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    Potential Scenario
    168

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    93

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    2014-Rogert_Smith-Mathematical Modeling of Zombies
    Here, we use diffusion to model the zombie population shuffling randomly over a one-dimensional domain.
    kineticsZombiezombificationinteraction times
    Potential Scenario
    202

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    75

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    2016-Devaki-Swathi-System of Differential Equations in Prey Predator Model
    Predation relationship exists in ecological niches throughout the world. This is the species interaction which will be mathematically analyzed and embodied in this work.
    extinctionCoevolutionpredatorLotka Volterra equationspre
    Potential Scenario
    169

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    52

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    2012-Ogunrinde-Sunday-On some models based on second order differential equation
    This paper presents some models based on second order differential equations. Such models include interaction between different kinds of species in an environment and pricing policy for optimum inventory level of a firm.
    species interactionpricing policyoptimal inventory
    Potential Scenario
    153

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    52

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    2004-Jones-Song-Thomas-Controlling wound healing through debridement
    In this article, a system of differential equations that models slough/wound interaction is developed.
    bacteriawound healinghealingderidingisocline
    Potential Scenario
    130

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    49

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    2012-Yuan_Yuan-A coupled plankton system with instantaneous and delayed predation
    We present two simple plankton population models: one has instantaneous predation, another has delayed predation.
    phytoplanktonbifurcationorbitsherbivorous zooplanktoneffect of fishmaturation time delay
    Potential Scenario
    111

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    40

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    2011-Therese-Keane-Combat modelling with partial differential equations
    We present work seeking to more realistically represent troop dynamics and to enable a deeper understanding of the nature of conflict.
    Lanchester modeltroop dynamicsswarming behaviortroop regroupinglossesnon-local termslocal terms
    Modeling Scenario
    278

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    291

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    6-006-ZombieGameHvZ-ModelingScenario
    Invented in 2005, Humans vs. Zombies, or HvZ, is a game of tag, predominantly played at US college campuses. In this activity, students use systems of non-linear differential equations to model the HvZ game.
    zombiesSIR modelsGame
    Potential Scenario
    205

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    57

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    1986-Istvan_Gyori-Connections between compartment systems pipes and integro-differential equations
    In this paper we give the mathematical description of models in which the mass transport between compartments requires a given definite time or transit times are distributed according to given probability distribution functions.
    physiologypipelinecompartmentbloodcirculationintegro-differential equation
    Modeling Scenario
    394

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    614

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    6-022-CannibalismPredatorPrey-ModelingScenario
    The Lotka-Volterra model tells us that the prey and predator exhibit a shifted cyclic behavior over time. In this module, we look at modifying this prey-predator model to consider the case when there is cannibalism in the predator species.
    stabilitypredator-preyequilibriaoscillationscannibalismphase planesspiral sinks
    Potential Scenario
    231

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    67

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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
    Modeling Scenario
    268

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    554

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    0

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    6-065-InternetPlatformUsers-ModelingScenario
    A model estimating the volume of users interacting through a two-sided Internet platform (allowing interaction of two types of users) will teach students how to analyze a 2-dimensional dynamical system.
    dynamicsflowconservedfixed pointscycletinternet platformdiverghenceJacobianattractingrepellingnodesstablesaddlespiral
    Potential Scenario
    162

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    84

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    2009-Su-EtAl-Fitting Compartmental Models to Multiple Dose Pharmacokinetic Data using SAS
    In the case of a multiple dose study where subjects experience different dosing times, a superposition principle can be used to recursively account for each additional dose.
    SASsuperpositionpharmacokineticscompartmental modelsmultiple dose
    Potential Scenario
    245

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    85

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    2017-Justin_Krueger-Parameter Estimation Methods for Ordinary Differential Equation Models with Applications to Microbiology
    We demonstrate the feasibility of principal differential analysis using simulation studies and then apply the method to intestinal and vaginal microbiota data.
    microbiologyLotka Volterrramicrobiota
    Potential Scenario
    140

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    55

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    2016-Lewnard-Townsend-Climatic and evolutionary drivers of phase shifts in the plague epidemics of colonial India
    Our analysis shows that historical datasets can yield powerful insights into the transmission dynamics of reemerging disease agents with which we have limited contemporary experience to guide quantitative modeling and inference.
    infectious diseasepVector-Borne Diseaselagueplague
    Potential Scenario
    222

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    65

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    2011-Lucas_Pulley-Analyzing Predator-Prey Models Using Systems of Ordinary Linear Differential Equations
    This research focused on applying biological mathematics to analyzing predation relationships, especially the relationship between the Canadian Lynx and the Snowshoe Hare.
    simulationpredator-preyLotka-VolterrapopulationCanadian LynxSnowshoe Harecritical values
    Potential Scenario
    151

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    53

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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
    177

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    58

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    1972-Suresh_Sethi-Optimal Control of the Vidale-Wolfe Advertising Model
    This paper considers an optimal-control problem for the dynamics of the Vidale-Wolfe advertising model, the optimal control being the rate of advertising expenditure to achieve a terminal market share within specified limits.
    Optimal Control Theoryadvertisingsales
    Potential Scenario
    134

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    52

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    2019-Radulescu-Lundgren-A_pharmacokinetic_model_of_lead_absorption_and_calcium_competitive_dynamics
    We build and analyze a compartmental model of lead pharmacokinetics, focused specifically on addressing neurotoxicity.
    QUBES Leadership Teamparametersabsorptionbifurcationpharmacokineticscalciumcognitive decline
    Potential Scenario
    173

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    45

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    2015-Sivakumar-EtAl-Approximate Analytical Expression of Concentrations in a Kinetic Model for Biogas Generation from Banana Waste
    The initial value problem in a kinetic model for biogas generation from banana waste is discussed. The model involves the system of non-linear differential equations which has variety of non-linear rate function.
    chemical kineticsMichaelis-Menten kineticsanaerobic digestionacidogenic stepsbananamethanogenic stepswastes
    Potential Scenario
    226

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    75

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    2014-Vance-Eads-Sensitivity Analysis of a Three-Species Nonlinear Response Omnivory Model with Predator Stage Structure
    We investigate a three-species nonlinear response omnivory model incorporating stage structure in the top predator. The model consists of four coupled ordinary differential equations involving fourteen parameters.
    stage structuresensitivity analysismortalityomnivoreomnivory modelsearch rates