Classification of link-breaking and link-creation updating rules in susceptible-infected-susceptible epidemics on adaptive networks

Abstract

In the classical susceptible-infected-susceptible (SIS) model, a disease or infection spreads over a given, mostly fixed graph. However, in many real complex networks, the topology of the underlying graph can change due to the influence of the dynamical process. In this paper, besides the spreading process, the network adaptively changes its topology based on the states of the nodes in the network. An entire class of link-breaking and link-creation mechanisms, which we name Generalized Adaptive SIS (G-ASIS), is presented and analyzed. For each instance of G-ASIS using the complete graph as initial network, the relation between the epidemic threshold and the effective link-breaking rate is determined to be linear, constant, or unknown. Additionally, we show that there exist link-breaking and link-creation mechanisms for which the metastable state does not exist. We confirm our theoretical results with several numerical simulations.

On the Coevolution Between Social Network Structure and Diffusion of the Coronavirus (COVID-19) in Spatial Compartmental Epidemic Models

“…Spatial distancing is implemented in the model in a very stylized way (cf. Achterberg et al, 2020;Horstmeyer et al, 2020;Corcoran and Clark, 2021, for related literature). The author assumes that the city government only tracks the evolution of Q agents and enforces SD when x t (Q) > q ⋆ , where x t (Q) is the current share of agents in the Q compartment and q ⋆ ∈ (0, 1).…”

“…However, some previous literature has shown that the (complex) structure of networks describing the way agents can meet and possibly get infected may affect the dynamics of the epidemic diffusion and its long-run properties (Keeling and Eames, 2005;Jin et al, 2014). Furthermore, as the virus spreads in the network, the structure of interactions between people may change over time, due to quarantining measures and/or SD policies, which may possibly introduce a coevolutionary effect dynamically linking disease diffusion and network properties (Achterberg et al, 2020;Horstmeyer et al, 2020;Corcoran and Clark, 2021).…”

Spreading Control in Two-Layer Multiplex Networks

“…Conditions (8), as alternative to Corollary 1, also suggests as sufficient condition, to adapt the parameters and/or . This adaptation requires disconnecting links from those nodes that do not satisfy condition (8) in order to reach the extinction state, resulting in an equivalent method as the one proposed in Adaptive Networks [ 39 , 46 ]. However, our approach keeps the network structure, modifying the parameters associated with the interaction probabilities of the model, avoiding disconnecting nodes.…”

“…In the present study the control of a spreading process in a complex multilayer network is addressed on the basis of the classical Markov-based susceptible-infected-susceptible (SIS) dynamics [40][41][42][43][44] in a multilayer version that has been adapted from [7] in such a way that the unit polytope is an invariant set for the dynamics. Following the global stability analysis and parametric control design studies for SIS processes in homogenous and inhomogeneous single-layer complex networks [36,38] and extensions of it including quarantine [37,45] a decentralized parametric control strategy is developed providing sufficient conditions for global stability of the extinction state without altering the topology of the networks as is suggested in other studies related to adaptive networks [39,46]. Instead of involving computationally expensive optimization procedures, simple analytic measures are provided which can be quickly determined for a given network topology and parameter set.…”

A minimal model for adaptive SIS epidemics

“…Gross et al [ 6 ] proposed a rewiring mechanism, which rewires the link between two connected susceptible-infected nodes to two susceptible nodes. Kiss et al [ 7 ] (and independently Achterberg et al [ 8 ]) introduced a Link Activation-Deactivation model, in which links can be broken or created between any two nodes, where the rate to break or create a link depends on the health state of the two nodes attached to that link. Jolad et al [ 9 ] assumes that all individuals have a preferred number of neighbours, subject to random link addition and removals.…”