Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior

1. Department of Mathematics, Shanghai University, 99 Shangda Road Shanghai 200444, P. R.
2. Department of Mathematics and, Research Center of Applied Mathematics (CIRAM), University of Bologna, Via Saragozza 8, 40123 Bologna
3. Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino

For HIV-infected individuals, cancer remains a significant burden. Gaining insight into the epidemiology and mechanisms that underlie AIDS-related cancers can provide us with a better understanding of cancer immunity and viral oncogenesis. In this paper, an HIV-1 dynamical model incorporating the AIDS-related cancer cells was studied. The model consists of three components, cancer cells, healthy CD4+ T lymphocytes and infected CD4+ T lymphocytes, and can have six steady states. We discuss the existence, the stability properties and the biological meanings of these steady states, in particular for the positive one: cancer-HIV-healthy cells steady state. We find conditions for Hopf bifurcation of the positive steady state, leading to periodic solutions, sequences of period doubling bifurcations and appearance of chaos. Further, chaos and periodic behavior alternate. Our results are consistent with some clinical and experimental observations.
  Article Metrics

Keywords chaos.; HIV-1 infection; Hopf bifurcation; stability; steady state; cancer

Citation: Jie Lou, Tommaso Ruggeri, Claudio Tebaldi. Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior. Mathematical Biosciences and Engineering, 2006, 3(2): 313-324. doi: 10.3934/mbe.2006.3.313


This article has been cited by

  • 1. Fathalla A. Rihan, Duaa H. Abdel Rahman, Delay differential model for tumour–immune dynamics with HIV infection of CD4+T-cells, International Journal of Computer Mathematics, 2013, 90, 3, 594, 10.1080/00207160.2012.726354
  • 2. Jorge Duarte, Cristina Januário, Nuno Martins, C. Correia Ramos, Carla Rodrigues, Josep Sardanyés, Optimal homotopy analysis of a chaotic HIV-1 model incorporating AIDS-related cancer cells, Numerical Algorithms, 2018, 77, 1, 261, 10.1007/s11075-017-0314-0
  • 3. Jie Lou, Tommaso Ruggeri, A time delay model about AIDS-related cancer: equilibria, cycles and chaotic behavior, Ricerche di Matematica, 2007, 56, 2, 195, 10.1007/s11587-007-0013-6
  • 4. Qingzhi Wen, Jie Lou, The global dynamics of a model about HIV-1 infection in vivo, Ricerche di Matematica, 2009, 58, 1, 77, 10.1007/s11587-009-0048-y
  • 5. F.A. Rihan, D.H. Abdel Rahman, S. Lakshmanan, A.S. Alkhajeh, A time delay model of tumour–immune system interactions: Global dynamics, parameter estimation, sensitivity analysis, Applied Mathematics and Computation, 2014, 232, 606, 10.1016/j.amc.2014.01.111
  • 6. Ana R. M. Carvalho, Carla M. A. Pinto, New developments on AIDS-related cancers: The role of the delay and treatment options, Mathematical Methods in the Applied Sciences, 2017, 10.1002/mma.4657
  • 7. Joseph Páez Chávez, Burcu Gürbüz, Carla M.A. Pinto, The effect of aggressive chemotherapy in a model for HIV/AIDS-cancer dynamics, Communications in Nonlinear Science and Numerical Simulation, 2019, 10.1016/j.cnsns.2019.03.021
  • 8. Jan Poleszczuk, Urszula Foryś, A delay-differential equation model of HIV related cancer--immune system dynamics, Mathematical Biosciences and Engineering, 2011, 8, 2, 627, 10.3934/mbe.2011.8.627
  • 9. Parvaiz Ahmad Naik, Kolade M. Owolabi, Mehmet Yavuz, Jian Zu, Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells, Chaos, Solitons & Fractals, 2020, 140, 110272, 10.1016/j.chaos.2020.110272

Reader Comments

your name: *   your email: *  

Copyright Info: 2006, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved