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Asymptotic Behavior Analysis of a Fractional-Order Tumor-Immune Interaction Model with Immunotherapy

Wenbin Yang, Xiaozhou Feng, Shuhui Liang, Xiaojuan Wang
2020 Complexity  
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

Fathalla A. Rihan
2013 Abstract and Applied Analysis  
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

D. Rodriguez-Perez, O. Sotolongo-Grau, R. Espinosa Riquelme, O. Sotolongo-Costa, J. A. Santos Miranda, J. C. Antoranz
2007 Mathematical Medicine and Biology  
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]

Dimitrios G. Patsatzis
2021 arXiv   pre-print
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

Paul A. Valle, Luis N. Coria, Diana Gamboa, Corina Plata
2018 Mathematical Problems in Engineering  
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"

Fathalla A. Rihan, ,UAE University, UAE, Yang Kuang, Gennady Bocharov, ,Arizona State University, USA, ,Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Russian Federation
2020 Discrete and Continuous Dynamical Systems. Series S  
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

Liuyong Pang, Lin Shen, Zhong Zhao
2016 Computational and Mathematical Methods in Medicine  
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]

Jason T George, Herbert Levine
2019 bioRxiv   pre-print
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

Luciana R. C. Barros, Emanuelle A. Paixão, Andrea M. P. Valli, Gustavo T. Naozuka, Artur C. Fassoni, Regina C. Almeida
2021 Cancers  
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

Afshin Dini, M. J. Yazdanpanah
2016 2016 4th International Conference on Control, Instrumentation, and Automation (ICCIA)  
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

Giulio Caravagna, Roberto Barbuti, Alberto d'Onofrio
2012 BMC Bioinformatics  
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]

Abdullah Abu-Rqayiq
2021 Advances in Precision Medicine Oncology  
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: /10.5772/intechopen.96963  ... 
doi:10.5772/intechopen.96963 fatcat:v4rj7abc3bhbnc676wyztsxsie

SimB16: Modeling Induced Immune System Response against B16-Melanoma

Francesco Pappalardo, Ivan Martinez Forero, Marzio Pennisi, Asis Palazon, Ignacio Melero, Santo Motta, Vladimir Brusic
2011 PLoS ONE  
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

Chang Gong, Alvaro Ruiz-Martinez, Holly Kimko, Aleksander S. Popel
2021 Cancers  
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

Kolade M. Owolabi, Albert Shikongo
2020 Alexandria Engineering Journal  
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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