An environment aware epidemic spreading model and immune strategy in complex networks

Epidemic dynamics on complex networks with general infection rate and immune strategies

“…Therefore, the node with more edges has a higher possibility of being infected. Recently, starting with the seminal works by Pastor-Satorras and Vespignani [20,21], there has been a burst of activity on investigating the effects of the network topology on the behavior of epidemic spreading (see [1], [3]- [8], [11], [13]- [16], [18], [19], [23], [25]- [29], [31], [32]).…”

“…Consequently, the probability to be infected is varying according to the environment. Under this consideration, Qin and Zhong et al [23] proposed the environment aware SIS model (abbr. EA-SIS) as follows:…”

“…ϕ(k) represents the infectivity of a node with degree k, i.e., ϕ(k) denotes the average number of occupied edges from which a node with degree k can transmit the disease [11,19]. This means that ϕ(k) ≤ k. Recently, various types of the infectivity ϕ(k) were studied, such as ϕ(k) = k [20,21,23,25]; ϕ(k) = A [28]; ϕ(k) = min{A, αk}, 0 < α ≤ 1 [5]; ϕ(k) = k α [3] and ϕ(k) = ρk α /(1 + νk α ), ρ > 0, ν ≥ 0 [6,7,29,32]. That is, the function ϕ(k) in (3) can take any of the above forms according to the degree of real networks.…”

“…, the function f k (Θ) covers some examples appearing in the literature. For instance, f k (Θ) = λkΘ [5,20,25,29]; f k (Θ) = λ(k)Θ [6,7,19,32]; f k (Θ) = 1 − (1 − λΘ) k [14,27] and f k (Θ) = 1 − (1 − λ) kΘ [23].…”

“…Some special cases of model (5) were studied, such as µ = 0, γ = 1, ϕ(k) = k and f k (Θ(t)) = λkΘ(t) in [20,21,25]; µ = 0, γ = 1, ϕ(k) = min{A, αk} and f k (Θ(t)) = λkΘ(t) in [5]; µ = 0, γ = 1 and f k (Θ(t)) = λkΘ(t) in [29]; f (Θ(t)) = λ(k)Θ(t) in [32]; µ = 0, γ = 1, ϕ(k) = k f k (Θ(t)) = 1 − (1 − λΘ(t)) k [14]; and µ = 0, γ = 1, ϕ(k) = k and f k (Θ(t)) = 1 − (1 − λ) kΘ(t) in [23].…”