Sparse Resource Allocation for Linear Network Spread Dynamics

Stability of SIS Spreading Processes in Networks With Non-Markovian Transmission and Recovery

“…Another interesting research direction is developing an optimal resource allocation strategy for non-Markovian epidemic spreading processes. Although we can find in the literature various research efforts [1], [13], [32], [39], [48] for designing containment methodologies for networked epidemic spreading processes, many of them are based on decay rates that are derived under the Markovian assumption on transmission and recovery events. In this direction, it is of practical interest to investigate how the non-Markovianity of spreading dynamics alters the optimal allocation strategies that have been investigated in the literature.…”

“…Since the sum ∑ n i=1 E[z i (t)] equals the expected number of infected nodes at time t, the decay rate λ quantifies how fast the infectious spreading process dies out in the network (in average). Besides quantifying the impact of contagious spreading processes over networks [12], [20], [47], the exponential decay rate has been used as a standard tool for measuring the performance of strategies aiming to contain epidemic outbreaks [1], [13], [39], [48]. We further remark that, although exponential distributions are not necessarily appropriate for modeling realistic transmission and recovery times as discussed in the Introduction, the exponential decay rate is still a valid quantity for measuring the spreading capability of epidemic processes.…”

Second-order moment-closure for tighter epidemic thresholds

“…In our simulations, we have shown that our lower-bound significantly improves on the first order lower-bound, in the cases of both random and realistic networks. This improvement suggests that incorporating second-order moments could allow us to drastically improve the performance of existing strategies for spreading control [8,9,10,11,15]. Therefore, the irreducibility of L is equivalent to that of the block matrix L = [L ij ] i,j having the block elements L ij = col j =i A j,\{i} , if i = j, V j (e j ⊗ A j,\{j} ), otherwise.…”

“…This framework was later extended to the cases where the underlying network in which the spreading process is taking place is uncertain [10], temporal [11,12], and adaptively changing [13,14]. Recently, the authors in [15] presented an approach for achieving an optimal resource allocation in order to maximize the decay rate under sparsity constraints.However, finding the decay rate of a spreading process is, in general, a computationally hard problem. Even for the case of the susceptible-infectedsusceptible (SIS) model [2], which is one of the simplest models of spread, the exact decay rate is given in terms of the eigenvalues of a matrix whose size grows exponentially fast with respect to the number of nodes in the networks [4].…”

A Binary Particle Swarm Optimizer With Priority Planning and Hierarchical Learning for Networked Epidemic Control

“…Resource costs are described as nonlinear functions of model parameters, and the resource allocation problems are to optimize parameters of epidemic models. Though the second category of studies facilitate the theoretical analysis [6], they do not facilitate engineering application. In the real world, resources are concrete goods or services, such as antibiotics, vaccines, hospital beds, nurses, and clinicians, isolation wards, which are discretely distributed and priced at per-unit basis.…”