On the analysis of a continuous-time bi-virus model

Abstract

Motivated by the spread of opinions on different social networks, we study a distributed continuous-time bi-virus model for a system of groups of individuals. An in-depth stability analysis is performed for more general models than have been previously considered, for the healthy and epidemic states. In addition, we investigate sensitivity properties of some nontrivial equilibria and obtain an impossibility result for distributed feedback control.

Analysis and Control of a Continuous-Time Bi-Virus Model

“…The first SIS model was introduced in [8]. In this paper, we focus on the study of distributed SIS epidemic models, where there are two ways to consider such a system: 1) the model consists of n > 1 interacting individuals and the evolution of the probability of each individual being infected is studied, or 2) the model consists of n > 1 groups of Some of the material in this paper was presented at the 55th IEEE Conference on Decision and Control [1].…”

“…In [30], [32], a necessary and sufficient condition for local exponential stability of the origin is provided for two competing heterogeneous viruses over strongly connected graphs. In addition, a geometric program 1 We say that a virus is homogeneous if all agents have the same infection rate and healing rate. Otherwise, the virus is called heterogeneous.…”

“…Note that the generalization of allowing δ i = 0 includes a susceptibleinfected (SI) model. Some of the material in this paper was presented in preliminary form in [1]; this paper presents a more comprehensive treatment of the work in [1]. Additional contributions of this paper, that are not in [1], include 1) complete proofs of all the results, 2) several extensions, including the establishment of uniqueness of the parallel equilibria in Theorems 6 and 7, 3) viewing the sensitivity analysis from a control perspective, 4) an impossibility result for a certain type of distributed feedback controller, and 5) an in-depth set of simulations, illustrating the results and some unproven phenomena.…”

Going Viral: Stability of Consensus-Driven Adoptive Spread

“…where B is the matrix of β ij 's and D = diag (δ i ). This is the well-known necessary and sufficient condition for asymptotic stability of the healthy state 0 N for the general networked SIS epidemic model [48], [62]. Note that the condition in Theorem 1 causes all the Gershgorin discs to be strictly in the left half plane, a sufficient condition for (11) to hold.…”

“…A geometric program is also formulated to control the spread arXiv:1809.04581v2 [cs.SY] 14 Feb 2019 of the virus. In [48], [49], Liu et al provide global analysis for the healthy and epidemic states for the bi-virus model over strongly connected graphs and investigate distributed control techniques. These models are related to the model proposed here because they are layered networks, they modify the spread of the virus, and they allow for more complex behavior, such as a possible spectrum of endemic equilibria [51].…”