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    Potential Scenario
    217

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    2001-Smith-Moore-The SIR Model for Spread of Disease
    A multiple part tour of SIR Models freely available with Maple, Mathematics, and MatLab support files at MAA site.
    epidemicSIR modelEuler's methodherd immunityHong Kong flu
    Potential Scenario
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    2016-Helena_Sofia_Rodrigues-Application of SIR epidemiological model new trends
    In this paper, the basic transmission model is analyzed, as well as simple tools that allows us to extract a great deal of information about possible solutions. A set of applications - traditional and new - is described to show importance of this...
    epidemiologybasic reproduction numberSIR
    Potential Scenario
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    2019-Lorelei_Koss-SIR_Models_Differential_Equations_that_Support_The_Common_Good
    This article surveys how SIR models have been extended beyond investigations of biologically infectious diseases to other topics that contribute to social inequality and environmental concerns.
    environmentSIRsocial justiceepidemiccommon good
    Potential Scenario
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    2015-Joshi-EtAl-Optimal control of an SIR model with changing behavior through an education campaign
    We study stability analysis and use optimal control theory on the system of differential equations to achieve the goal of minimizing the infected population (while minimizing the cost).
    SIR modelsvaccinepopulationwater treatmentsusceptibleeducation campaignminimizing costinfected
    Potential Scenario
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    57

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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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    63

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    2015-Just-Callender-Differential equation models of disease transmission
    The work give full analyses of standard epidemic model and then shows how to do it with differential equations and agent-based modeling. Then it compares the results.
    disease transmissionSIR modelsepidemicagent-based
    Potential Scenario
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    62

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    2011-Cruz-Aponte-Herrera-Valdez-Mitigating effects of vaccination on influenza outbreaks given constraints in stockpile size and daily administrati
    We present a SIR-like model that explicitly takes into account vaccine supply and the number of vaccines administered per day and places data-informed limits on these parameters.
    vaccinationinfectionSIRepidemic
    Potential Scenario
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    2009-Munz-EtAl-When Zombies Attack-Mathematical modelling of an Outbreak of Zombie Infection
    We introduce a basic model for zombie infection, determine equilibria and their stability, and illustrate the outcome with numerical solutions.
    zombiesinfectionepidemicwater treatmentlatent infectionquarantineimpulsive eradication
    Potential Scenario
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    2018-Arden_Baxter-Modeling Public Opinion
    In this paper, we adapt the epidemiological models to model the dynamics of public opinion. Public opinion is any view prevalent among the general public. Our model considers any topic or issue in which the public has two decisive and opposing...
    epidemiologypopulationpublic opinion
    Free Online Textbook
    210

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    79

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    2016-Rob_deBoer-Population Dynamics  A Graphical Approach
    This book is an introduction into modeling population dynamics in ecology. Because there are several good textbooks on this subject, the book needs a novel ecological niche to justify its existence.
    mathematical modelstabilitycompetitionSIRbifurcationconsumptionpopulation population dynamicsgeneral replicationnonlinear density dependenciesfunctional responsepersistencephase plan analysis
    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
    Article or Presentation
    189

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    84

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    1979-Brian_Winkel-Elementary_My_Dear_Watson_Differential_Equation
    Sherlock Homes explains to Doctor Watson how he solves a murdermystery using Newton's Law of Cooling.
    Newton's Law of CoolingSherlock Holmestime of detah
    Potential Scenario
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    44

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    2007-Hui_Luo-Population Modeling by Differential Equations
    A general model for the population of Tibetan antelope is constructed. The present model shows that the given data is reasonably logistic.
    population dynamicsextinctionlogisticTibetan antelope
    Potential Scenario
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    2017-Xiang_Liu-Mathematical Studies of Optimal Economic Growth Model with Monetary
    In this paper, efforts will be made to study an extended Neoclassic economic growth model derived from Solow-Swan Model and Ramsey-Cass-Koopsman Model.
    Optimal Control TheoryJacobianSolow-Swan modelMonetary policyoptimal economic growth
    Potential Scenario
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    2014-XM-Huang-Ordinary Differential Equation Model and its Application in the Prediction Control of Population
    In this paper, we study two kinds of ordinary differential equation models, i.e., Malthus model and Logistic model, and discuss their applications in the prediction control of population.
    population dynamicsLogistic modelMalthus ModelPopulation Prediction Control
    Potential Scenario
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    2008-Yang-EtAl-Differential Equation Model of HIV Infection of CD T-Cells with Delay 
    Abstract: An epidemic model of HIV infection of CD4+ T-cells with cure rate and delay is studied. We include a baseline ODE version of the model, and a differential-delay model with a discrete time delay.
    virusT cellsHopf bifurcationendemic equilibrium
    Potential Scenario
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    2006-Graves-Peckham-Pastor-2D differential equations model for mutualism
    We develop from basic principles a two-species differential equations model which exhibits mutualistic population interactions.
    population dynamicsLotka-Volterragrowth ratemutualismLichen
    Potential Scenario
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    1975-Rodda-Sampson-Smith-The One-Compartment Open Model Parameter Estimation
    A new estimation procedure is proposed for estimating the parameters of the simplest pharmacokinetic model, the one-compartment open model.
    compartment modelpharmacokineticsnonlinear estimationone compartment model
    Potential Scenario
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    2018-Hu-Huang-Dynamic Regulation Responding to an External Stimulus
    This study examines the dynamic regulation process responding to an external stimulus. This study introduces the driven damped oscillator model which has an additional parameter to identify different patterns of the steady state.
    dynamical systemsregulationsteady statesales modelexternal stimulus
    Potential Scenario
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    2010-Kijek-Kijek-Modelling of Innovation Diffusion
    This paper offers a first order differential equation model for innovation diffusion, solves it, and offers qualitative analysis as well as approaches to estimating parameters with some data on final parameters for various countries.
    Bass modelinnovation diffusionLogistic modeldynamic model