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    Potential Scenario
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    2018-Dyjuan_Tatro-The_Mathematics_of_Cancer-Fitting_Gompertz_Equation_to_Tumor_Growth
    Fitting the Gompertz Model to long term breast cancer study data, this project ascertains gompertzian parameters that can be used to predicts tumor growth as a function of time.
    tumorgrowthGompertzfittingparameter
    Modeling Scenario
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    272

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    1-102C-CancerGrowth-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and study treatment outcomes. Several classical models for cancer growth are presented including exponential, power law, Bertalanffy, logistic, and...
    optimizationcancerlogisticexponentialpredictiontumorgrowthdata fittingpower lawBertanffyGompertz
    Potential Scenario
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    2016-Wilkie-EtAl-Using ODEs to Explore Cancer-Immune Dynamics and Tumor Dormancy
    Here we present a general method using ordinary differential equations (ODEs) to model and analyze cancer-immune interactions, and in particular, immune-induced tumor dormancy.
    cancertumor-inhibiting cytotoxic actiontumor-promoting inflammationimmune-induced tumor dormancytumor growth dynamics
    Modeling Scenario
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    398

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    1-102-CancerTumor-ModelingScenario
    This module guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including exponential, power law, Bertalanffy, logistic, and...
    optimizationlogisticpredictiondata fittingpower lawGompertzcancer growtheponentialBertalanaffy
    Potential Scenario
    209

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    93

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    2014-Enderling-Chaplain-Mathematical Modeling of Tumor Growth and Treatment
    Herein we describe fundamentals of mathematical modeling of tumor growth and tumor-host interactions, and summarize some of the seminal and most prominent approaches.
    cancertumor modelingangiogenesistumor growthpatient care
    Modeling Scenario
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    1-150-CancerTherapy-ModelingScenario
    This activity builds upon elementary models on population growth. In particular, we compare two different treatment models of cancer therapy where in one, surgery happens before therapy and in the other, surgery happens after therapy.
    population dynamicsphage therapyexponential growthcancerwater treatmentdecaysurgery
    Potential Scenario
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    2020-Stepien_Kostelich_Kuang-Mathematics Cancer An Undergraduate Bridge Course in Applied Mathematics
    Most undergraduates have limited experience with mathematical modeling. This paper describes a course on the mathematical models of cancer growth and treatment.
    differential equationsmodelingundergraduate educationcancertumor
    Potential Scenario
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    2015-Khan-EtAl-How differential equations influence the tumor growth via mathematical models
    This work demonstrates the importance of differential equations to develop mathematical model of tumor growth.
    tumorcancdercancerous cellsimmunotherapymalignant
    Potential Scenario
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    2012-José_Sérgio_Domingues-Gompertz Model - Resolution and Analysis for Tumors
    The main objective of this paper is to use the Gompertz equation in order to study the development of blood irrigated solid tumors, using parameters defined in some important bibliographic references about the mathematical modelling of tumors.
    tumorGompertz equationgrowth tumor
    Potential Scenario
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    87

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    2015-Heiko_Enderling-Integrating experimental data to calibrate quantitative cancer models
    For quantitative cancer models to be meaningful and interpretable the number of unknown parameters must be kept minimal. We focus on a tumor hierarchy of cancer stem and progenitor non-stem cancer cells.
    cancertumorfittingagent-based
    Article or Presentation
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    2015-European_Bioinformatics_Institute-Bio-Models-Database
    Bio Models Database is a repository of computational models of biological processes. Models described from literature are manually curated and enriched with cross-references. All models are provided in the Public Domain.
    biologydatabasebioinformaticsModelscomputational models
    Potential Scenario
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    2004-Ledzewicz-Schattler-Application of Control Theory in Modelling Cancer Chemotherapy
    In this paper we discuss how to incorporate more realistic medical aspects of chemotherapy which hitherto have been neglected in the models.
    optimal controldrug resistancepharmacokineticspharmacodynamicschemotherapy
    Potential Scenario
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    1999-Peter_Deuflhard-Differential Equations in Technology and Medicine
    It deals with a variety of challenging real life problems selected from clinical cancer therapy, communication technology, polymer production, and pharmaceutical drug design.
    cancerdesigntumordrugpolymertherapy
    Modeling Scenario
    462

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    130

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    6-017-OncolyticViruses-ModelingScenario
    Students explore oncolytic virotherapy using systems of differential equations and numerical simulations.
    cancercancer-immune dynamicsimmune suppressor drugoncolytic virusvirotherapy
    Potential Scenario
    198

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    64

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    2011-Brian_Winkel-Parameter Estimates in Differential Equation Models for Population Growth
    We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and multiple species competition models.
    logisticpopulationparameciaGausegradient search
    Potential Scenario
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    2012-Gilbert_Koch-Modeling of Pharmacokinetic and Pharmacodynamics of Cancer and Arthritis
    In this work we develop preclinical PKPD models based on fundamental biological and pharmacological principles. Equipped with a PKPD model, different dosing schedules could be simulated.
    cancerpharmacodynamicsPKPD modelarthritisPharmacokineticanticancer
    Potential Scenario
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    64

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    1988-EY_Rodin-N_Taber-Yeast Growth Modelling in a Laboratory
    Modeling simple growth with some missing data and doing linear regression for parameter estimation in closed form solution of differential equation model and data.
    regressionyeastgrowth
    Potential Scenario
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    2017-Lia_Vas-Modeling With Differential Equations
    This is a set of class notes for Lia Vas in which examples from population, falling objects, tank mixing, growth and threshold, are offered.
    thresholdsfalling objectgrowthtank mixing
    Potential Scenario
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    2004-Mitchell-von Meien-Krieger-Dalsenter-A review of recent developments in modeling of microbial growth kinetics
    Mathematical models are important tools for optimizing the design and operation of solid-state fermentation (SSF) bioreactors. Such models must describe the kinetics of microbial growth.
    Filamentous Fungisolid-state fermentationgrowth kineticsdiffusion-reactionoxygen transfer
    Potential Scenario
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    2015-Beier-EtAl-Building Context with Tumor Growth Modeling Projects in Differential Equations
    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 reinforce and extend course content via a writing or research experience.
    tummor growthresearch experience