Demonstration of the impact of fluctuations on inhomogeneous networks. Two confined populations with exchange of individuals are shown. In each population, the dynamics is governed by the SIR reaction scheme (). Individuals travel from one population to the other at a rate γ. Parameters are

*N*_{A} =

*N*_{B} = 10,000,

*R*_{0} = 4, and an initial number of infecteds

*I*_{0} = 20 in population

*A*. (

*Left*) The probability

*p*(γ) of an outbreak occurring in population

*B* as a function of transition rate γ. (

*Insets*) Histograms of the time lag

*T* between the outbreaks in

*A* and

*B* for those realizations for which an outbreak occurs in

*B*. The circles are results of the simulations of 100,000 realizations; the solid curve is the analytic result of Eq.

**8.** (

*Right*) A star-shaped network with a central population

*A* connected to

*M* – 1 populations

*B*_{1},...,

*B*_{M}_{-1} with rates γ

_{1},..., γ

_{M}_{-1}. The cumulated variance (see text) for a star network with 32 populations is depicted as a function of the average transmission rate

. Two cases are exemplified: equal rates (circles) and distributed rates according to Eq.

**10** with γ

_{max}/γ

_{min} ≈ 1,000 (squares). The solid lines show the analytical results given by Eqs.

**8** and

**9**. Parameters are

*N*_{A} =

*N*_{B} = 10,000,

*R*_{0} = 4, and an initial number of infecteds

*I*_{0} = 20 in population

*A*. The numerical values are obtained by calculating the variance of the fluctuations of 100 different realizations of the epidemic outbreak for each

.

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