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.
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9 September 2009
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2
18–22 September 2009
Rethymno, Crete (Greece)
Research Article|
September 09 2009
The Higher Moments Dynamic on SIS Model
Alberto Pinto;
Alberto Pinto
aDepartamento de Matemática, Escola de Ciências da Universidade do Minho, Campus de Gualtar, 4710‐057 Braga, Portugal
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José Martins;
José Martins
bDep. de Matemática, Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Leiria, Apartado 4163, 2411‐901 Leiria, Portugal
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Nico Stollenwerk
Nico Stollenwerk
cCentro de Matemática e Aplicações Fundamentais, Faculdade de Ciências, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649‐003 Lisboa, Portugal
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AIP Conf. Proc. 1168, 1527–1530 (2009)
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
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