An application of queuing theory to SIS and SEIS epidemic models

  • 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, $\rho$.

    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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  • 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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