Susceptible-infected-susceptible epidemics on networks with general infection and cure times

Abstract

The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous Nintertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.

Nodal infection in Markovian susceptible-infected-susceptible and susceptible-infected-removed epidemics on networks are non-negatively correlated

“…II B. Section IV A exemplifies a simple graph with non-Markovian epidemics [21,22], in the sense that the infection and curing processes are not Poisson processes anymore, but general renewal processes, for which there can be a negative correlation. Thus, non-Markovian epidemic processes on graphs can violate the inequalities (1) and (2).…”

Discrete and continuous SIS epidemic models: A unifying approach

“…Van Segbroeck et al (2010). In the stochastic framework, the inner variability of individuals can lead to non-Markovian dynamics as statistically observed in Yang (1972);Becker (1989) and this motivated the development of corresponding non-Markov models Mieghem (2013); Cator et al (2013). In connection with these two classical models, our main aim is to introduce a continuous model that will approximate the stochastic model, in the large population regime, but that will also approximate the deterministic model in many circumstances.…”

Domination-time dynamics in susceptible-infected-susceptible virus competition on networks

“…A further line of research is to investigate two viruses that have different spreading and curing rate distributions, but the same average number of spreading events during an infection period. The average number of spreading events during an infection period is a more natural way to express the spreading effectiveness in SIS processes [20,24].…”