SIS epidemics on open networks: A replacement-based approximation
CoRR(2024)
Abstract
In this paper we analyze continuous-time SIS epidemics subject to arrivals
and departures of agents, by using an approximated process based on
replacements. In defining the SIS dynamics in an open network, we consider a
stochastic setting in which arrivals and departures take place according to
Poisson processes with similar rates, and the new value of the infection
probability of an arriving agent is drawn from a continuous distribution. Since
the system size changes with time, we define an approximated process, in which
replacements take place instead of arrivals and departures, and we focus on the
evolution of an aggregate measure of the level of infection. So long as the
reproduction number is less than one, the long-term behavior of this function
measures the impact of the changes of the set of agents in the epidemic. We
derive upper bounds for the expectation and variance of this function and we
include a numerical example to show that the approximated process is close to
the original SIS process.
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Key words
Network Operators,Susceptible-infected-susceptible,Susceptible-infected-susceptible Epidemic,Reproduction Number,Continuous-time,Functional Behavior,Continuous Distribution,Set Of Changes,Poisson Process,Set Of Agents,Stochastic Setting,Dynamical,Types Of Models,Number Of Agents,Multi-agent Systems,Epidemic Model,Aggregation Function,Variance Function,Homogeneous Poisson Process
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