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, R0 and the server utilization,p.
Highlights
Queuing theory deals with the analysis of serving customers arriving to a facility with a fixed number of servers
We derived the exact distribution of the approximation “one permanently infected individual” to the quasistationary distribution (QSD) of the number of susceptible in an SIS model for N → ∞ keeping N/ρ constant
The QSD had a similar distribution than that of the number of busy servers in an M/G/N queuing process, and we showed that the QSD holds for a general distribution for the duration of the latent state with finite mean
Summary
Queuing theory deals with the analysis of serving customers arriving to a facility with a fixed number of servers. The approximation to the quasi-stationary distribution of the number of susceptible for non- exponential duration of the illness state: An application of queuing theory.
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