A class of stochastic epidemic models and its deterministic counterpart |
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Authors: | Raúl Fierro |
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Institution: | Laboratorio de Análisis Estocástico. Instituto de Matemática, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile;Centro de Investigación y Modelamiento de Fenómenos Aleatorios, Universidad de Valparaíso, Casilla 5030, Valparaíso, Chile |
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Abstract: | A general stochastic model for the spread of an epidemic developing in a closed population is introduced. Each model consisting of a discrete-time Markov chain involves a deterministic counterpart represented by an ordinary differential equation. Our framework involves various epidemic models such as a stochastic version of the Kermack and McKendrick model and the SIS epidemic model. We prove the asymptotic consistency of the stochastic model regarding a deterministic model; this means that for a large population both modelings are similar. Moreover, a Central Limit Theorem for the fluctuations of the stochastic modeling regarding the deterministic model is also proved. |
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