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    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
    Potential Scenario
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    2013-Fathalla_Rihan-Delay Differential Equations in Biosciences - Parameter estimation and sensitivity analysis
    This is a review article to show that delay differential models have a richer mathematical framework (compared with models without memory or after-effects) and a better consistency with biological phenomena such dynamical diseases and cell growth...
    epidemiologysensitivityImmunologyphysiologyRK-methodstime-lags
    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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    2010-Shianga-EtAl-Computational model of the human glucose-insulin regulatory system
    A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced. The
    glucose tolerance testsum of squared residualsmultiple shooting methodcost function
    Free Online Textbook
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    2015-H_Sayama-Intro to Modeling and Analysis of Complex Systems
    Introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science.
    textbooktext
    Potential Scenario
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    2017-Sim-EtAl-Optimal control of a coupled tanks system with model-reality differences
    In this paper, an efficient computational approach is proposed to optimize and control a coupled tanks system.
    optimal controlflowtankscoupled tanks
    Potential Scenario
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    2018-Nyanginja-Angwenyi-Musyoka-Orwa - Mathematical modeling of the effects of public health education on tungiasis
    In this paper, we formulate and study a mathematical model for the dynamics of jigger infestation incorporating public health education using systems of ordinary differential equations and computational simulations.
    diseaseendemicreproduction numbertungiasisjigger infestation
    Potential Scenario
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    2007-Bellomo-De_Angelis-Delitala-Lecture Notes on Mathematical Modelling in Applied Sciences
    The Lectures Notes correspond to the first part of the course devoted to modelling issues to show how the application of models to describe real world phenomena generates mathematical problems to be solved by appropriate mathematical methods.
    spring massLegendre polynomialsintegro-differential equationskinetic theory
    Technique Narrative
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    5-010-MatrixExponential-TechniqueNarrative
    The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick introduction to the technique, with examples and...
    matrix esponentialPutzer's Algorithmdiagonalizationeigenvalueseigenvectors
    Potential Scenario
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    2018-Franklin_Chen-Teaching Kinetics through Differential Equations Constructed with a Berkeley MadonnaTM Flow Chart Model
    This kinetics manual has been successfully implemented in Physical Chemistry at UW-Green Bay in the fall semester of 2017, with the students’ success rate greater than 80%.
    kineticsPhysical ChemistryLotka Volterra equationsBerkeley Madonna platform
    Potential Scenario
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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
    Potential Scenario
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    2018-Winkle-Igoshin-Bennett-Josic-Ott-Modeling_Mechanical_Interactions_in_Growing_Populations_of_Rod-Shaped_Bacteria
    Here, we present an agent-based model that allows growing cells to detect and respond to mechanical interactions.
    bacteriaagent-basedpopulationbrod-shapedcellular growth
    Free Online Textbook
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    2012-Brian_Ingalls-Mathematical Modelling in Systems Biology An Introduction
    This is a comprehensive text with much biology background to motivate the mathematical modeling, exercises and answers, and many rich examples.
    spatialsensitivity analysisgene regulatory networksstochasticbifurcationmetabolic networkselectrophysiologytransductionrate lawsbiochemical reactions
    Potential Scenario
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    2009-Noakes-Sleigh-Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards
    Understanding the risk of airborne transmission can provide important information for designing safe healthcare environments with an appropriate level of environmental control for mitigating risks.
    infectioncompartmenthospitalventilationairbornesthochasticWells–Riley
    Potential Scenario
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    2006-Wilensky-Reisman-Thinking Like a Wolf a Sheep or a Firefly
    We describe a computation-based approach that enables students to investigate the connections between different biological levels using agent-based, embodied modeling tools.
    simulationNetLogopredator-preyagent-basedwolffox
    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