We are living amidst a pandemic caused by a ravaging coronavirus and an accompanying pandemic of misinformation that has strained our economy and socio-political institutions. A key scientific goal is to examine mechanisms that lead to the widespread propagation of contagions, e.g., misinformation and pathogens, and identify risk factors that can trigger widespread outbreaks. A common phenomenon underlying the spread of disease and misinformation epidemics is the evolution of the contagion as it propagates, leading to the emergence of different strains, e.g., through genetic mutations in pathogens and alterations in the information content. Recent studies have revealed that models that do not account for heterogeneity in transmission risks associated with different strains of the circulating contagion can lead to inaccurate predictions. However, existing results on multi-strain spreading assume that the network has a vanishingly small clustering coefficient, whereas, clustering is widely known to be a fundamental property of real-world social networks. In this work, we investigate spreading processes that entail evolutionary adaptations on random graphs with tunable clustering and arbitrary degree distributions. We derive a mathematical framework that predicts the epidemic threshold and the probability of emergence as functions of the characteristics of the spreading object, the evolutionary pathways of the pathogen/misinformation, and the structure of the underlying network as given by the joint degree distribution of single-edges and triangles. To the best of our knowledge, our work is the first to jointly characterize the impact of clustering and evolution on the emergence of epidemic outbreaks. We supplement our theoretical finding with numerical simulations and case studies, shedding light on how clustering can offer pathways for mutation, thereby altering the course of the epidemic.

The spread of COVID-19 has been among the most devastating events affecting the health and well-being of humans worldwide since World War II. A key scientific goal concerning COVID-19 is to develop mathematical models that help us to understand and predict its spreading behavior, as well as to provide guidelines on what can be done to limit its spread. In this paper, we discuss how our recent work on a multiple-strain spreading model with mutations can help address some key questions concerning the spread of COVID-19. We highlight the recent reports on a mutation of SARS-CoV-2 that is thought to be more transmissible than the original strain and discuss the importance of incorporating mutation and evolutionary adaptations (together with the network structure) in epidemic models. We also demonstrate how the multiple-strain transmission model can be used to assess the effectiveness of mask-wearing in limiting the spread of COVID-19. Finally, we present simulation results to demonstrate our ideas and the utility of the multiple-strain model in the context of COVID-19.

We investigate the connectivity of inhomogeneous random K-out graphs, denoted H(n;μ,Kn), where each of the n nodes is assigned to a class i = 1, ..., r independently according to a probability distribution μ = {μ1, ..., μr}. Each class-i node chooses Ki,ndistinct nodes uniformly at random from among all other nodes. A pair of nodes are adjacent in H(n;μ,Kn) if at least one selects the other. Without loss of generality, we assume that K1,n≤ K2,n≤ ... ≤ Kr,n. From earlier results on homogeneous random K-out graphs (where all nodes choose the same number K of nodes), it is known that H(n;μ,Kn) is connected with high probability (whp) if Kn≥ 2. In this paper, we study the case where K1,n= 1 and seek conditions on K2,n, ..., Kr,n, and μ such that the resulting graph is connected. We show that H(n;μ,Kn) is connected whp if Kr,nis chosen such that limn→∞Kr,n= ∞. However, any bounded choice of the sequence Kr,ngives a positive probability of H(n;μ,Kn) being not connected. A numerical study is provided to validate our results in the finite node regime.

We consider secure and reliable connectivity in wireless sensor networks that utilize the heterogeneous random key predistribution scheme. We model the unreliability of wireless links by an on/off channel model that induces an Erdos-Rényi graph, while the heterogeneous scheme induces an inhomogeneous random key graph. The overall network can thus be modeled by the intersection of both graphs. We present conditions (in the form of zero-one laws) on how to scale the parameters of the intersection model, so that with high probability: i) all of its nodes are connected to at least k other nodes, i.e., the minimum node degree of the graph is no less than k, and ii) the graph is k-connected, i.e., the graph remains connected even if any k - 1 nodes leave the network. These results are shown to complement and generalize several previous results in the literature. We also present numerical results to support our findings in the finitenode regime. Finally, we demonstrate via simulations that our results are also useful when the on/off channel model is replaced with the more realistic disk communication model.

We consider a wireless sensor network secured by a heterogeneous random key predistribution scheme and investigate its reliability against both link and node failures. The heterogeneous random key predistribution scheme is a lightweight security mechanism proposed to secure sensor networks that include nodes with varying levels of resources, features, or connectivity requirements; e.g., regular nodes vs. cluster heads. To capture the reliability of the network against both link and node failures, we consider the case when each link fails independently with probability 1 - α and present conditions (in the form of zero-one laws) on how to scale the parameters of the resulting network so that it is k-connected with high probability, i.e., the network remains connected even if any k - 1 nodes fail or leave the network. Collectively, we obtain a network that is reliable against the probabilistic failure of each link and against the failure of any k - 1 nodes. We present numerical results to support these conditions in the finite-node regime.

We study the connectivity of a random graph formed by the intersection of an inhomogeneous random key graph with an inhomogeneous Erdös-Rényi graph. The former graph is naturally induced by a heterogeneous random key predistribution scheme introduced for securing wireless sensor network communications. In this scheme, nodes are divided into r classes according to a probability distribution μ = {μ1,..., μr}, and a class-i sensor is assigned Ki cryptographic keys that are selected uniformly at random from a common pool of P keys. The latter graph represents a heterogeneous on/off channel model, where the wireless channel between a class-j node and a class-j node is on (resp. off) with probability αij(resp. 1 - αij) independently from others. We present conditions on how to scale the parameters of the intersection model so that it is connected with high probability as the number of nodes gets large. The result is given in the form of a zero-one law and is supported by a numerical study in the finite-node regime.

Low-Power Wide Area Networks (LP-WANs) are an attractive emerging platform to connect the Internet-of-things. LP-WANs enable low-cost devices with a 10-year battery to communicate at few kbps to a base station, kilometers away. But deploying LP-WANs in large urban environments is challenging, given the sheer density of nodes that causes interference, coupled with attenuation from buildings that limits signal range. Yet, state-of-the-art techniques to address these limitations demand inordinate hardware complexity at the base stations or clients, increasing their size and cost.

We consider wireless sensor networks under a heterogeneous random key predistribution scheme and an on-off channel model. The heterogeneous key predistribution scheme has recently been introduced by Yağan - as an extension to the Eschenauer and Gligor scheme - for the cases when the network consists of sensor nodes with varying level of resources and/or connectivity requirements, e.g., regular nodes vs. cluster heads. The network is modeled by the intersection of the inhomogeneous random key graph (induced by the heterogeneous scheme) with an Erdös-Rényi graph (induced by the on/off channel model). We present conditions (in the form of zero-one laws) on how to scale the parameters of the intersection model so that with high probability all of its nodes are connected to at least k other nodes; i.e., the minimum node degree of the graph is no less than k. We also present numerical results to support our results in the finite-node regime. The numerical results suggest that the conditions that ensure k-connectivity coincide with those ensuring the minimum node degree being no less than k.

Friendly jamming is a PHY-layer technique used to secure wireless communications. Unlike previous efforts that fix the placement of the friendly jamming devices, in this paper we consider small- scale multi-link wireless networks, e.g., peer-to- peer or multihop, and jointly optimize the powers and locations of the friendly jamming devices so as to minimize the total jamming power while simultaneously achieving a given secrecy constraint. We use distributed MIMO techniques and incorporate the necessary conditions to ensure nullification of the friendly jamming signals at legitimate receivers. Two optimization strategies are explored: per-link and network-wide. Our optimization framework is based on formulating a signomial programming problem using condensation techniques to approximate the problem as a geometric program, which can then be transformed into a convex problem. We also consider the secrecy-aware routing problem for multihop networks and propose a routing metric based on the total jamming power along the path. Simulations show that our proposed schemes outperform previous schemes in terms of energy efficiency (55%-99% power saving). Moreover, our formulation ensures protecting legitimate transmissions by nullifying friendly jamming signals at legitimate receivers.

Cognitive radios emerged as a solution to spectrum scarcity problem. The integration of cognitive radios and wireless sensor networks enables a new paradigm of communication, in which the sensor nodes can avoid heavily‐crowded transmission bands by tuning their transmission parameters to less‐crowded bands. The authors consider the problem of spectrum assignment for cognitive radio sensor network (CRSN) under coverage, interference, minimum data rate and power budget constraints. A mixed‐integer non‐linear programming problem formulation that addresses optimal power allocation, channel selection and node scheduling is presented. Following a practical assumption, that any CRSN node can only access one channel for its transmission with the CRSN base station, the problem is transformed to a binary linear programming (BLP) problem. Using the relaxation techniques, the problem is transformed to a linear programming problem that is solvable in polynomial time, and has the same optimal solution of the BLP problem. Hence, the minimum power algorithm that achieves the optimal solution of our problem is proposed. To further reduce the complexity of the solution, three heuristic lower‐complexity algorithms are proposed to solve the problem: random, greedy and two‐stage (decoupled) algorithms.