A delayed fractional-order tumor virotherapy model: Stability and Hopf bifurcation
Author
Abstract
Suggested Citation
DOI: 10.1016/j.chaos.2022.112396
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000.
"Fractional calculus and continuous-time finance II: the waiting-time distribution,"
Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Papers cond-mat/0006454, arXiv.org, revised Nov 2000.
- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004. "Fractional calculus and continuous-time finance II: the waiting- time distribution," Finance 0411008, University Library of Munich, Germany.
- Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000.
"Fractional calculus and continuous-time finance,"
Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
- Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2000. "Fractional calculus and continuous-time finance," Papers cond-mat/0001120, arXiv.org.
- Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004. "Fractional calculus and continuous-time finance," Finance 0411007, University Library of Munich, Germany.
- Bourafa, S. & Abdelouahab, M-S. & Moussaoui, A., 2020. "On some extended Routh–Hurwitz conditions for fractional-order autonomous systems of order α ∈ (0, 2) and their applications to some population dynamic models," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
- Kim, Kwang Su & Kim, Sangil & Jung, Il Hyo, 2018. "Hopf bifurcation analysis and optimal control of Treatment in a delayed oncolytic virus dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 1-16.
- Deshpande, Amey S. & Daftardar-Gejji, Varsha & Sukale, Yogita V., 2017. "On Hopf bifurcation in fractional dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 189-198.
- Xu, Changjin & Liao, Maoxin & Li, Peiluan & Yuan, Shuai, 2021. "Impact of leakage delay on bifurcation in fractional-order complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
- Li, Hui-zhong & Liu, Xiang-dong & Yan, Rui & Liu, Cheng, 2020. "Hopf bifurcation analysis of a tumor virotherapy model with two time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
- Kumar, Pushpendra & Erturk, Vedat Suat & Yusuf, Abdullahi & Kumar, Sunil, 2021. "Fractional time-delay mathematical modeling of Oncolytic Virotherapy," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
- Xu, Changjin & Liu, Zixin & Yao, Lingyun & Aouiti, Chaouki, 2021. "Further exploration on bifurcation of fractional-order six-neuron bi-directional associative memory neural networks with multi-delays," Applied Mathematics and Computation, Elsevier, vol. 410(C).
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Düring, B. & Toscani, G., 2007.
"Hydrodynamics from kinetic models of conservative economies,"
Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 493-506.
- Düring, B. & Toscani, Giuseppe, 2007. "Hydrodynamics from kinetic models of conservative economies," CoFE Discussion Papers 07/06, University of Konstanz, Center of Finance and Econometrics (CoFE).
- Jiang, Yubing & Chen, Hu & Sun, Tao & Huang, Chaobao, 2024. "Efficient L1-ADI finite difference method for the two-dimensional nonlinear time-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 471(C).
- Marseguerra, Marzio & Zoia, Andrea, 2008. "Pre-asymptotic corrections to fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2668-2674.
- Afzaal Mubashir Hayat & Muhammad Bilal Riaz & Muhammad Abbas & Moataz Alosaimi & Adil Jhangeer & Tahir Nazir, 2024. "Numerical Solution to the Time-Fractional Burgers–Huxley Equation Involving the Mittag-Leffler Function," Mathematics, MDPI, vol. 12(13), pages 1-23, July.
- Zheng, Guang-Hui & Zhang, Quan-Guo, 2018. "Solving the backward problem for space-fractional diffusion equation by a fractional Tikhonov regularization method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 148(C), pages 37-47.
- Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006.
"Waiting times between orders and trades in double-auction markets,"
Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
- Enrico Scalas & Taisei Kaizoji & Michael Kirchler & Juergen Huber & Alessandra Tedeschi, 2006. "Waiting times between orders and trades in double-auction markets," Papers physics/0608273, arXiv.org.
- Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002.
"Waiting-times and returns in high-frequency financial data: an empirical study,"
Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
- M. Raberto & E. Scalas & F. Mainardi, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Papers cond-mat/0203596, arXiv.org.
- Marco Raberto & Enrico Scalas & Francesco Mainardi, 2004. "Waiting-times and returns in high-frequency financial data: an empirical study," Finance 0411014, University Library of Munich, Germany.
- Fan Yang & Ping Fan & Xiao-Xiao Li & Xin-Yi Ma, 2019. "Fourier Truncation Regularization Method for a Time-Fractional Backward Diffusion Problem with a Nonlinear Source," Mathematics, MDPI, vol. 7(9), pages 1-13, September.
- Torricelli, Lorenzo, 2020. "Trade duration risk in subdiffusive financial models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
- Ren, Fei & Gu, Gao-Feng & Zhou, Wei-Xing, 2009.
"Scaling and memory in the return intervals of realized volatility,"
Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(22), pages 4787-4796.
- Fei Ren & Gao-Feng Gu & Wei-Xing Zhou, 2009. "Scaling and memory in the return intervals of realized volatility," Papers 0904.1107, arXiv.org, revised Aug 2009.
- Ponta, Linda & Trinh, Mailan & Raberto, Marco & Scalas, Enrico & Cincotti, Silvano, 2019.
"Modeling non-stationarities in high-frequency financial time series,"
Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 173-196.
- Linda Ponta & Mailan Trinh & Marco Raberto & Enrico Scalas & Silvano Cincotti, 2012. "Modeling non-stationarities in high-frequency financial time series," Papers 1212.0479, arXiv.org, revised Feb 2017.
- Hajipour, Ahamad & Hajipour, Mojtaba & Baleanu, Dumitru, 2018. "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 139-153.
- Hosseininia, M. & Heydari, M.H., 2019. "Legendre wavelets for the numerical solution of nonlinear variable-order time fractional 2D reaction-diffusion equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 400-407.
- Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Dynamic intersectoral models with power-law memory," Papers 1712.09087, arXiv.org.
- Scalas, Enrico, 2007.
"Mixtures of compound Poisson processes as models of tick-by-tick financial data,"
Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 33-40.
- Enrico Scalas, 2006. "Mixtures of compound Poisson processes as models of tick-by-tick financial data," Papers physics/0608217, arXiv.org.
- Gerd Baumann & Frank Stenger, 2017. "Fractional Fokker-Planck Equation," Mathematics, MDPI, vol. 5(1), pages 1-19, February.
- Álvaro Cartea & Thilo Meyer-Brandis, 2010.
"How Duration Between Trades of Underlying Securities Affects Option Prices,"
Review of Finance, European Finance Association, vol. 14(4), pages 749-785.
- Cartea, Álvaro & Meyer-Brandis, Thilo, 2009. "How Duration Between Trades of Underlying Securities Affects Option Prices," MPRA Paper 16179, University Library of Munich, Germany.
- Scalas, Enrico & Gallegati, Mauro & Guerci, Eric & Mas, David & Tedeschi, Alessandra, 2006.
"Growth and allocation of resources in economics: The agent-based approach,"
Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 86-90.
- Eric Guerci & Enrico Scalas & Mauro Gallegati & David Mas & Alessandra Tedeschi, 2006. "Growth and allocation of resources in economics: The agent-based approach," Post-Print halshs-00871047, HAL.
- Enrico Scalas & Mauro Gallegati & Eric Guerci & David Mas & Alessandra Tedeschi, 2006. "Growth and Allocation of Resources in Economics: The Agent-Based Approach," Papers physics/0608221, arXiv.org.
- Schumer, Rina & Baeumer, Boris & Meerschaert, Mark M., 2011. "Extremal behavior of a coupled continuous time random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(3), pages 505-511.
- Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2008.
"Scaling in the distribution of intertrade durations of Chinese stocks,"
Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5818-5825.
- Zhi-Qiang Jiang & Wei Chen & Wei-Xing Zhou, 2008. "Scaling in the distribution of intertrade durations of Chinese stocks," Papers 0804.3431, arXiv.org, revised Apr 2008.
More about this item
Keywords
Cancer treatment; Virotherapy; Two delays; Immune response; Local stability; Hopf bifurcation;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922006063. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.