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Differential Equations, Lecture 8.1: Modeling with nonlinear systems
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Differential Equations, Lecture 8.1: Modeling with nonlinear systems
Most systems of ODEs that arise naturally are nonlinear. We begin this lecture with the popular SIR model in epidemiology. This models a disease in a population, where people transition from being Susceptible, to Infected, to Recovered. We also see many other similar models, such as the SI, SIS, SIRS, SEIR, and SIR model with birth and death rates. Next, we turn our attention to population dynamics, and we derive models of two species that are competing for a share resource. Finally, we look at how to model a predator-prey relationship, as well as a few other related population models.
Most systems of ODEs that arise naturally are nonlinear. We begin this lecture with the popular SIR model in epidemiology. This models a disease in a population, where people transition from being Susceptible, to Infected, to Recovered. We also see many other similar models, such as the SI, SIS, SIRS, SEIR, and SIR model with birth and death rates. Next, we turn our attention to population dynamics, and we derive models of two species that are competing for a share resource. Finally, we look at how to model a predator-prey relationship, as well as a few other related population models.
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