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Mathematical Biosciences and Engineering (MBE)
 

An application of queuing theory to SIS and SEIS epidemic models

Pages: 809 - 823, Volume 7, Issue 4, October 2010      doi:10.3934/mbe.2010.7.809

 
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Carlos M. Hernández-Suárez - Facultad de Ciencias, Universidad de Colima, Apdo. Postal 25, Colima, Colima, Mexico (email)
Carlos Castillo-Chavez - Mathematics, Computational and Modeling Sciences Center, Arizona State University PO Box 871904, Tempe, AZ, 85287, United States (email)
Osval Montesinos López - Facultad de Ciencias, Universidad de Colima, Apdo. Postal 25, Colima, Colima, Mexico (email)
Karla Hernández-Cuevas - Facultad de Ciencias, Universidad de Colima, Apdo. Postal 25, Colima, Colima, Mexico (email)

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, $\rho$.

Keywords:  SIS; SEIS; Queuing theory; $R_{0}$; basic reproductive number; stochastic epidemic models.
Mathematics Subject Classification:  Primary: 92B05; Secondary: 62J27.

Received: February 2010;      Accepted: May 2010;      Available Online: October 2010.

 References