The University of Arizona

Mathematical Modeling of Human Activity Patterns and its Applications to Contaminant Exposure

Mathematical Modeling of Human Activity Patterns and its Applications to Contaminant Exposure

Series: Program in Applied Mathematics Brown Bag Seminar
Location: Math 402
Presenter: Hannah Kravitz, Program in Applied Mathematics, University of Arizona

An overview of mathematical methods for modeling human activity patterns within exposure models is provided.

In the past, exposure science researchers have published comparisons among a few methods, but a comprehensive survey of exposure science models has not previously been conducted in this context. This presentation will cover a small selection of the most mathematically interesting exposure science models. First, a Markov chain model for MRSA bacteria transmission in hospital rooms is discussed. Originally developed in 2015 King, et al., this model was adapted and rerun to determine the feasibility of using it in future University of Arizona research. Next, a thorough survey of mathematical models in disease transmission is conducted, with emphasis on those models that consider the role of human behavior in exposure to pathogens. The Susceptible-Infected-Recovered (SIR) dynamical systems model is discussed, as well as variations on this model for different transmission pathways and disease characteristics. Hidden Markov chain models are presented as an alternative to basic Markov models for more complex systems. Finally, several agent-based models are discussed, including a small-scale agent-based SIR model and a global agent-based generalized disease transmission model.

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