This article reviews and presents various solved and open problems in the development,
analysis, and control of epidemic models. The proper modeling and analysis of spreading …

During the ongoing COVID-19 pandemic, mathematical models of epidemic spreading have
emerged as powerful tools to produce valuable predictions of the evolution of the pandemic …

We develop a novel approach for pricing cyber insurance contracts. The considered cyber
threats, such as viruses and worms, diffuse in a structured data network. The spread of the …

We consider the contact process on a random graph with fixed degree distribution given by
a power law. We follow the work of Chatterjee and Durrett (2009), who showed that for …

The style of mathematical models known to probabilists as Interacting Particle Systems and
exemplified by the Voter, Exclusion and Contact processes have found use in many …

The concept of active cyber defense has appeared in the literature in recent years. However,
there are no mathematical models for characterizing the effectiveness of active cyber …

In this paper we establish the necessary and sufficient criterion for the contact process on
Galton–Watson trees (resp., random graphs) to exhibit the phase of extinction (resp., short …

We consider cumulative merging percolation (CMP), a long-range percolation process
describing the iterative merging of clusters in networks, depending on their mass and mutual …

The key to our investigation is an improved (and in a sense sharp) understanding of the
survival time of the contact process on star graphs. Using these results, we show that for the …

We consider the contact process with infection rate λ on a random (d+1)-regular graph with n
vertices, G_n. We study the extinction time τ_G_n (that is, the random amount of time until …