SIMIODE: Resources

Modeling Scenario

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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

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2006-Loyd-Wodarz-Drug Resistance in Acute Viral Infections-Rhinovirus as a Case Study

We develop an epidemiological model that can be used to address the spread of resistance at the population level, and a virus dynamics model that can be used to study the dynamics of virus over the time course of an individual’s infection.

stabilityresistancevirusdrugepidemic competitionimmune responserhinovirus

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

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2012-Jambhekar-Breen-Extravascular Routes Of Drug Administration in Basic Pharamacokinetics

This provides an excellent step-by-step of the physiology, construction of model, and notions like peak concentration as well as issues like lag time.

concentrationphysiologydrugslag timeExtravascularPharamacokineticspeak time

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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

Modeling Scenario

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1-085-DrugBolus-ModelingScenario

Given data on the concentration of a drug in the plasma of a human in mg/L at certain time intervals in hours can we determine the rate at which the drug leaves the plasma as well as the initial amount administered in a intravenous bolus of the drug?

concentrationsum of square errorsbolusdrugrate constantadminister

Potential Scenario

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2012-Shargel-Yu-AccessPharmacy-Applied Biopharmaceutics and Pharmacokinetics

Step by step formation of drug absorption models is shown with many good graphics of system and plots. Solutions are offered but no solution methods are shown.

Michaelis-MentenEnzymesubstratecompartmentpharmacokineticsrate constanturinary dataabsorption rate

Modeling Scenario

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1-080-DrugAdministration-ModelingScenario

A simple drug administration situation is modeled with only two observations.

decaybloodstreamdrugrate constantadminister

Potential Scenario

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2017-Bonin-EtAl-Mathematical modeling based on ordinary differential equations - promising approach to vaccinology

As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature.

immune systemyellow fevercomputational immunologycomputational vaccinology

Potential Scenario

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2016-Bonin-EtAl-Mathematical modeling based on ordinary differential equations-vaccinology

We developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature.

Immunologyimmune systemAntigenvaccinologyyellow fever

Modeling Scenario

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7-010-MultipleDoses-ModelingScenario

Two multiple dose drug administration regimens are offered. A drug is to maintain a certain level (above a set minimum and below a set maximum) in the blood stream and one regimen involves bolus injections and another involves steady drip flow...

drug discoverystep functiondoseDiracdrug administrationinverse Laplace Transformintraveneousbolussteady drip

Potential Scenario

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2017-ASHP-Intro to Pharmacokinetics and Pharmacodynamics

This is the introductory Lesson 1 in an online set of materials to introduce Pharmacokinetics and Pharmacodynamics.

absorptioncompartmentbloodstreamplasmapharmacokineticspharmacodynamicstherapeutic concentration rangedrug dispositiondrug response

Modeling Scenario

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5-022-ColdPill-ModelingScenario

A model for the flow of a cold pill drug through the gastrointestinal compartment to the bloodstream compartment of a human subject is proposed. Students solve the system of differential equation model, use known parameter values, and plot solutions.

ratesmedicinedrug discoverycompartmentcold pillgastrointestinalbloodstream

Potential Scenario

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2017-Fred_Adler-Mathematically Modeling Asthma

Our Asthma models have examined how a viral infection can tip the immune system into a different state, with the potential to predispose an individual to future asthma

infectionasthmaimmune responserhinovirus

Potential Scenario

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2008-Huangi-Lu-Modeling long-term longitudinal HIV dynamics with applications to an AIDS clinical study

To better understand the factors responsible for the virological failure, this paper develops the mechanism-based nonlinear differential equation models for characterizing long-term viral dynamics with ARV therapy.

longitudinal dataAIDSantiretroviral drug therapyBayesian nonlinear mixed-effectstime-varying drug efficacyHIV dynamics

Potential Scenario

133

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2017-ASHP-Intro to Pharmacokinetics and Pharmacodynamics

This is the introductory Lesson 1 in an online set of materials to introduce Pharmacokinetics and Pharmacodynamics.

absorptioncompartmentbloodstreamplasmapharmacokineticsdrugpharmacodynamics

Modeling Scenario

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1-131-CaffeineElimination-ModelingScenario

We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.

caffeineeliminationpharmacokineticsdrug

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

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1-130-AspirinAbsorption-ModelingScenario

We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zero-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.

pharmacokineticsdrugaspirin

Modeling Scenario

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1-132-DigoxinElimination-ModelingScenario

We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.

nullclinespharmacokineticsdigoxindrug eliminationtwo compartment

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6-017-OncolyticViruses-ModelingScenario

2006-Loyd-Wodarz-Drug Resistance in Acute Viral Infections-Rhinovirus as a Case Study

2016-Wilkie-EtAl-Using ODEs to Explore Cancer-Immune Dynamics and Tumor Dormancy

2012-Jambhekar-Breen-Extravascular Routes Of Drug Administration in Basic Pharamacokinetics

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

1-085-DrugBolus-ModelingScenario

2012-Shargel-Yu-AccessPharmacy-Applied Biopharmaceutics and Pharmacokinetics

1-080-DrugAdministration-ModelingScenario

2017-Bonin-EtAl-Mathematical modeling based on ordinary differential equations - promising approach to vaccinology

2016-Bonin-EtAl-Mathematical modeling based on ordinary differential equations-vaccinology

7-010-MultipleDoses-ModelingScenario

2017-ASHP-Intro to Pharmacokinetics and Pharmacodynamics

5-022-ColdPill-ModelingScenario

2017-Fred_Adler-Mathematically Modeling Asthma

2008-Huangi-Lu-Modeling long-term longitudinal HIV dynamics with applications to an AIDS clinical study

2017-ASHP-Intro to Pharmacokinetics and Pharmacodynamics

1-131-CaffeineElimination-ModelingScenario

1999-Peter_Deuflhard-Differential Equations in Technology and Medicine

1-130-AspirinAbsorption-ModelingScenario

1-132-DigoxinElimination-ModelingScenario

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