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| Threshold of Effective Degree SIR Model |
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| KeyWord:Generating function, effective degree model, basic reproduction number, spectral stability, nonlinear stability, steady states |
| Author Name | Affiliation | | Slim Ibrahim | Department of Mathematics and Statistics, University of Victoria, Victoria, BC/V8W 2Y2, Canada | | Meili Li | College of Science, Donghua University, Shanghai, 201620, China | | Junling Ma | Department of Mathematics and Statistics, University of Victoria, Victoria, BC/V8W 2Y2, Canada | | Kurtis Manke | Department of Mathematics and Statistics, University of Victoria, Victoria, BC/V8W 2Y2, Canada |
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| Abstract: |
| The effective degree SIR model is a precise model for the SIR disease dynamics on a network. The original ODE model is only applicable for a network with finite degree distributions. The new generating function approach rewrites with model as a PDE and allows infinite degree distributions. In this paper, we first prove the existence of a global solution. Then we analyze the linear and nonlinear stability of the disease-free steady state of the PDE effective degree model, and show that the basic reproduction number still determines both the linear and the nonlinear stability. Our method also provides a new tool to study the effective degree SIS model, whose basic reproduction number has been elusive so far. |
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