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Minicourse: Modeling infectious diseases. Profs. Helen Wearing and Deborah Sulsky.

The goal of this minicourse will be to introduce students to, and engage them in, the biological modeling process. Specifically, they will learn how to construct, analyze and simulate mathematical models that describe the transmission of infectious disease, and compare these models to data. We will combine lectures, group learning, problem sessions, hands-on computer labs, and student projects. We will make connections to multiscale dynamical systems, numerical analysis and Fourier analysis minicourses, either as a follow on or introduction to these topics, depending on scheduling. The main course components are
(1) Introduction to mathematical epidemiology. Derive and explore the classic Susceptible-Infectious-Recovered (SIR) ordinary differential equation (ODE) model, specifying model assumptions. Explore model behavior using phase-plane analysis and simulation. Calculate and understand the basic reproductive ratio $R_0$. Discuss methods for determining model parameters for specific diseases, for example, by fitting epidemic curves to single outbreak data (influenza in a boarding school) using trajectory matching. Discuss model limitations and implications.
(2) Discrete-time models of infectious disease. Use data collected at discrete intervals to construct maps over the same intervals. Compute solutions of iterated maps; discuss stability and bifurcations and solve linear difference equations. Make connections to continuous-time ODE models and numerical solution.
(3) The role of seasonality: extending simple models : the role of seasonality, by adding temporal forcing to the models in (1) and (2). Classify model behavior using bifurcation analysis and Fourier analysis to quantify periodicity. Here we will explore period doubling and chaos.
(4) Modeling public health interventions, Model different scenarios such as the implementation of vaccination, anti-microbial drugs, and social distancing. Quantify impacts on model outcomes. Discuss public health and policy implications.

Professor Wearing holds a joint position with the Biology Department and has much experience with disease modeling. She has lead the excellent undergraduate student theses of Bobby Sena and Alex Washburn, and has helped attract students to mathematics and applications to biology.

Professor Sulsky works in biomathematics, continuum mechanics and scientific computation. Over the years, she has developed numerical algorithms for studying problems in embryology, population ecology, suspension flow, fluid mechanics, and solid mechanics. Her recent work involves development of the Material-Point Method (MPM) for solving large-deformation continuum mechanics problems.