title: Nodal infection in Markovian susceptible-infected-susceptible and susceptible-infected-removed epidemics on networks are non-negatively correlated.
abstract: By invoking the famous Fortuin, Kasteleyn, and Ginibre (FKG) inequality, we prove the conjecture that the correlation of infection at the same time between any pair of nodes in a network cannot be negative for (exact) Markovian susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) epidemics on networks. The truth of the conjecture establishes that the N-intertwined mean-field approximation (NIMFA) upper bounds the infection probability in any graph so that network design based on NIMFA always leads to safe protections against malware spread. However, when the infection or/and curing are not Poisson processes, the infection correlation between two nodes can be negative.
authors.affiliation: Faculty of Science, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands.
authors.forename: E
authors.initials: E
authors.lastname: Cator
authors.affiliation: Faculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, Delft, The Netherlands.
authors.forename: P
authors.initials: P
authors.lastname: Van Mieghem
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D004198:Disease Susceptibility / Q000453:epidemiology*; D058872:Epidemics / Q000517:prevention & control* / Q000706:statistics & numerical data*; D006801:Humans; D015994:Incidence; D008390:Markov Chains; D015233:Models, Statistical; D016016:Proportional Hazards Models; D018570:Risk Assessment / Q000379:methods