Del Ciello, Sarah, Jack Clementi, and Nailah Hart. 2010. Modeling Disease – FinalReport. http://educ.jmu.edu/~strawbem/math_201/final_reports/Clementi_DelCiello_Hart_Final.pdf . Acessed 8 September 2017.
Abstract: This paper models the progression of a disease through a set population using differential equations. Two cases were examined. Model 1 models an asymptomatic disease within a static population while accounting for a constant recovery without the chance of immunity. The equation for model 1 was first order, separable, and linear. Its resulting logistic solution entailed a scenario where the disease had no chance of dying out. Model 2 is a more realistic yet complicated model; it modeled a disease being transmitted through a population with both asymptomatic and symptomatic carriers while accounting for a constant recovery rate, constant death rate from both the infected and healthy population, and constant birth rate within the healthy population. The model for model 2 resulted in a system of nonlinear homogeneous equations that we were unable to solve explicitly. Instead their solutions were graphed.
Problem Statement: We seek to model the transmission of a disease through a population. Such modeling is very important to the study of epidemiology and the practice of medicine, since examining the relative effect of factors that govern the spread of a disease can help communities and health workers better prepare for and combat an outbreak.
Keywords: differential equation, disease, spread, first order, separable, population, carriers, symptomatic, asymptomatic, model
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