SIMIODE: Resources

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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

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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

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2011-Radouane_Yafia-A Study of Differential Equations Modeling Malignant Tumor Cells in Competition with Immune System

In this paper, we present a competition model of malignant tumor growth that includes the immune system response. The model considers two populations: immune system (effector cells) and population of tumor (tumor cells).

Immunologytumorhopf bifrucation

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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

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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

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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

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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

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1-081-TumorGrowth-ModelingScenario

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.

logisticpopulationtumorGompertz

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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

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6-029-TumorGrowth-ModelingScenario

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.

Pop_Growth Pilotlogisticcomparmenttumorsynthetic datasum of squares error

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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

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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

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2023-TechShareNotes. Differential Equations Modeling

TechShareNotes is a web site with rich differential equation modeling html pages and this one is about mixing in one, two, and three tanks, with interesting questions and problems as well as excellent diagrams and explanations.

population dynamicspredator-preycircuitreactionspring masspharmacokineticscooling

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5-024-PhGreatLakes

In this teaching modeling scenario, we demonstrate how lessons on salt-tank compartmental modeling can be used to predict phosphorus levels in the Great Lakes.

Great Lakeslimnologycomparmentpollutioncompartmental modelsphosphorous

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