Generating function approach for the effective degree SIR Model




Manke, Kurtis

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The effective degree model has been applied to both SIR and SIS type diseases (those which confer permanent immunity and those which do not, respectively) with great success. The original model considers a large system of ODEs to keep track of the number of infected and susceptible neighbours of an individual. In this thesis, we use a generating function approach on the SIR effective degree model to transform the system of ODEs into a single PDE. This has the advantage of allowing the con- sideration of infinite networks. We derive existence and uniqueness of solutions to the PDE. Furthermore, we show that the linear stability of the PDE is governed by the same disease threshold derived by the ODE model, and we also show the nonlinear instability of the PDE agrees with the same disease threshold.



math epidemiology, partial differential equations, SIR disease model