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Asymptotic Behavior Analysis of a Fractional-Order Tumor-Immune Interaction Model with Immunotherapy
2020
Complexity
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A fractional-order tumor-immune interaction model with immunotherapy is proposed and examined. The existence, uniqueness, and nonnegativity of the solutions are proved. ...
The results indicate that the fractional order has a stabilization effect, and it may help to control the tumor extinction. ...
To the best of the authors' knowledge, the dynamical analysis of a fractional-order tumor-immune interaction system with immunotherapy has not been performed before. ...
doi:10.1155/2020/7062957
fatcat:mxd4joi3zzeargryj4vckza4pm
Numerical Modeling of Fractional-Order Biological Systems
2013
Abstract and Applied Analysis
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We provide a class of fractional-order differential models of biological systems with memory, such as dynamics of tumor-immune system and dynamics of HIV infection of CD4 + T cells. ...
The numerical simulations confirm the advantages of the numerical technique and using fractional-order differential models in biological systems over the differential equations with integer order. ...
In this paper, we presented a class of fractional-order differential models of biological systems with memory to model the interaction of immune system with tumor cells and with HIV infection of CD4 + ...
doi:10.1155/2013/816803
fatcat:rfcyv23tobcore3qxvn43ogrce
Assessment of cancer immunotherapy outcome in terms of the immune response time features
2007
Mathematical Medicine and Biology
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A cytokine based periodic immunotherapy treatment is included in a model of tumor growth with a delay. ...
The effects of dose schedule are studied in the case of a weak immune system and a growing tumor. ...
Acknowledgements This study was supported by research grants FIS-G03/185, FIS-04/1885 and FIS-05/1192 of the Fondo de Investigación Sanitaria, Instituto Carlos III, Madrid, Spain. ...
doi:10.1093/imammb/dqm003
pmid:17652107
fatcat:donvk6oqfnbljkhu3xc3z4s6ly
Algorithmic asymptotic analysis: extending the arsenal of cancer immunology modeling
[article]
2021
arXiv
pre-print
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In this work, the dynamics of a fundamental model formulating the interactions of tumor cells with natural killer cells, CD8^+ T cells and circulating lymphocytes is examined. ...
This present analysis demonstrates the potential of algorithmic asymptotic analysis to simplify the complex, overeparameterized and multi-scale nature of cancer immunology models and to indicate the interactions ...
With the prospect to gain mechanistic understanding, various systems-level modeling approaches have been utilized to explore the interactions of the immune system with cancerous tumor [11] , including ...
arXiv:2103.02000v2
fatcat:jwoh7modyjecfbzyh4z3ytxmda
Bounding the Dynamics of a Chaotic-Cancer Mathematical Model
2018
Mathematical Problems in Engineering
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Several ODE mathematical models concerning tumor evolution and immune response have been formulated through the years, but only a few may exhibit chaotic attractors and oscillations such as stable limit ...
One that may allow us to better comprehend the behavior of cancer cells, in both short- and long-term, is mathematical modelling through ordinary differential equations. ...
The analysis of the dynamics of a superficial bladder cancer model with Bacillus Calmette-Guérin immunotherapy is shown in [24] , in which sufficient conditions of global asymptotic stability of the tumor-free ...
doi:10.1155/2018/9787015
fatcat:cwly4ufzqnexjmapuh24xyf7vi
From the guest editors: "Delay Differential Equations: Theory, Applications and New Trends"
2020
Discrete and Continuous Dynamical Systems. Series S
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Therefore, studying qualitative behaviors of such models, using stability or bifurcation analysis are essential. ...
Introduction of such time-delays in a differential model significantly increases the complexity of the model. ...
with time-delay and noise", the authors propose a model of tumor-immune interaction with time delay in immune reaction and noise in tumor cell reproduction. ...
doi:10.3934/dcdss.2020404
fatcat:zmm7ij26ifdyff5luo62q7iq34
Mathematical Modelling and Analysis of the Tumor Treatment Regimens with Pulsed Immunotherapy and Chemotherapy
2016
Computational and Mathematical Methods in Medicine
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In addition, since most types of tumors are resistant to common chemotherapy drugs, we consider the impact of drug resistance on therapeutic results and propose a new mathematical model to explain the ...
In comparison, mixed immunotherapy with combination chemotherapy can achieve a better treatment effect. ...
Conflict of Interests The authors declare that there is no conflict of interests regarding the publishing of this paper. ...
doi:10.1155/2016/6260474
pmid:26997972
pmcid:PMC4779848
fatcat:c5hjxgmks5gajggncmdrarewf4
Sustained Co-evolution in a Stochastic Model of the Cancer-Immune Interaction
[article]
2019
bioRxiv
pre-print
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Fitting the model to TRACERx evolutionary data argues in favor of substantial and sustained immune pressure exerted on a developing tumor, suggesting that measured incidence is a small proportion of all ...
The dynamical interaction between a growing cancer population and the adaptive immune system generates diverse evolutionary trajectories which ultimately result in tumor clearance or immune escape. ...
The efficacy 5 of immunotherapy stems from anti-tumor immunity imparted by the cytotoxic CD8+ T-cell repertoire, occurring as a result of effective targeting of tumor associated antigens (Coulie et al ...
doi:10.1101/679746
fatcat:ptjsjpfztfbqlkftsaiyl7vwta
CARTmath—A Mathematical Model of CAR-T Immunotherapy in Preclinical Studies of Hematological Cancers
2021
Cancers
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In this work, we develop a three-population mathematical model to describe tumor response to CAR-T cell immunotherapy in immunodeficient mouse models, encompassing interactions between a non-solid tumor ...
The absence of a functional immune system in these mice makes them simple and suitable for use as mathematical models. ...
Next, we investigated the model behavior in a different scenario with a fast growth tumor cell. ...
doi:10.3390/cancers13122941
fatcat:hsvt43yehndtlg3i5m4b5whecq
Estimation of the domain of attraction of free tumor equilibrium point of perturbed tumor immunotherapy model
2016
2016 4th International Conference on Control, Instrumentation, and Automation (ICCIA)
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In this paper, we are going to estimate the domain of attraction of tumor-free equilibrium points in a perturbed cancer tumor model describing the tumor-immune system competition dynamics. ...
We find a specific Lyapunov function in order to vanish maximum perturbation of modeling error, aging or uncertainties which exist in this system. ...
In this paper, we present a perturbed tumor immunotherapy model in Section 2 which is selected from non-polynomial nonlinear systems of such models, and compared with other models, it describes the behavior ...
doi:10.1109/icciautom.2016.7483138
fatcat:7zx4dohefrhsxom5iwu5y4bl4i
Fine-tuning anti-tumor immunotherapies via stochastic simulations
2012
BMC Bioinformatics
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Anti-tumor therapies aim at reducing to zero the number of tumor cells in a host within their end or, at least, aim at leaving the patient with a sufficiently small number of tumor cells so that the residual ...
Results: This work generalizes our previous study on hybrid models of such an interplay where interleukins are modeled as a continuous variable, and the tumor and the immune system as a discrete-state ...
The research of AdO has been done in the framework of the Integrated Project "P-medicine -from data sharing and integration via VPH models to personalized medicine" (project ID: 270089), partially funded ...
doi:10.1186/1471-2105-13-s4-s8
pmid:22536975
pmcid:PMC3303725
fatcat:jmc7kxslxvetvf7vooqwktrvdy
Mathematical Modeling and Dynamics of Oncolytic Virotherapy
[chapter]
2021
Advances in Precision Medicine Oncology
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We show how the dynamical system's theory can capture the behavior of the solutions of those models and provide different approaches to studying the models. ...
Fractional-derivative approach tells us about the memory of the derivative and related solutions of the models. We also study the affect of introducing control parameters on the cost of the therapy. ...
13 Mathematical Modeling and Dynamics of Oncolytic Virotherapy DOI: http://dx.doi.org /10.5772/intechopen.96963 ...
doi:10.5772/intechopen.96963
fatcat:v4rj7abc3bhbnc676wyztsxsie
SimB16: Modeling Induced Immune System Response against B16-Melanoma
2011
PLoS ONE
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We report the application of an agent-based model to recapitulate both the effect of a specific immunotherapy strategy against B16-melanoma in mice and the tumor progression in a generic tissue section ...
A comparison of the in silico results with the in vivo experiments shows excellent agreement. ...
strictly correlated with the specific biological scenario we want to simulate, i.e. parameters that measure the B16-OVA melanoma dynamics, its behavior and its interactions with the immune system of the ...
doi:10.1371/journal.pone.0026523
pmid:22028894
pmcid:PMC3197530
fatcat:l5a5w3skorcydiaezyzoc4psde
A Spatial Quantitative Systems Pharmacology Platform spQSP-IO for Simulations of Tumor—Immune Interactions and Effects of Checkpoint Inhibitor Immunotherapy
2021
Cancers
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Using a model of non-small-cell lung cancer developed based on this platform, we studied the role of the tumor microenvironment and cancer–immune cell interactions in tumor development and applied anti-PD ...
We developed a hybrid computational model platform, spQSP-IO, to extend QSP models of immuno-oncology with spatially resolved agent-based models (ABM), combining their powers to track whole patient-scale ...
Conflicts of Interest: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. ...
doi:10.3390/cancers13153751
fatcat:axwngqjhhbeetblfwpajgnjc5u
Mathematical modelling of multi-mutation and drug resistance model with fractional derivative
2020
Alexandria Engineering Journal
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Owolabi, A. Shikongo, Mathematical modelling of multi-mutation and drug resistance model with fractional derivative, Alexandria Eng. J. (2020), https://doi. ...
to include spatial effects of the involved cells, establish the physiological levels and asymptotic stability condition(s) of the equilibrium points of both models. ...
rate of cells, the manner in which tumor cells' progression is affected by immune system, mutual interaction of tumor cells with surrounding normal cells, and tumor cells response to treatment strategies ...
doi:10.1016/j.aej.2020.02.014
fatcat:atwi6pw4xvcblhe7awnbnxjihe
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