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    Potential Scenario
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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
    Potential Scenario
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    2009-Marten-EtAl-Derivation and analysis of an ordinary differential equation for epilepsy dynamics
    In this paper we describe how an ordinary differential equation model of corticothalamic interactions may be obtained from a more general system of delay differential equations.
    delayepilepsy dynamicsepilepsybistabilityseizure activity
    Potential Scenario
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    2014-Bozkurt-Peker-Mathematical modelling of HIV epidemic and stability analysis
    A nonlinear mathematical model of differential equations with piecewise constant arguments is proposed. This model is analyzed by using the theory of both differential and difference equations to show the spread of HIV in a homogeneous population.
    diseaselogisticHIVpiecewise constantIndia
    Potential Scenario
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    1999-PS_Crooke-S_Hota_JJ_Martini-JR_Hochkiss-A Mathematical Model for Carbon Dioxide Exchange
    A mathematical model is presented to study the effect of Tracheal Gas Insufflation (TGI) on the alveolar ventilation during passive, mechanical ventilation.
    mechanical ventilationventilationcarbon dioxide exchangetracheal gas insufflationalveolar ventilationshunttwo-compartment model
    Modeling Scenario
    256

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    102

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    6-009-FakeNews-ModelingScenario
    In modern society, creating and disseminating information is easier than ever. In this project, you will model the spread of fake news and investigate ways to deter distributing misinformation.
    sensitivity analysisSIR modelsSIS modelfake news
    Potential Scenario
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    42

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    2008-Ribbing-EtAl-Mathematical models of diabetes progression
    Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. underlying the
    physiologyclinical trialsdiabetesdiabetes progression
    Potential Scenario
    108

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    38

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    2020-Chen_Et_Al-MathModel_Simulation_Phase-Based_Transmissability_Corona_Virus
    In this study, we developed a Bats-Hosts-Reservoir-People transmission network model for simulating the potential transmission from the infection source (probably be bats) to the human infection.
    basic reproduction numbercoronavirusnext generation matrixtransmissibilitynovel coronavirus
    Potential Scenario
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    1991-JR_Lobry-P_Flandois-Comparison of Monod's Growth Model Parameters from the Same Data Set
    The paper obtains the parameters in Monod's Growth model using a minimization of the sum of square errors with a given data set and obtains confidence intervals
    Confidence intervalssum of square errorslinearizationgrowthModo Growth model
    Potential Scenario
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    1999-T_Chen-HL_He-GM_Church-S_Shafer-Modeling Gene Expression with Differential Equations
    The paper proposes and give great detail for a differential equation model for gene expression with two methods for constructing the model from a set of temporal data.
    gene expressiongenekineticgene translationgene transcription
    Potential Scenario
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    50

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    1988-Michael Intriligator-Dagobert Brito-A Predator-Prey Model of Guerrilla Warfare
    The authors present a three variable: numbers of guerrillas, numbers of regular (government) soldiers, and size of population controlled by the guerrillas, at time t), nonlinear system of three differential equations.
    combat modelguerrilla warfaregovernment
    Modeling Scenario
    212

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    167

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    1-093-SucroseReaction-ModelingScenario
    We offer data on the hydrolysis of sucrose in the presence of catalyst sucrase. We present students with several models and ask which model is best. We ask students to estimate parameters for the best model.
    kineticsMichaelis-Mentenhydrolysisreactionsucrose
    Potential Scenario
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    59

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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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    39

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    2011-Nguyen-Shi-Modeling the absorption circulation and metabolism of tirapazamine
    This apparently is a student project and it develops the kinetic model, uses Matlab for numerical solution, analytic solution and numerical solution.
    absorptionMichaelis-MentenMetabolismdrug metabolismcirculation
    Potential Scenario
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    2005-Albert_Tarantola-Inverse Problem Theory and Methods for Model Parameter Estimation
    This is a bible of approaches to support parameter estimation approaches in inverse problems. Theory and algorithms are offers with examples.
    Algorithminverse probleminverse
    Potential Scenario
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    2017-Biswasa-EtAl-Mathematical Modeling Applied to Sustainable Management of Marine Resources
    We study a nonlinear mathematical model of fishery management to understand dynamics of a fishery resource system in an aquatic environment that consists of two zones; one free fishing zone and another reserve zone where fishing is strictly...
    natural resourcesmarine resourcesfishery model
    Potential Scenario
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    62

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    2015-Zhang-EtAl-On the Selection of ODE Models with Application to Predator-Prey Dynamical Models
    We propose a computationally inexpensive approach that employs statistical estimation of the full model, followed by a combination of a least squares approximation (LSA) and the adaptive Lasso.
    least-squares approximationSpline modelingMonte Carlo simulationsvariable selectionadaptive LASSO
    Potential Scenario
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    2012-Rusinko-Swan-Agent-Based Fabric Modeling Using Differential Equations
    We use an agent-based modeling software, NetLogo, to simulate fabric drape by applying a modified mass spring system.
    NetLogospring massagent-baseddrapingyarnfabric
    Potential Scenario
    107

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    46

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    2007-Choisy-Guégan-Rohani-Mathematical Modeling of Infectious Diseases Dynamics
    After presenting general notions of mathematical modeling (Section 22.2) and the nature of epidemiological data available to the modeler (Section 22.3), we detail the very basic SIR epidemiological model (Section 22.5).
    stochasticSIR modeldeterministicincubationinfectives
    Potential Scenario
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    2006-Ousmane_Mousa_Tessa-Mathematical model for control of measles by vaccination
    In this article, we use a compartmental mathematical model of the dynamics of measles spread within a population with variable size to provide this framework.
    vaccinationcompartmentherd immunitymeaslesoptimal strategy
    Modeling Scenario
    194

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    1-125-DiceyPopulation-ModelingScenario
    We offer students an opportunity to generate data for their team on a death and immigration model using 12 and 20 sided dice and then pass on the data to another student team for analysis with a model they built. The key is to recover the...
    simulationimmigrationdeathdice