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Risk-Based Transmission Dynamics and Reproduction Number Calculations in SEIR-Type Models
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SEIR-type epidemic models have been widely used in the study of infectious diseases and other contagion in human and nonhuman populations. Most recently, these were widely used in the response to the COVID-19 pandemic. Models that include nonlinear feedback, such as those arising from behavioral changes during an epidemic, can often exhibit different dynamics from simpler models that lack these nonlinearities. In the case of COVID-19, there was a suspicion early in the pandemic that human behavior could lead to ``waves", like those observed in the 1918 flu pandemic. In such applications, with more complex higher dimensional models, it can also be a challenge to calculate the basic reproduction number, $\R$, and to properly interpret all of its component parts. In this thesis, I present results from the investigation of an SEIR-type model in which the perception of risk mediates the rates of disease transmission. I also will present results on generalizing an approach for calculating reproduction numbers for a general family of SEIR-type models.