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6-029-S-TumorGrowth
04 Aug 2021 | | Contributor(s):: Allison Leigh Lewis
This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time. Students should have prior experience with solving ODEs using the separable...
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2017-Byrne, Helen - Further Mathematics Biology. Lecture notes.
05 Apr 2020 | | Contributor(s):: Brian Winkel
2017-Byrne-FurtherMathBiology-NotesByrne, Helen. 2017. Further Mathematics Biology. Lecture notes. University of Oxford. See https://www.maths.ox.ac.uk/system/files/attachments/MathBioNotes2017.pdf . An outline for this course. We will observe that many...
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2011-Yafia, Radouane - A Study of Differential Equations Modeling Malignant Tumor Cells in Competition with Immune System.
04 Apr 2020 | | Contributor(s):: Brian Winkel
Yafia, Radouane. 2011. A Study of Differential Equations Modeling Malignant Tumor Cells in Competition with Immune System. International Journal of Biomathematics. 4(2): 185-206.See https://www.worldscientific.com/doi/10.1142/S1793524511001404 .Abstract: In this paper, we...
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2018-Tatro, Dyjuan - The Mathematics of Cancer: Fitting the Gompertz Equation to Tumor Growth. Senior Project.
01 Apr 2020 | | Contributor(s):: Brian Winkel
Tatro, Dyjuan. 2018. The Mathematics of Cancer: Fitting the Gompertz Equation to Tumor Growth. Bard CollegeBard Digital Commons. Senior Projects Spring 2018 Bard Undergraduate Senior Projects. 23 pages.Abstract: Mathematical models are finding increased use in biology, and...
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2016-Wilkie, Kathleen P., Philip Hahnfeldt, and Lynn Hlatky - Using Ordinary Differential Equations to Explore Cancer-Immune Dynamics and Tumor Dormancy. Preprint.
20 Mar 2020 | | Contributor(s):: Brian Winkel
Wilkie, Kathleen P., Philip Hahnfeldt, and Lynn Hlatky. 2016. Using Ordinary Differential Equations to Explore Cancer-Immune Dynamics and Tumor Dormancy. Preprint. 3 pp.See https://www.biorxiv.org/content/10.1101/049874v1. Abstract: Cancer is not solely a disease...
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2015-Khan, Moharram A., Sirazul Haq, Umaru Musa, and Aligarh Muslim - How differential equations influence the tumor growth via mathematical models.
12 Mar 2020 | | Contributor(s):: Brian Winkel
Khan, Moharram A., Sirazul Haq, Umaru Musa, and Aligarh Muslim. 2015. How differential equations influence the tumor growth via mathematical models. Mathematical Theory and Modeling. 5(8):...
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1-081-S-TumorGrowth
09 Jun 2018 | | Contributor(s):: Randy Boucher, Ryan Edmund Miller
Students will transform, solve, and interpret a tumor growth scenario using non-linear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth. Students use technology to solve the Gompertz model and answer a series of questions...
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2018-Schneebeli, Hans R. - Population Modeling
01 Mar 2018 | | Contributor(s):: Hans Rudolf Schneebeli, Claudio Marsan
This paper offers many problems inolving a single population model while introducing several specific models. Both numerical methods and qualitative anlyses are offered.The paper is in German and is entitled, "Populationsmodelle: Eine Einführung in...
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2012-Domingues, José Sérgio - Gompertz Model: Resolution and Analysis for Tumors.
28 Nov 2017 | | Contributor(s):: Brian Winkel
Domingues, José Sérgio. 2012. Gompertz Model: Resolution and Analysis for Tumors. Journal of Mathematical Modelling and Application. 1(7): 70-77.See https://www.docenti.unina.it/webdocenti-be/allegati/materiale-didattico/620247 .Abstract: It is called cancer...
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2015-Enderling, Heiko - Integrating experimental data to calibrate quantitative cancer models. preprint.
23 Sep 2017 | | Contributor(s):: Brian Winkel
Enderling, Heiko. 2015. Integrating experimental data to calibrate quantitative cancer models. Preprint. 3 pp.See https://www.biorxiv.org/content/10.1101/032102v1.Abstract: For quantitative cancer models to be meaningful and interpretable the number of unknown parameters...
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2002-de Pillis, L. G. and A. E. Radunskaya - Parameter Estimation for Tumor-Immune ODE System. Slides.
21 Sep 2017 | | Contributor(s):: Brian Winkel
de Pillis, L. G. and A. E. Radunskaya. 2002. Parameter Estimation for Tumor-Immune ODE System, 24 slides. See https://pages.pomona.edu/~aer04747/TumorModule/parameter_estimation.pdf . This is a very thorough and complete introduction to estimating parameters for a simple differential...
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2011-Barbarossa, Maria.. 2011. Delay models for cancer and tumor growth. PowerPoint Slides.
10 Sep 2017 | | Contributor(s):: Brian Winkel
Barbarossa, Maria.. 2011. Delay models for cancer and tumor growth. PowerPoint. 81 slides. From the slides: Background: Delay Equations Ordinary vs. Delay Differential Equations Applications in Biology ...
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2015-Beier, Julie C., Jana L. Gevertz, and Keith E. Howard - Building Context with Tumor Growth Modeling Projects in Differential Equations.
08 Sep 2017 | | Contributor(s):: Brian Winkel
Beier, Julie C., Jana L. Gevertz, and Keith E. Howard. 2015. Building Context with Tumor Growth Modeling Projects in Differential Equations. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies. 25(4):...
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2015-McIlwain, Hope - Tumor growth/Gompertz model article in PRIMUS
14 Jul 2015 | | Contributor(s):: Hope McIlwain
Abstract of the article: The use of modeling projects serves to integrate, reinforce, and extend student knowledge. Here we present two projects related to tumor growth appropriate for a first course in differential equations. They illustrate the use of problem-based learning to...