Introduction to Mathematical Epidemiology
Introduction to Mathematical Epidemiology
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Dr. Stacey Smith? and Mr. Abel Lucido
Dr. Stacey Smith? and Mr. Abel Lucido
The workshop deals with the basics of constructing a model. We construct Ordinary Differential Equation (ODE) models for classic disease models and show how to alter these models to include other factors, such as vaccination. We demonstrate how the “diagram” of the model is often as useful as the equations and how to get from one to the other. We also deal with the basic reproductive ratio, one of the fundamental concepts in mathematical biology. We introduce the Jacobian matrix method, one of the most useful things you can learn in disease modeling. We discuss how to derive the basic reproductive ratio from the Jacobian, as well as a few other methods. By the end of this workshop, you should understand how to “read” a model, how to draw the diagram of a model, and how the ODEs and the diagram are related. You should also be able to distinguish between R0 and a threshold parameter, calculate the Jacobian matrix for a system of ODEs, apply the next-generation matrix, and derive a threshold from an endemic equilibrium.
The workshop deals with the basics of constructing a model. We construct Ordinary Differential Equation (ODE) models for classic disease models and show how to alter these models to include other factors, such as vaccination. We demonstrate how the “diagram” of the model is often as useful as the equations and how to get from one to the other. We also deal with the basic reproductive ratio, one of the fundamental concepts in mathematical biology. We introduce the Jacobian matrix method, one of the most useful things you can learn in disease modeling. We discuss how to derive the basic reproductive ratio from the Jacobian, as well as a few other methods. By the end of this workshop, you should understand how to “read” a model, how to draw the diagram of a model, and how the ODEs and the diagram are related. You should also be able to distinguish between R0 and a threshold parameter, calculate the Jacobian matrix for a system of ODEs, apply the next-generation matrix, and derive a threshold from an endemic equilibrium.
Prior reading/prerequisites
Prior reading/prerequisites
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