Primary: 92B05; Secondary: 62J27.

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An application of queuing theory to SIS and SEIS epidemic models

1. Facultad de Ciencias, Universidad de Colima, Apdo. Postal 25, Colima, Colima
2. Mathematics, Computational and Modeling Sciences Center, Arizona State University PO Box 871904, Tempe, AZ, 85287

## Abstract

In this work we consider every individual of a population to be a server whose state can be either busy (infected) or idle (susceptible). This server approach allows to consider a general distribution for the duration of the infectious state, instead of being restricted to exponential distributions. In order to achieve this we first derive new approximations to quasistationary distribution (QSD) of SIS (Susceptible- Infected- Susceptible) and SEIS (Susceptible- Latent- Infected- Susceptible) stochastic epidemic models. We give an expression that relates the basic reproductive number, $R_0$ and the server utilization, $\rho$.
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Citation: Carlos M. Hernández-Suárez, Carlos Castillo-Chavez, Osval Montesinos López, Karla Hernández-Cuevas. An application of queuing theory to SIS and SEIS epidemic models. Mathematical Biosciences and Engineering, 2010, 7(4): 809-823. doi: 10.3934/mbe.2010.7.809