Framework for cyber risk loss distribution of hospital infrastructure: Bond percolation on mixed random graphs approach.

Networks like those of healthcare infrastructure have been a primary target of cyberattacks for over a decade. From just a single cyberattack, a healthcare facility would expect to see millions of dollars in losses from legal fines, business interruption, and loss of revenue. As more medical devices become interconnected, more cyber vulnerabilities emerge, resulting in more potential exploitation that may disrupt patient care and give rise to catastrophic financial losses.

Survival and extinction results for a patch model with sexual reproduction.

We consider a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in each patch at a rate proportional to the number of pairs of individuals in the patch (sexual reproduction) rather than simply the number of individuals as in the basic contact process. Offspring produced at a given patch either stay in their parents' patch or are sent to a nearby patch with some fixed probabilities.

Expansion or extinction: deterministic and stochastic two-patch models with Allee effects.

We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment. Our main focus is on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes a global extinction. Our study is based on the combination of analytical and numerical results for both a deterministic two-patch model and a stochastic counterpart.