The impact that each individual non-pharmaceutical intervention (NPI) had on the spread rate of COVID-19 is difficult to estimate, since several NPIs were implemented in rapid succession in most countries. In this article, we analyze the detectability of sudden changes in a parameter of nonlinear dynamical systems, which could be used to represent NPIs or mutations of the virus, in the presence of measurement noise. Specifically, by taking an agnostic approach, we provide necessary conditions for when the best possible unbiased estimator is able to isolate the effect of a sudden change in a model parameter, by using the Hammersley–Chapman–Robbins (HCR) lower bound. Several simplifications to the calculation of the HCR lower bound are given, which depend on the amplitude of the sudden change and the dynamics of the system. We further define the concept of the most informative sample based on the largest (Formula presented.) distance between two output trajectories, which is a good indicator of when the HCR lower bound converges. These results are thereafter used to analyze the susceptible-infected-removed model. For instance, we show that performing analysis using the number of recovered/deceased, as opposed to the cumulative number of infected, may be an inferior signal to use since sudden changes are fundamentally more difficult to estimate and seem to require more samples. Finally, these results are verified by simulations and applied to real data from the spread of COVID-19 in France.

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.

This article studies epidemic processes over discrete-time periodic time-varying networks. We focus on the susceptible-infected-susceptible (SIS) model that accounts for a (possibly) mutating virus. We say that an agent is in the disease-free state if it is not infected by the virus. Our objective is to devise a control strategy which ensures that all agents in a network exponentially (respectively asymptotically) converge to the disease-free equilibrium (DFE). Toward this end, we first provide 1) sufficient conditions for exponential (respectively, asymptotic) convergence to the DFE and 2) a necessary and sufficient condition for asymptotic convergence to the DFE. The sufficient condition for global exponential stability (GES) [respectively global asymptotic stability (GAS)] of the DFE is in terms of the joint spectral radius of a set of suitably defined matrices, whereas the necessary and sufficient condition for GAS of the DFE involves the spectral radius of an appropriately defined product of matrices. Subsequently, we leverage the stability results in order to design a distributed control strategy for eradicating the epidemic.

We provide corrections to two typos (in Assumption 3 and Corollary 2) and three misstatements (in Corollary 1 and Theorems 3 and 4) of [1].

In this paper we introduce a discrete time competing virus model and the assumptions necessary for the model to be well posed. We analyze the system exploring its different equilibria. We provide necessary and sufficient conditions for the estimation of the model parameters from time series data and introduce an online estimation algorithm. We employ a dataset of two competing subsidy programs from the US Department of Agriculture to validate the model by employing the identification techniques. To the best of our knowledge, this work is the first to study competing virus models in discretetime, online identification of spread parameters from time series data, and validation of said models using real data. These new contributions are important for applications since real data is naturally sampled.

This paper formulates and studies the problem of controlling a networked SIS model using a single input in which the network structure is described by a connected undirected graph. A necessary and sufficient condition on the values of curing and infection rates for the healthy state to be exponentially stable is obtained via the analysis of signed Laplacians when the control input is the curing budget of a single agent. In the case when the healthy state is stabilizable, an explicit expression for the minimum curing budget is provided. The utility of the algorithm is demonstrated using a simulation over a network of cities in the northeastern United States.

Smart building management systems rely on sensors to optimize the operation of buildings. If an unauthorized user gains access to these sensors, a privacy leak may occur. This paper considers such a potential leak of privacy in a smart residential building, and how it may be mitigated by corrupting the measurements with additive Gaussian noise. This corruption is done in order to hide when the occupancy changes in an apartment. A lower bound on the variance of any estimator that estimates the change time is derived. The bound is then used to analyze how different model parameters affect the variance. It is shown that the signal to noise ratio and the system dynamics are the main factors that affect the bound. These results are then verified on a simulator of the KTH Live-In Lab Testbed, showing good correspondence with theoretical results.

The spread of new products in a networked population is often modeled as an epidemic. However, in the case of "complex" contagion, these models do not capture nuanced, dynamic social reinforcement effects in adoption behavior. In this paper, we investigate a model of complex contagion which allows a coevolutionary interplay between adoption, modeled as an SIS epidemic spreading process, and social reinforcement effects, modeled as consensus opinion dynamics. Asymptotic stability analysis of the all-adopt as well as the none-adopt equilibria of the combined opinion-adoption model is provided through the use of Lyapunov arguments. In doing so, sufficient conditions are provided which determine the stability of the "flop" state, where no one adopts the product and everyone's opinion of the product is least favorable, and the "hit" state, where everyone adopts and their opinions are most favorable. These conditions are shown to extend to the bounded confidence opinion dynamic under a stronger assumption on the model parameters. Additional analysis is provided for the case where the product is neither a hit nor a flop. To conclude, numerical simulations demonstrate behaviors indicated in the sociology literature such as tipping points.

Privacy breaches of cyber-physical systems could expose vulnerabilities to an adversary. Here, privacy leaks of step inputs to linear time-invariant systems are mitigated through additive Gaussian noise. Fundamental lower bounds on the privacy are derived, which are based on the variance of any estimator that seeks to recreate the input. Fully private inputs are investigated and related to transmission zeros. Thereafter, a method to increase the privacy of optimal step inputs is presented and a privacy-utility trade-off bound is derived. Finally, these results are verified on data from the KTH Live-In Lab Testbed, showing good correspondence with theoretical results. 

This paper proposes a network continuous-time susceptible-infected-susceptible (SIS) model coupled with individual opinion dynamics, where the opinion dynamics models an individual's perceived severity of illness or perceived susceptibility. The effects of opinion dynamics on the network SIS model are studied by analyzing the limiting behaviors of the system model, equilibria of the system and their stability.