Interaction tumor-immune model with time-delay and immuno-chemotherapy protocol

被引:4
作者
Cherraf, Amina [1 ]
Li, Mingchu [2 ]
Moulai-Khatir, Anes [3 ]
机构
[1] Dalian Univ Technol, Sch Appl Math, Dalian, Peoples R China
[2] Dalian Univ Technol, Sch Software Technol, Dalian, Peoples R China
[3] Univ Oran1, Dept Math, Oran 31000, Algeria
关键词
Time-delay; Dynamic analysis; Tumor-immune system; Hopf bifurcation; Differential equations; DIFFERENTIAL-EQUATIONS; BIFURCATION-ANALYSIS; DYNAMICS; SYSTEM; STABILITY;
D O I
10.1007/s12215-021-00615-9
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This research explores a delay differential model to describe the dynamics of tumour-immune interactions in presence of immuno-chemotherapy. The model includes a constant delay in the recruitment term of the immune cells to illustrate the time lag between the stimulated accumulations of immune cells in the vicinity of cancer cells. The efficiency of solutions and the boudness have been supported by the findings. Also, the conditions for local stability and the existence of Hopf bifurcation are investigated. In particular, sufficient conditions dependent on the delay parameter under which the interior equilibrium is asymptotically stable are constructed. Afterwards, we established the length of delay to preserve stability. The numerical simulations show that the combination of immuno-chemotherapy protocol reduces the tumor load in a few months of therapy. The numerical simulations are presented to illustrate our theoretical results and show that the blend of immuno-chemotherapy convention decreases the tumour load in a couple of long periods of treatment.
引用
收藏
页码:869 / 887
页数:19
相关论文
共 34 条
  • [1] Delay-induced model for tumor-immune interaction and control of malignant tumor growth
    Banerjee, Sandip
    Sarkar, Ram Rup
    [J]. BIOSYSTEMS, 2008, 91 (01) : 268 - 288
  • [2] Bifurcations in Delay Differential Equations and Applications to Tumor and Immune System Interaction Models
    Bi, Ping
    Ruan, Shigui
    [J]. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2013, 12 (04): : 1847 - 1888
  • [3] Dynamics of delay-differential equations modelling immunology of tumor growth
    Buric, N
    Todorovic, D
    [J]. CHAOS SOLITONS & FRACTALS, 2002, 13 (04) : 645 - 655
  • [4] The effect of time delays on the dynamics of avascular tumor growth
    Byrne, HM
    [J]. MATHEMATICAL BIOSCIENCES, 1997, 144 (02) : 83 - 117
  • [5] A time delay dynamic system with external source for the local outbreak of 2019-nCoV
    Chen, Yu
    Cheng, Jin
    Jiang, Yu
    Liu, Keji
    [J]. APPLICABLE ANALYSIS, 2022, 101 (01) : 146 - 157
  • [6] Cooke K. L., 1986, FUNKC EKVACIOJ-SER I, V29, P77
  • [7] ROUTH-HURWITZ CRITERION IN THE EXAMINATION OF EIGENVALUES OF A SYSTEM OF NONLINEAR ORDINARY DIFFERENTIAL-EQUATIONS
    DEJESUS, EX
    KAUFMAN, C
    [J]. PHYSICAL REVIEW A, 1987, 35 (12): : 5288 - 5290
  • [8] THE TRADE-OFF BETWEEN MUTUAL INTERFERENCE AND TIME LAGS IN PREDATOR PREY SYSTEMS
    FREEDMAN, HI
    RAO, VSH
    [J]. BULLETIN OF MATHEMATICAL BIOLOGY, 1983, 45 (06) : 991 - 1004
  • [9] Galach M., 2003, International Journal of Applied Mathematics and Computer Science, V13, P395
  • [10] Prediction of Treatment Response for Combined Chemo- and Radiation Therapy for Non-Small Cell Lung Cancer Patients Using a Bio-Mathematical Model
    Geng, Changran
    Paganetti, Harald
    Grassberger, Clemens
    [J]. SCIENTIFIC REPORTS, 2017, 7