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We consider a susceptible-infected-susceptible (SIS) epidemic model in which a large group of individuals decide whether to adopt partially effective protection without being aware of their individual infection status. Each individual receives a signal which conveys noisy information about its infection state, and then decides its action to maximize its expected utility computed using its posterior probability of being infected conditioned on the received signal. We first derive the static signal which minimizes the infection level at the stationary Nash equilibrium under suitable assumptions. We then formulate an optimal control problem to determine the optimal dynamic signal that minimizes the aggregate infection level along the solution trajectory. We compare the performance of the dynamic signaling scheme with the optimal static signaling scheme, and illustrate the advantage of the former through numerical simulations.

The nature of the magnetic field structure throughout the Galactic Center (GC) has long been of interest. The recent Far-InfraREd Polarimetric Large-Area CMZ Exploration (FIREPLACE) Survey reveals preliminary connections between the seemingly distinct vertical and horizontal magnetic field distributions previously observed in the GC. We use the statistical techniques of the Histogram of Relative Orientation (HRO) and the Projected Rayleigh Statistic (PRS) to assess whether the CMZ magnetic field preferentially aligns with the column density gradient derived from CMZ molecular clouds or the morphology of the non-thermal emission of the GC NTF population. We find that there is a range of magnetic field orientations throughout the population of CMZ molecular clouds, ranging from parallel to perpendicular orientation. This range of orientations contrasts with what is observed in Galactic Disk star-forming regions. We also compare the magnetic field orientation from dust polarimetry with individual prominent NTFs, finding a preferred perpendicular relative orientation. This perpendicular orientation indicates that the vertical field component found in the FIREPLACE observations is not spatially confined to the NTFs, providing evidence for a more pervasive vertical field in the GC. We estimate an upper limit on the magnetic field strength for this vertical field of 4 mG. A field close to this upper limit would indicate that the NTFs are likely not local enhancements of a weaker background field and that the locations of the NTFs depend on proximity to sites of cosmic ray production., Comment: Submitted to ApJ

This letter explores the implementation of a safe control law for systems of dynamically coupled cooperating agents. Under a CBF-based collaborative safety framework, we examine how the maximum safety capability for a given agent, which is computed using a collaborative safety condition, influences safety requests made to neighbors. We provide conditions under which neighbors may be resilient to non-compliance of neighbors to safety requests, and compute an upper bound for the total amount of non-compliance an agent is resilient to, given its 1-hop neighborhood state and knowledge of the network dynamics. We then illustrate our results via simulation on a networked susceptible-infected-susceptible (SIS) epidemic model., Comment: This work is under review for publication in IEEE Control Systems Letters (L-CSS)

In this paper, we develop a framework for the automatic taxiing of aircraft between hangar and take-off given a graph-based model of an airport. We implement a high-level path-planning algorithm that models taxiway intersections as nodes in an undirected graph, algorithmically constructs a directed graph according to the physical limitations of the aircraft, and finds the shortest valid taxi path through the directed graph using Dijkstra's algorithm. We then use this shortest path to construct a reference trajectory for the aircraft to follow that considers the turning capabilities of a given aircraft. Using high-order control barrier functions (HOCBFs), we construct safety conditions for multi-obstacle avoidance and safe reference tracking for simple 2D unicycle dynamics with acceleration control inputs. We then use these safety conditions to design an MPC-CBF framework that tracks the reference trajectory while adhering to the safety constraints. We compare the performance of our MPC-CBF controller with a PID-CBF control method via simulations., Comment: This work is under review to be presented at the 2025 American Control Conference

This work explores a collaborative method for ensuring safety in multi-agent formation control problems. We formulate a control barrier function (CBF) based safety filter control law for a generic distributed formation controller and extend our previously developed collaborative safety framework to an obstacle avoidance problem for agents with acceleration control inputs. We then incorporate multi-obstacle collision avoidance into the collaborative safety framework. This framework includes a method for computing the maximum capability of agents to satisfy their individual safety requirements. We analyze the convergence rate of our collaborative safety algorithm, and prove the linear-time convergence of cooperating agents to a jointly feasible safe action for all agents under the special case of a tree-structured communication network with a single obstacle for each agent. We illustrate the analytical results via simulation on a mass-spring kinematics-based formation controller and demonstrate the finite-time convergence of the collaborative safety algorithm in the simple proven case, the more general case of a fully-connected system with multiple static obstacles, and with dynamic obstacles., Comment: This work is under review for publication in Automatica. arXiv admin note: text overlap with arXiv:2311.11156

Partial difference operators for a large class of functors between presheaf categories are introduced, extending our difference operator from \cite{Par24} to the multivariable case. These combine into the Jacobian profunctor which provides the setting for a lax chain rule. We introduce a functorial version of multivariable Newton series whose aim is to recover a functor from its iterated differences. Not all functors are recovered but we get a best approximation in the form of a left adjoint, and the induced comonad is idempotent. Its fixed points are what we call soft analytic functors, a generalization of the multivariable analytic functors of Fiore et al.~\cite{FioGamHylWin08}., Comment: 69 pages

In this paper, we propose an SIR spread model in a population network coupled with an infrastructure network that has a pathogen spreading in it. We develop a threshold condition to characterize the monotonicity and peak time of a weighted average of the infection states in terms of the global (network-wide) effective reproduction number. We further define the distributed reproduction numbers (DRNs) of each node in the multilayer network which are used to provide local threshold conditions for the dynamical behavior of each entity. Furthermore, we leverage the DRNs to predict the global behavior based on the node-level assumptions. We use both analytical and simulation results to illustrate that the DRNs allow a more accurate analysis of the networked spreading process than the global effective reproduction number.

A population of structures unique to the Galactic Center (GC), known as the non-thermal filaments (NTFs), has been studied for over 40 years, but much remains unknown about them. In particular, there is no widely-accepted and unified understanding for how the relativistic electrons illuminating these structures are generated. One possibility is that there are compact and extended sources of Cosmic Rays (CRs), which then diffuse along magnetic flux tubes leading to the illumination of the NTFs through synchrotron emission. In this work, we present and discuss the polarimetric distributions associated with a set of faint NTFs in the GC that have only been studied in total intensity previously. We compare the derived polarized intensity, rotation measure, and intrinsic magnetic field distributions for these structures with the results obtained for previously observed GC NTFs. The results are then used to enhance our understanding of the large-scale polarimetric properties of the GC. We then use the derived polarimetric distributions to constrain models for the mechanisms generating the relativistic electrons that illuminate these structures., Comment: Accepted for publication in the Astrophysical Journal

We study the impact of parameter estimation and state measurement errors on a control framework for optimally mitigating the spread of epidemics. We capture the epidemic spreading process using a susceptible-infected-removed (SIR) epidemic model and consider isolation as the control strategy. We use a control strategy to remove (isolate) a portion of the infected population. Our goal is to maintain the daily infected population below a certain level, while minimizing the resource captured by the isolation rate. Distinct from existing works on leveraging control strategies in epidemic spreading, we propose a parameter estimation strategy and further characterize the parameter estimation error bound. In order to deal with uncertainties, we propose a robust control strategy by overestimating the seriousness of the epidemic and study the feasibility of the system. Compared to the optimal control strategy, we establish that the proposed strategy under parameter estimation and measurement errors will sacrifice optimality to flatten the curve., Comment: arXiv admin note: text overlap with arXiv:2209.01508

We establish a calculus of differences for taut endofunctors of the category of sets, analogous to the classical calculus of finite differences for real valued functions. We study how the difference operator interacts with limits and colimits as categorical versions of the usual product and sum rules. The first main result is a lax chain rule which has no counterpart for mere functions. We also show that many important classes of functors (polynomials, analytic functors, reduced powers, ...) are taut, and calculate explicit formulas for their differences. Covariant Dirichlet series are introduced and studied. The second main result is a Newton summation formula expressed as an adjoint to the difference operator., Comment: 80 pages

In this work, we first show that the problem of parameter identification is often ill-conditioned and lacks the persistence of excitation required for the convergence of online learning schemes. To tackle these challenges, we introduce the notion of optimal and greedy excitation sets which contain data points with sufficient richness to aid in the identification task. We then present the greedy excitation set-based recursive least squares algorithm to alleviate the problem of the lack of persistent excitation, and prove that the iterates generated by the proposed algorithm minimize an auxiliary weighted least squares cost function. When data points are generated from time-varying parameters, online estimators tend to underfit the true parameter trajectory, and their predictability deteriorates. To tackle this problem, we propose a memory resetting scheme leveraging change point detection techniques. Finally, we illustrate the performance of the proposed algorithms via several numerical case studies to learn the (time-varying) parameters of networked epidemic dynamics, and compare it with results obtained using conventional approaches.

We have designed a Python-based Domain Specific Language (DSL) for modeling synchronous digital circuits. In this DSL, hardware is modeled as a collection of transactions -- running in series, parallel, and loops. When the model is executed by a Python interpreter, synthesizable and behavioural Verilog is generated as output, which can be integrated with other RTL designs or directly used for FPGA and ASIC flows. In this paper, we describe - 1) the language (DSL), which allows users to express computation in series/parallel/loop constructs, with explicit cycle boundaries, 2) the internals of a simple Python implementation to produce synthesizable Verilog, and 3) several design examples and case studies for applications in post-quantum cryptography, stereo-vision, digital signal processing and optimization techniques. In the end, we list ideas to extend this framework., Comment: 9 pages, 13 figures

Despite the high measurement fidelity that can now be reached, the dispersive qubit readout of circuit quantum electrodynamics is plagued by a loss of its quantum nondemolition character and a decrease in fidelity with increased measurement strength. In this work we elucidate the nature of this dynamical process, which we refer to as transmon ionization. We develop a comprehensive framework which provides a unified physical picture of the origin of transmon ionization. This framework consists of three complementary levels of descriptions: a fully quantized transmon-resonator model, a semiclassical model where the resonator is treated as a classical drive on the transmon, and a fully classical model. Crucially, all three approaches preserve the full cosine potential of the transmon, and lead to similar predictions. This framework identifies the multiphoton resonances responsible for transmon ionization. It also allows us to efficiently compute numerical estimates of the photon number threshold for ionization, which are in remarkable agreement with recent experimental results. The set of tools developed within this work are both conceptually and computationally simple, and we expect them to become an integral part of the theoretical support of all circuit QED experiments.

Model predictive control (MPC) has been shown to significantly improve the energy efficiency of buildings while maintaining thermal comfort. Data-driven approaches based on neural networks have been proposed to facilitate system modelling. However, such approaches are generally nonconvex and result in computationally intractable optimization problems. In this work, we design a readily implementable energy management method for small commercial buildings. We then leverage our approach to formulate a real-time demand bidding strategy. We propose a data-driven and mixed-integer convex MPC which is solved via derivative-free optimization given a limited computational time of 5 minutes to respect operational constraints. We consider rooftop unit heating, ventilation, and air conditioning systems with discrete controls to accurately model the operation of most commercial buildings. Our approach uses an input convex recurrent neural network to model the thermal dynamics. We apply our approach in several demand response (DR) settings, including a demand bidding, a time-of-use, and a critical peak rebate program. Controller performance is evaluated on a state-of-the-art building simulation. The proposed approach improves thermal comfort while reducing energy consumption and cost through DR participation, when compared to other data-driven approaches or a set-point controller.

We present the second data release (DR2) of the Far-Infrared Polarimetric Large-Area CMZ Exploration (FIREPLACE) survey. This survey utilized the Stratospheric Observatory for Infrared Astronomy (SOFIA) High-resolution Airborne Wideband Camera plus (HAWC+) instrument at 214 $\mu$m (E-band) to observe dust polarization throughout the Central Molecular Zone (CMZ) of the Milky Way. DR2 consists of observations that were obtained in 2022 covering the region of the CMZ extending roughly from the Brick to the Sgr C molecular clouds (corresponding to a roughly 1$^{\circ}$ $\times$ 0.75$^{\circ}$ region of the sky). We combine DR2 with the first FIREPLACE data release to obtain full coverage of the CMZ (a 1.5$^{\circ}$ $\times$0.75$^{\circ}$ region of the sky). After applying total and polarized intensity significance cuts on the full FIREPLACE data set we obtain $\rm\sim$65,000 Nyquist-sampled polarization pseudovectors. The distribution of polarization pseudovectors confirms a bimodal distribution in the CMZ magnetic field orientations, recovering field components that are oriented predominantly parallel or perpendicular to the Galactic plane. These magnetic field orientations indicate possible connections between the previously observed parallel and perpendicular distributions. We also inspect the magnetic fields toward a set of prominent CMZ molecular clouds (the Brick, Three Little Pigs, 50 km s$\rm^{-1}$, Circum-nuclear Disk, CO 0.02-0.02, 20 km s$\rm^{-1}$, and Sgr C), revealing spatially varying magnetic fields that generally trace the morphologies of the clouds. We find evidence that compression from stellar winds and shear from tidal forces are prominent mechanisms influencing the structure of the magnetic fields observed within the clouds., Comment: 35 pages, 23 figures, 3 tables. Article is accepted for publication in ApJ

We present the detection of a magnetized dust ring (M0.8-0.2) in the Central Molecular Zone (CMZ) of the Galactic Center. The results presented in this paper utilize the first data release (DR1) of the Far-Infrared Polarimetric Large Area CMZ Exploration (FIREPLACE) survey (i.e., FIREPLACE I; Butterfield et al. 2023). The FIREPLACE survey is a 214 $\mu$m polarimetic survey of the Galactic Center using the SOFIA/HAWC+ telescope. The M0.8-0.2 ring is a region of gas and dust that has a circular morphology with a central depression. The dust polarization in the M0.8-0.2 ring implies a curved magnetic field that traces the ring-like structure of the cloud. We posit an interpretation in which an expanding shell compresses and concentrates the ambient gas and magnetic field. We argue that this compression results in the strengthening of the magnetic field, as we infer from the observations toward the interior of the ring., Comment: Accepted for publication in ApJ

Modeling epidemic spread is critical for informing policy decisions aimed at mitigation. Accordingly, in this work we present a new data-driven method based on Gaussian process regression (GPR) to model epidemic spread. We bound the variance of the predictions made by GPR, which quantifies the impact of epidemic data on the proposed model. Next, we derive a high-probability error bound on the prediction error in terms of the distance between the training points and a testing point, the posterior variance, and the level of change in the spreading process, and we assess how the characteristics of the epidemic spread and infection data influence this error bound. We present examples that use GPR to model and predict epidemic spread by using real-world infection data gathered in the UK during the COVID-19 epidemic. These examples illustrate that, under typical conditions, the prediction for the next twenty days has 94.29% of the noisy data located within the 95% confidence interval, validating these predictions.

The safe control of multi-robot swarms is a challenging and active field of research, where common goals include maintaining group cohesion while simultaneously avoiding obstacles and inter-agent collision. Building off our previously developed theory for distributed collaborative safety-critical control for networked dynamic systems, we propose a distributed algorithm for the formation control of robot swarms given individual agent dynamics, induced formation dynamics, and local neighborhood position and velocity information within a defined sensing radius for each agent. Individual safety guarantees for each agent are obtained using rounds of communication between neighbors to restrict unsafe control actions among cooperating agents through safety conditions derived from high-order control barrier functions. We provide conditions under which a swarm is guaranteed to achieve collective safety with respect to multiple obstacles using a modified collaborative safety algorithm. We demonstrate the performance of our distributed algorithm via simulation in a simplified physics-based environment., Comment: This work has been accepted to be presented at the 2024 European Control Conference

Effective containment of spreading processes such as epidemics requires accurate knowledge of several key parameters that govern their dynamics. In this work, we first show that the problem of identifying the underlying parameters of epidemiological spreading processes is often ill-conditioned and lacks the persistence of excitation required for the convergence of adaptive learning schemes. To tackle this challenge, we leverage a relaxed property called initial excitation combined with a recursive least squares algorithm to design an online adaptive identifier to learn the parameters of the susceptible-infected-susceptible (SIS) epidemic model from the knowledge of its states. We prove that the iterates generated by the proposed algorithm minimize an auxiliary weighted least squares cost function. We illustrate the convergence of the error of the estimated epidemic parameters via several numerical case studies and compare it with results obtained using conventional approaches.

During the COVID-19 pandemic, different countries, regions, and communities constructed various epidemic models to evaluate spreading behaviors and assist in making mitigation policies. Model uncertainties, introduced by complex transmission behaviors, contact-tracing networks, time-varying spreading parameters, and human factors, as well as insufficient data, have posed arduous challenges for model-based approaches. To address these challenges, we propose a novel framework for data-driven counterfactual analysis, strategy evaluation, and feedback control of epidemics, which leverages statistical information from epidemic testing data instead of constructing a specific model. Through reverse engineering the reproduction number by quantifying the impact of the intervention strategy, this framework tackles three primary problems: 1) How severe would an outbreak have been without the implemented intervention strategies? 2) What impact would varying the intervention strength have had on an outbreak? 3) How can we adjust the intervention intensity based on the current state of an outbreak? Specifically, we consider the epidemic intervention policies such as the testing-for-isolation strategy as an example, which was successfully implemented by the University of Illinois Urbana-Champaign (UIUC) and Purdue University (Purdue) during the COVID-19 pandemic. By leveraging data collected by UIUC and Purdue, we validate the effectiveness of the proposed data-driven framework.

The inner hundred parsecs of the Milky Way hosts the nearest supermassive black hole, largest reservoir of dense gas, greatest stellar density, hundreds of massive main and post main sequence stars, and the highest volume density of supernovae in the Galaxy. As the nearest environment in which it is possible to simultaneously observe many of the extreme processes shaping the Universe, it is one of the most well-studied regions in astrophysics. Due to its proximity, we can study the center of our Galaxy on scales down to a few hundred AU, a hundred times better than in similar Local Group galaxies and thousands of times better than in the nearest active galaxies. The Galactic Center (GC) is therefore of outstanding astrophysical interest. However, in spite of intense observational work over the past decades, there are still fundamental things unknown about the GC. JWST has the unique capability to provide us with the necessary, game-changing data. In this White Paper, we advocate for a JWST NIRCam survey that aims at solving central questions, that we have identified as a community: i) the 3D structure and kinematics of gas and stars; ii) ancient star formation and its relation with the overall history of the Milky Way, as well as recent star formation and its implications for the overall energetics of our galaxy's nucleus; and iii) the (non-)universality of star formation and the stellar initial mass function. We advocate for a large-area, multi-epoch, multi-wavelength NIRCam survey of the inner 100\,pc of the Galaxy in the form of a Treasury GO JWST Large Program that is open to the community. We describe how this survey will derive the physical and kinematic properties of ~10,000,000 stars, how this will solve the key unknowns and provide a valuable resource for the community with long-lasting legacy value., Comment: This White Paper will be updated when required (e.g. new authors joining, editing of content). Most recent update: 24 Oct 2023

As modern systems become ever more connected with complex dynamic coupling relationships, developing safe control methods becomes paramount. In this paper, we discuss the relationship of node-level safety definitions for individual agents with local neighborhood dynamics. We define a collaborative control barrier function (CCBF) and provide conditions under which sets defined by these functions will be forward invariant. We use collaborative node-level control barrier functions to construct a novel \edit{decentralized} algorithm for the safe control of collaborating network agents and provide conditions under which the algorithm is guaranteed to converge to a viable set of safe control actions for all agents. We illustrate these results on a networked susceptible-infected-susceptible (SIS) model., Comment: This work is under review for publication in the IEEE Transactions on Automatic Control

The basic reproduction number of a networked epidemic model, denoted $R_0$, can be computed from a network's topology to quantify epidemic spread. However, disclosure of $R_0$ risks revealing sensitive information about the underlying network, such as an individual's relationships within a social network. Therefore, we propose a framework to compute and release $R_0$ in a differentially private way. First, we provide a new result that shows how $R_0$ can be used to bound the level of penetration of an epidemic within a single community as a motivation for the need of privacy, which may also be of independent interest. We next develop a privacy mechanism to formally safeguard the edge weights in the underlying network when computing $R_0$. Then we formalize tradeoffs between the level of privacy and the accuracy of values of the privatized $R_0$. To show the utility of the private $R_0$ in practice, we use it to bound this level of penetration under privacy, and concentration bounds on these analyses show they remain accurate with privacy implemented. We apply our results to real travel data gathered during the spread of COVID-19, and we show that, under real-world conditions, we can compute $R_0$ in a differentially private way while incurring errors as low as $7.6\%$ on average., Comment: 8 pages, 3 figures

Transportation networks play a critical part in the spread of infectious diseases between populations. In this work, we define a networked susceptible-exposed-infected-recovered epidemic process with loss of immunity over time (SEIRS) that explicitly models the flow of individuals between sub-populations, which serves as the propagating mechanism for infection. We provide sufficient conditions for local stability and instability of the healthy state of the system and show that no perturbation of population flows can change the local stability of any healthy state. We also provide sufficient conditions for the existence and uniqueness of an endemic state. We then develop tools and methods for applying our model to real-world data, including spreading parameter estimation and disease arrival time prediction, and apply them in a case study using both travel and infection data from counties in Minnesota during the first year of the COVID-19 pandemic., Comment: Submitted to and under revision in IEEE Transactions on Network Science and Engineering

The notion of retrocell in a double category with companions is introduced and its basic properties established. Explicit descriptions in some of the usual double categories are given. Monads in a double category provide an important example where retrocells arise naturally. Cofunctors appear as a special case. The motivating example of vertically closed double categories is treated in some detail., Comment: As referee suggested: References added, typos corrected, table of contents included

We present the first data release (DR1) of the Far-Infrared Polarimetric Large Area CMZ Exploration (FIREPLACE) survey. The survey was taken using the 214-micron band of the HAWC+ instrument with the SOFIA telescope (19.6$'$ resolution; 0.7 pc). In this first data release we present dust polarization observations covering a ~0.5$\deg$ region of the Galactic Center's Central Molecular Zone (CMZ), approximately centered on the Sgr B2 complex. We detect ~25,000 Nyquist-sampled polarization pseudovectors, after applying the standard SOFIA cuts for minimum signal-to-noise in fractional polarization and total intensity of 3 and 200, respectively. Analysis of the magnetic field orientation suggests a bimodal distribution in the field direction. This bimodal distribution shows enhancements in the distribution of field directions for orientations parallel and perpendicular to the Galactic plane, which is suggestive of a CMZ magnetic field configuration with polodial and torodial components. Furthermore, a detailed analysis of individual clouds included in our survey (i.e., Sgr B2, Sgr B2-NW, Sgr B2-Halo, Sgr B1, and Clouds-E/F) shows these clouds have fractional polarization values of 1--10% at 214-micron, with most of the emission having values $<$5%. A few of these clouds (i.e., Sgr B2, Clouds-E/F) show relatively low fractional polarization values toward the cores of the cloud, with higher fractional polarization values toward the less dense periphery. We also observe higher fractional polarization towards compact HII regions which could indicate an enhancement in the grain alignment in the dust surrounding these sources., Comment: Accepted for publication in ApJ

This paper proposes a novel discrete-time multi-virus susceptible-infected-recovered (SIR) model that captures the spread of competing epidemics over a population network. First, we provide sufficient conditions for the infection level of all the viruses over the networked model to converge to zero in exponential time. Second, we propose an observation model which captures the summation of all the viruses' infection levels in each node, which represents the individuals who are infected by different viruses but share similar symptoms. Third, we present a sufficient condition for the model to be strongly locally observable, assuming that the network has only infected or recovered individuals. Fourth, we propose a Luenberger observer for estimating the states of our system. We prove that the estimation error of our proposed estimator converges to zero asymptotically with the observer gain. Finally, we present a distributed feedback controller which guarantees that each virus dies out at an exponential rate. We then show via simulations that the estimation error of the Luenberger observer converges to zero before the viruses die out., Comment: arXiv admin note: text overlap with arXiv:2204.00708

We introduce a multi-layer networked compartmental $SIRS-V_o$ model that captures opinion dynamics, disease spread, risk perception, and self-interest vaccine-uptake behavior in an epidemic process. We characterize the target vaccination criterion of the proposed model and conditions that guarantee the criterion is obtainable by influencing opinions on disease prevalence. We leverage this result to design an eradication strategy that leverages opinions and vaccination. Through numerical simulations, we show that the proposed eradication strategy is able to stabilize the epidemic process around a healthy state equilibrium, and the outbreak rebounds after the control signal is relaxed., Comment: This work has been accepted to be presented at European Control Conference (ECC 2023)

We study the spread of multi-competitive viruses over a (possibly) time-varying network of individuals accounting for the presence of shared infrastructure networks that further enables transmission of the virus. We establish a sufficient condition for exponentially fast eradication of a virus for: 1) time-invariant graphs, 2) time-varying graphs with symmetric interactions between individuals and homogeneous virus spread across the network (same healing and infection rate for all individuals), and 3) directed and slowly varying graphs with heterogeneous virus spread (not necessarily same healing and infection rates for all individuals) across the network. Numerical examples illustrate our theoretical results and indicate that, for the time-varying case, violation of the aforementioned sufficient conditions could lead to the persistence of a virus.

Reproduction numbers are widely used for the estimation and prediction of epidemic spreading processes over networks. However, reproduction numbers do not enable estimation and prediction in individual communities within networks, and they can be difficult to compute due to the aggregation of infection data that is required to do so. Therefore, in this work we propose a novel concept of distributed reproduction numbers to capture the spreading behaviors of each entity in the network, and we show how to compute them using certain parameters in networked SIS and SIR epidemic models. We use distributed reproduction numbers to derive new conditions under which an outbreak can occur. These conditions are then used to derive new conditions for the existence, uniqueness, and stability of equilibrium states. Finally, in simulation we use synthetic infection data to illustrate how distributed reproduction numbers provide more fine-grained analyses of networked spreading processes than ordinary reproduction numbers.

This paper proposes a feedback design that effectively copes with uncertainties for reliable epidemic monitoring and control. There are several optimization-based methods to estimate the parameters of an epidemic model by utilizing past reported data. However, due to the possibility of noise in the data, the estimated parameters may not be accurate, thereby exacerbating the model uncertainty. To address this issue, we provide an observer design that enables robust state estimation of epidemic processes, even in the presence of uncertain models and noisy measurements. Using the estimated model and state, we then devise optimal control policies by minimizing a predicted cost functional. To demonstrate the effectiveness of our approach, we implement it on a modified SIR epidemic model. The results show that our proposed method is efficient in mitigating the uncertainties that may arise in epidemic monitoring and control., Comment: To appear in the proceedings of IFAC World Congress 2023