TY - JOUR
T1 - Explicit non-Markovian susceptible-infected-susceptible mean-field epidemic threshold for Weibull and Gamma infections but Poisson curings
AU - Van Mieghem, Piet
AU - Liu, Qiang
PY - 2019
Y1 - 2019
N2 - Although non-Markovian processes are considerably more complicated to analyze, real-world epidemics are likely non-Markovian, because the infection time is not always exponentially distributed. Here, we present analytic expressions of the epidemic threshold in a Weibull and a Gamma SIS epidemic on any network, where the infection time is Weibull, respectively, Gamma, but the recovery time is exponential. The theory is compared with precise simulations. The mean-field non-Markovian epidemic thresholds, both for a Weibull and Gamma infection time, are physically similar and interpreted via the occurrence time of an infection during a healthy period of each node in the graph. Our theory couples the type of a viral item, specified by a shape parameter of the Weibull or Gamma distribution, to its corresponding network-wide endemic spreading power, which is specified by the mean-field non-Markovian epidemic threshold in any network.
AB - Although non-Markovian processes are considerably more complicated to analyze, real-world epidemics are likely non-Markovian, because the infection time is not always exponentially distributed. Here, we present analytic expressions of the epidemic threshold in a Weibull and a Gamma SIS epidemic on any network, where the infection time is Weibull, respectively, Gamma, but the recovery time is exponential. The theory is compared with precise simulations. The mean-field non-Markovian epidemic thresholds, both for a Weibull and Gamma infection time, are physically similar and interpreted via the occurrence time of an infection during a healthy period of each node in the graph. Our theory couples the type of a viral item, specified by a shape parameter of the Weibull or Gamma distribution, to its corresponding network-wide endemic spreading power, which is specified by the mean-field non-Markovian epidemic threshold in any network.
UR - http://www.scopus.com/inward/record.url?scp=85072132574&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.100.022317
DO - 10.1103/PhysRevE.100.022317
M3 - Article
VL - 100
SP - 022317-1 - 022317-15
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 2
M1 - 022317
ER -