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The Higher Moments Dynamic on SIS Model
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| The basic contact process or the SIS model is a well known epidemic process and have been studied for a wide class of people. In an epidemiological context, many authors worked on the SIS model considering only the dynamic of the first moments of infecteds, i.e., the mean value and the variance of the infected individuals. In this work, we study not only the dynamic of the first moments of infecteds but also on the dynamic of the higher moments. Recursively, we consider the dynamic equations for all the moments of infecteds and, applying the moment closure approximation, we obtain the stationary states of the state variables. We observe that the stationary states of the SIS model, in the moment closure approximation, can be used to obtain good approximations of the quasi-stationary states of the SIS model. | 402.64 KB | Adobe PDF |
Advisor(s)
Abstract(s)
The basic contact process or the SIS model is a well known epidemic process and have been studied for a wide class of people. In an epidemiological context, many authors worked on the SIS model considering only the dynamic of the first moments of infecteds, i.e., the mean value and the variance of the infected individuals. In this work, we study not only the dynamic of the first moments of infecteds but also on the dynamic of the higher moments. Recursively, we consider the dynamic equations for all the moments of infecteds and, applying the moment closure approximation, we obtain the stationary states of the state variables. We observe that the stationary states of the SIS model, in the moment closure approximation, can be used to obtain good approximations of the quasi-stationary states of the SIS model.
Description
International Conference on Numerical Analysis and Applied Mathematics 2009, ICNAAM-2009, 18 September 2009 through 22 September 2009
Keywords
Contact process Quasi-stationary distribution Moment closure approximation
Pedagogical Context
Citation
Alberto Pinto, José Martins, Nico Stollenwerk; The Higher Moments Dynamic on SIS Model. AIP Conf. Proc. 9 September 2009; 1168 (1): 1527–1530. https://doi.org/10.1063/1.3241390.
Publisher
American Institute of Physics