Delay differential model for tumour–immune dynamics with HIV infection of CD4⁺ T-cells

References

• Bellman , R. and Cooke , K. 1963 . Differential-Difference Equations , New York, London : Academic Press .
   Google Scholar
• Bocharov , G. A. and Rihan , F. A. 2000 . Numerical modelling in biosciences using delay differential equations . J. Comput. Appl. Math. , 125 : 183 – 199 . (doi:10.1016/S0377-0427(00)00468-4)
   Web of Science ®Google Scholar
• Bodnar , M. , Foryś , U. and Szymańska , Z. 2008 . A model of AIDS-related tumor with time delay . : 12 – 17 . Proceedings of the Fourteenth National Conference on Application of Mathematics in Biology and Medicine, University of Warsaw
   Google Scholar
• Bodnar , M. , Foryś , U. and Szymańska , Z. 2009 . Model of AIDS-related tumor with time delay . Appl. Math. (Warsaw) , 36 : 263 – 278 . (doi:10.4064/am36-3-2)
   Google Scholar
• Bonnet , F. , Lewden , C. , May , T. , Heripret , L. , Jougla , E. , Bevilacqua , S. , Costagliola , D. , Salmon , C. , Chéne , G. and Morlat , P. 2004 . Malignancy-related causes of death in human immunodeficiency virus-infected patients in the era of highly active antiretroviral therapy . Cancer , 101 : 317 – 324 . (doi:10.1002/cncr.20354)
   PubMed Web of Science ®Google Scholar
• Boshoff , C. and Weiss , R. 2002 . AIDS-related malignancies . Nat. Rev. Cancer , 2 : 373 – 382 . (doi:10.1038/nrc797)
   PubMed Web of Science ®Google Scholar
• Culshaw , R. V. and Ruan , S. 2000 . A delay-differential equation model of HIV infection of CD4+ T-cells . Math. Biosci. , 165 : 27 – 39 . (doi:10.1016/S0025-5564(00)00006-7)
   PubMed Web of Science ®Google Scholar
• Cushing , J. M. 1977 . Integrodifferential Equations and Delay Models in Population Dynamics , Spring, Heidelberg (doi:10.1007/978-3-642-93073-7)
   Google Scholar
• Dhooge , A. , Govaerts , W. and Kuznetsov , Yu. A. 2003 . MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs . ACM Trans. Math. Softw. , 29 : 141 – 164 . (doi:10.1145/779359.779362)
   Web of Science ®Google Scholar
• Feizabadi , M. S. and Witten , T. M. 2011 . Modeling the effects of a simple immune system and immunodeficiency on the dynamics of conjointly growing tumor and normal cells . Int. J. Biol. Sci. , 7 : 700 – 707 . (doi:10.7150/ijbs.7.700)
   PubMed Web of Science ®Google Scholar
• Foryś , U. and Poleszczuk , J. 2011 . A delay-differential equation model of HIV related cancer-immune system dynamics . Math. Biosci. Eng. , 2 : 627 – 641 .
   Google Scholar
• Freedman , H. I. and Sree Hari Rao , V. 1983 . The trade-off between mutual interference and time lags in predator–prey systems . Bull. Math. Biol. , 45 : 991 – 1003 .
   Web of Science ®Google Scholar
• J. Golab, M. Jakóbisiak, and W. Lasek, Immunologia (in Polish), PWN, Warszawa, 2002.
   Google Scholar
• Gopalsamy , K. 1992 . “ Stability and Oscillations in Delay-Differential Equations of Population Dynamics ” . Dordrecht : Kluwer .
   Google Scholar
• Hale , J. and Verduyn Lunel , S. 1993 . Introduction to Functional Differential Equations , New York : Springer-Verlag . Vol. 99 of Applied Mathem-atical Sciences.
   Google Scholar
• Kuang , Y. 1993 . Delay-Differential Equations with Applications in Population Dynamics , New York : Academic Press .
   Google Scholar
• Lou , J. , Ruggeri , T. and Tebaldi , C. 2006 . Modeling cancer in HIV-1 infected individuals: equilibria, cycles and chaotic behavior . Math. Biosci. and Eng. , 3 : 313 – 324 . (doi:10.3934/mbe.2006.3.313)
   PubMed Web of Science ®Google Scholar
• MacDonald , N. 1978 . Time Delays in Biological Models , Heidelberg : Spring .
   Google Scholar
• Murray , J. D. 2001 . Mathematical Biology. An Introduction , New York, Berlin : Springer .
   Google Scholar
• Naim , R. and Helbert , M. 2007 . Immunology for Medical Students , 2 , Mosby Elsevier .
   Google Scholar
• Nelson , P. W. 1998 . Mathematical models in immunology and HIV pathogenesis , Seattle, WA : University of Washington . Ph.D. thesis, Department of Applied Mathematics
   Google Scholar
• Nelson , P. W. , Murray , J. D. and Perelson , A. S. 2000 . Delay model for the dynamics in HIV infection . Math. Biosci. , 163 : 201 – 215 . (doi:10.1016/S0025-5564(99)00055-3)
   PubMed Web of Science ®Google Scholar
• Palefsky , J. 2007 . Human papillomavirus infection in HIV-infected persons . Top HIV Med. , 15 : 130 – 133 .
   PubMedGoogle Scholar
• Perelson , A. S. and Nelson , P. W. 1999 . Mathematical models of HIV-1 dynamics in vivo . SIAM Rev. , 43 : 3 – 44 . (doi:10.1137/S0036144598335107)
   Web of Science ®Google Scholar
• Perko , L. 1991 . “ Differential Equations and Dynamical Systems ” . In , 2 , New York : Springer-Verlag .
   Google Scholar
• Plaat , O. 1971 . Ordinary Differential Equation . Holden-Day, Inc., San Francisco, CA
   Google Scholar
• Preziosi , L. 2003 . “ Cancer Modeling and Simulation ” . Boca Raton : Chapman & Hall/CRC .
   Google Scholar
• A.S. Qi and Y. Du, The Nonlinear Models for Immunity, Shanghai Scientific and Technological Education Publishing House, 1998.
   Google Scholar
• F.A. Rihan, Numerical treatment of delay differential equations in bioscience, Ph.D. thesis, University of Manchester, 2000.
   Google Scholar
• Rihan , F. A. Delay differential models in dynamic diseases . The Proceedings of the International Conference on Bioinformatics and Computational Biology, BICoB 2010 . March 24–26 , Hawaii . pp. 73 – 79 .
   Google Scholar
• Shampine , L. F. and Thompson , S. 2001 . Solving DDEs in MATLAB . Appl. Numer. Math. , 37 : 441 – 458 . (doi:10.1016/S0168-9274(00)00055-6)
   Web of Science ®Google Scholar
• Thomlinson , R. 1982 . Measurement and management of carcinoma of the breast . Clin. Radiol. , 33 : 481 – 492 . (doi:10.1016/S0009-9260(82)80153-0)
   PubMed Web of Science ®Google Scholar
• Wheldon , T. E. 1988 . “ Mathematical Models in Cancer Research ” . Bristol : IOP Publishing Ltd .
   Google Scholar
• Wiggins , S. 1990 . Introduction to Applied Nonlinear Dynamical Systems and Chaos , New York : Springer .
   Google Scholar