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Mathematical models of infectious disease dynamics focus primarily on two basic parameters that govern the spread of pathogens through a population: rate of transmission and rate of recovery. These parameters and the crucial threshold (i.e. basic reproductive number) can be used to predict the potential impact of each disease. Two commonly implemented models are the SIR and the SEIR models. The SIR model takes into account only those diseases which cause an individual to be able to infect others immediately upon their infection, whereas the SEIR model describes diseases with an incubation period, during which the individual is infected but not contagious. In this project, I investigate when the two models generate similar results. I first prove that the SEIR model converges to the SIR model as the incubation period approaches zero, then summarize realistic epidemiological parameters for the two epidemic models from available literature and implement these values in SIR and SEIR simulations. I also show that for the SIR and SEIR models to agree, both basic reproductive number and rate of recovery need to be small.
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Yuan, Yongqing, "The Collision Regions Between Two Epidemic Models: SIR vs. SEIR" (2012). Senior Projects Spring 2012. 198.