An epidemic model on a network with two group structures having tunable overlap

Abstract A network epidemic model is studied. The underlying social network has two different types of group structures, households and workplaces, such that each individual belongs to exactly one household and one workplace. The random network is constructed such that a parameter theta θ $\theta$ controls the degree of overlap between the two group structures: theta equals 0 θ = 0 $\theta=0$ , corresponding to all household members belonging to the same workplace, and theta equals 1 θ = 1 $\theta=1$ , corresponding to all household members belonging to distinct workplaces. On the network a stochastic SIR epidemic is defined, having an arbitrary but specified infectious period distribution, with global (community), household, and workplace infectious contacts. The stochastic epidemic model is analysed as the population size n right arrow normal infinity n → ∞ $n\to\infty$ , with the asymptotic probability, and size, of a major outbreak obtained. In addition to allowing for a tunable overlap 0 less than or equals theta less than or equals 1 0 ≤ θ ≤ 1 $0 \leq \theta \leq 1$ between the two group structures, we also extend the model by allowing for a non-constant infectious period, the presence or absence of global infection, and potentially asymptotically infinite local outbreaks.