Epidemic Spread on Weighted Networks
The distributions in the number of contacts (k) and interaction events per time (l) are either homogeneous (Poisson) or heterogeneous (power law). For the number of interaction events, we also show the linear case in which l is strictly proportional to the number of contacts k, i.e. . k and l are drawn from joint distributions with (except for the analytical model's linear case where being compensated by a double transmission rate). The figures show the epidemic prevalence I as the outcome of the simulation runs (grey, dotted lines), of the the numerical solution of the analytical model with (red, solid line) and (red, dashed line). In addition, we show the epidemic prevalence when excluding individuals with only one contact () which is relevant for epidemics on networks with heterogeneous numbers of contacts including many individuals with in combination with a (nearly) constant number of interaction events, as realised through a Poisson distribution (orange line, cf. specifically power law, Poisson). Parameters chosen correspond to (Poisson case: , , power law case: , , ). Epidemiological parameters are β = 0.01 (0.02 for the analytical model's linear case), γ = 0.004 in arbitrary units and I(0) = 20. The insets show the same data for the early epidemic expansion in logarithmic scale showing early exponential growth according to (black line) with from Table 2.