We use a deterministic model to study two competing viruses spreading over a two-layer network in the Susceptible–Infected–Susceptible (SIS) framework, and address a central problem of identifying the winning virus in a “survival-of-the-fittest” battle. Almost all existing conditions ensure that the same virus wins regardless of initial states. In the present paper, we ask the following question: can we systematically construct SIS bivirus networks with an arbitrary but finite number of nodes such that either of the viruses can win the survival-of-the-fittest battle, depending on the initial states? We answer this question in the affirmative. More specifically, we show that given almost any network layer of one virus, we can (using our proposed systematic four-step procedure) construct the network layer for the other virus such that in the resulting bivirus network, either of the two viruses can win the survival-of-the-fittest battle. Conclusions from numerical case studies, including a real-world mobility network that captures the commuting patterns for people between 107 provinces in Italy, illustrate and extend the theoretical result and its consequences.

The paper studies multi-competitive continuous-time epidemic processes. We consider the setting where two viruses are simultaneously prevalent, and the spread occurs due to individual-to-individual interaction. In such a setting, an individual is either not affected by any of the viruses, or infected by one and exactly one of the two viruses. One of the equilibrium points is the coexistence equilibrium, i.e., multiple viruses simultaneously infect separate fractions of the population. We provide a sufficient condition for the existence of a coexistence equilibrium. We identify a condition such that for certain pairs of spread matrices either every coexistence equilibrium lies on a line that is locally exponentially attractive, or there is no coexistence equilibrium. We then provide a condition that, for certain pairs of spread matrices, rules out the possibility of the existence of a coexistence equilibrium, and, as a consequence, establishes global asymptotic convergence to the endemic equilibrium of the dominant virus. Finally, we provide a mitigation strategy that employs one virus to ensure that the other virus is eradicated. The theoretical results are illustrated using simulations.

In this article, we develop a layered networked spread model for a susceptible-infected-susceptible pathogen-borne disease spreading over a human contact network and an infrastructure network, and refer to it as a layered networked susceptible-infected-water-susceptible model (SIWS). The "W" in SIWS represents any infrastructure network contamination, not necessarily restricted to a water distribution network. We identify sufficient conditions for the existence, uniqueness, and stability of various equilibria of the aforementioned model. Further, we study an observability problem, where, assuming that the measurements of the pathogen levels in the infrastructure network are available, we provide a necessary and sufficient condition for estimation of the sickness levels of the nodes in the human contact network. Our results are illustrated through an in-depth set of simulations.

In this paper, we introduce a continuous-time competing virus model with a shared resource. We say that the system is in the healthy state if all the agents are healthy, and the shared resource is not contaminated. If the epidemic remains persistent, and the shared resource is contaminated, we say that the system is in the endemic state. First of all we show, under appropriate assumptions, that the model we introduce is well-posed. Secondly, we establish sufficient conditions for exponential (resp. asymptotic) eradication of a virus. Thirdly, for the single-virus case with a shared resource, we establish conditions that lead to existence of an endemic equilibrium. Finally, we provide a necessary and sufficient condition for uniqueness of the healthy state.