Amath 504


AMATH 504
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Objectives

At the end of this course, the student should be able to

Formulate SIS and SIR deterministic models of epidemic and endemic infectious disease transmission.
Define, estimate, and interpret the contact number, the basic reproduction number Ro and the replacement number in infectious disease models.
Distinguish among the standard frequency-dependent incidence, mass action incidence, and nonlinear incidence in model formulations.
Discuss the purposes of infectious disease epidemiological modeling.
Explain how an infectious disease can affect a predator-prey process.
Describe the concept of a core group in a sexually transmitted disease such as gonorrhea.
Discuss the application of mathematical transmission models to describe the infection transmission process and the effects of intervention programs.
Describe the process of combining a disease transmission model with a demographic model into an age-structured transmission model.
Give examples of how the demographics can influence the disease transmission in a population.
Explain the advantages and disadvantages of the two basic vaccination strategies for rubella.
Describe the impacts on disease incidence of pertussis vaccinations of children, adults, adolescents, and household members (cocoon strategy).
Explain the effects of childhood and adult varicella vaccination strategies on cases of chickenpox (varicella) and shingles (herpes zoster).
Discuss the mechanisms in transmission models that can lead to periodicity and oscillations in disease incidence.
Explain how the combination of horizontal incidences, waiting times, and epidemiological-demographic interactions can affect the behavior in models with variable population sizes.
Use basic components to formulate a deterministic model that is designed to answer a question about a specific infectious disease.