Non-Markovian Infection Spread Dramatically Alters the Susceptible-Infected-Susceptible Epidemic Threshold in Networks

Non-Markovian Infection Spread Dramatically Alters the Susceptible-Infected-Susceptible Epidemic Threshold in Networks

Van Mieghem, P.F.A.
Van de Bovenkamp, R.

Electrical Engineering, Mathematics and Computer Science

Intelligent Systems

2013-03-05

Most studies on susceptible-infected-susceptible epidemics in networks implicitly assume Markovian behavior: the time to infect a direct neighbor is exponentially distributed. Much effort so far has been devoted to characterize and precisely compute the epidemic threshold in susceptible-infected-susceptible Markovian epidemics on networks. Here, we report the rather dramatic effect of a nonexponential infection time (while still assuming an exponential curing time) on the epidemic threshold by considering Weibullean infection times with the same mean, but different power exponent ?. For three basic classes of graphs, the Erd?s-Rényi random graph, scale-free graphs and lattices, the average steady-state fraction of infected nodes is simulated from which the epidemic threshold is deduced. For all graph classes, the epidemic threshold significantly increases with the power exponents ?. Hence, real epidemics that violate the exponential or Markovian assumption can behave seriously differently than anticipated based on Markov theory.

http://resolver.tudelft.nl/uuid:e8208515-8091-4530-bc48-9081e9816f06

https://doi.org/10.1103/PhysRevLett.110.108701

American Physical Society

0031-9007

http://link.aps.org/doi/10.1103/PhysRevLett.110.108701

Physical Review Letters, 110 (10), 2013

Institutional Repository

journal article

© 2013 American Physical Society