'Onofrio-Gandolfi models. For comparison we use also the value α = 1/2.

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“…The time delays are also often introduced to the systems describing the avascular tumour growth [14,15,[35][36][37][38][39][40][41] or HIV-related tumour growth models [42][43][44][45].…”

Section: Discussionmentioning

confidence: 99%

Analysis of the Hopf bifurcation for the family of angiogenesis models

Piotrowska

Foryś

2011

Journal of Mathematical Analysis and Applications

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“…Tumour growth patterns in HIV‐infected people have also been considered a hot research topic for the last few years. As mentioned above, there is a higher risk for HIV‐infected patients for developing certain types of cancer . de Pillis et al propose a mathematical model to describe cancer growth, on a cell population level, with combination immune, vaccine, and chemotherapy treatments.…”

Section: Introductionmentioning

confidence: 99%

New developments on AIDS‐related cancers: The role of the delay and treatment options

Carvalho

Pinto

2017

Math Methods in App Sciences

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We propose a simple delay mathematical model for the dynamics of AIDSrelated cancers with treatment of HIV and chemotherapy. The main goals are to study the effects of the delay and of treatment (HAART and chemotherapy) in cancer cells growth. The model was simulated for several biologically reasonable values of the delay, of HAART efficacies and of chemotherapeutic drugs decay rates. The results of the simulations reveal an epidemiologically well-defined model. Important inferences are drawn for designing future treatment protocols.

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“…In the last decades, many mathematical models have been developed to describe the immunological response to infection with human immunodeficiency virus (HIV), for example, [8][9][10][11][12] and so on. These models have been used to explain different phenomena.…”

Section: Introductionmentioning

confidence: 99%

A mathematical model on Acquired Immunodeficiency Syndrome

Mahato

Mishra

Jayswal

et al. 2014

Journal of the Egyptian Mathematical Society

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A mathematical model SEIA (susceptible-exposed-infectious-AIDS infected) with vertical transmission of AIDS epidemic is formulated. AIDS is one of the largest health problems, the world is currently facing. Even with anti-retroviral therapies (ART), many resource-constrained countries are unable to meet the treatment needs of their infected populations. We consider a function of number of AIDS cases in a community with an inverse relation. A stated theorem with proof and an example to illustrate it, is given to find the equilibrium points of the model. The disease-free equilibrium of the model is investigated by finding next generation matrix and basic reproduction number R 0 of the model. The disease-free equilibrium of the AIDS model system is locally asymptotically stable if R 0 6 1 and unstable if R 0 > 1. Finally, numerical simulations are presented to illustrate the results. 2010 MATHEMATICS SUBJECT CLASSIFICATION: 92D30; 34D23; 34D05 ª 2014 Production and hosting by Elsevier B.V. on behalf of Egyptian Mathematical Society.

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A time delay model about AIDS-related cancer: equilibria, cycles and chaotic behavior

Cited by 18 publications

References 14 publications

Analysis of the Hopf bifurcation for the family of angiogenesis models

Analysis of the Hopf bifurcation for the family of angiogenesis models

New developments on AIDS‐related cancers: The role of the delay and treatment options

A mathematical model on Acquired Immunodeficiency Syndrome

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