An application of queuing theory to SIS and SEIS epidemic models

Carlos M. Hernández-Suárez; Carlos Castillo-Chavez; Osval Montesinos López; Karla Hernández-Cuevas; Carlos M. Hernández-Suárez; Carlos Castillo-Chavez; Osval Montesinos López; Karla Hernández-Cuevas

doi:10.3934/mbe.2010.7.809

Mathematical Biosciences and Engineering

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

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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

Received: 01 February 2010 Accepted: 29 June 2018 Published: 01 October 2010
MSC : Primary: 92B05; Secondary: 62J27.

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.

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[J]. Mathematical Biosciences and Engineering, 2010, 7(4): 809-823. doi: 10.3934/mbe.2010.7.809

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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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