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Register a new userParameter Estimation in Epidemic Spread Networks Using Limited Measurements
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We study the problem of estimating the parameters (i.e., infection rate and recovery rate) governing the spread of epidemics in networks. Such parameters are typically estimated by measuring various characteristics (such as the number of infected and recovered individuals) of the infected populations over time. However, these measurements also incur certain costs, depending on the population being tested and the times at which the tests are administered. We thus formulate the epidemic parameter estimation problem as an optimization problem, where the goal is to either minimize the total cost spent on collecting measurements, or to optimize the parameter estimates while remaining within a measurement budget. We show that these problems are NP-hard to solve in general, and then propose approximation algorithms with performance guarantees. We validate our algorithms using numerical examples.
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One of the popular dynamics on complex networks is the epidemic spreading. An epidemic model describes how infections spread throughout a network. Among the compartmental models used to describe epidemics, the Susceptible-Infected-Susceptible (SIS) model has been widely used. In the SIS model, each node can be susceptible, become infected with a given infection rate, and become again susceptible with a given curing rate. In this paper, we add a new compartment to the classic SIS model to account for human response to epidemic spread. Each individual can be infected, susceptible, or alert. Susceptible individuals can become alert with an alerting rate if infected individuals exist in their neighborhood. An individual in the alert state is less probable to become infected than an individual in the susceptible state; due to a newly adopted cautious behavior. The problem is formulated as a continuous-time Markov process on a general static graph and then modeled into a set of ordinary differential equations using mean field approximation method and the corresponding Kolmogorov forward equations. The model is then studied using results from algebraic graph theory and center manifold theorem. We analytically show that our model exhibits two distinct thresholds in the dynamics of epidemic spread. Below the first threshold, infection dies out exponentially. Beyond the second threshold, infection persists in the steady state. Between the two thresholds, the infection spreads at the first stage but then dies out asymptotically as the result of increased alertness in the network. Finally, simulations are provided to support our findings. Our results suggest that alertness can be considered as a strategy of controlling the epidemics which propose multiple potential areas of applications, from infectious diseases mitigations to malware impact reduction.
Accurate tracking of the internal electrochemical states of lithium-ion battery during cycling enables advanced battery management systems to operate the battery safely and maintain high performance while minimizing battery degradation. To this end, techniques based on voltage measurement have shown promise for estimating the lithium surface concentration of active material particles, which is an important state for avoiding aging mechanisms such as lithium plating. However, methods relying on voltage often lead to large estimation errors when the model parameters change during aging. In this paper, we utilize the in-situ measurement of the battery expansion to augment the voltage and develop an observer to estimate the lithium surface concentration distribution in each electrode particle. We demonstrate that the addition of the expansion signal enables us to correct the negative electrode concentration states in addition to the positive electrode. As a result, compared to a voltage only observer, the proposed observer can successfully recover the surface concentration when the electrodes stoichiometric window changes, which is a common occurrence under aging by loss of lithium inventory. With a 5% shift in the electrodes stoichiometric window, the results indicate a reduction in state estimation error for the negative electrode surface concentration. Under this simulated aged condition, the voltage based observer had 9.3% error as compared to the proposed voltage and expansion observer which had 0.1% error in negative electrode surface concentration.
This paper describes an adaptive method in continuous time for the estimation of external fields by a team of $N$ agents. The agents $i$ each explore subdomains $Omega^i$ of a bounded subset of interest $Omegasubset X := mathbb{R}^d$. Ideal adaptive estimates $hat{g}^i_t$ are derived for each agent from a distributed parameter system (DPS) that takes values in the scalar-valued reproducing kernel Hilbert space $H_X$ of functions over $X$. Approximations of the evolution of the ideal local estimate $hat{g}^i_t$ of agent $i$ is constructed solely using observations made by agent $i$ on a fine time scale. Since the local estimates on the fine time scale are constructed independently for each agent, we say that the method is strictly decentralized. On a coarse time scale, the individual local estimates $hat{g}^i_t$ are fused via the expression $hat{g}_t:=sum_{i=1}^NPsi^i hat{g}^i_t$ that uses a partition of unity ${Psi^i}_{1leq ileq N}$ subordinate to the cover ${Omega^i}_{i=1,ldots,N}$ of $Omega$. Realizable algorithms are obtained by constructing finite dimensional approximations of the DPS in terms of scattered bases defined by each agent from samples along their trajectories. Rates of convergence of the error in the finite dimensional approximations are derived in terms of the fill distance of the samples that define the scattered centers in each subdomain. The qualitative performance of the convergence rates for the decentralized estimation method is illustrated via numerical simulations.
The integration of renewables into electrical grids calls for optimization-based control schemes requiring reliable grid models. Classically, parameter estimation and optimization-based control is often decoupled, which leads to high system operation cost in the estimation procedure. The present work proposes a method for simultaneously minimizing grid operation cost and optimally estimating line parameters based on methods for the optimal design of experiments. This method leads to a substantial reduction in cost for optimal estimation and in higher accuracy in the parameters compared with standard Optimal Power Flow and maximum-likelihood estimation. We illustrate the performance of the proposed method on a benchmark system.
In the real world, many complex systems interact with other systems. In addition, the intra- or inter-systems for the spread of information about infectious diseases and the transmission of infectious diseases are often not random, but with direction. Hence, in this paper, we build epidemic model based on an interconnected directed network, which can be considered as the generalization of undirected networks and bipartite networks. By using the mean-field approach, we establish the Susceptible-Infectious-Susceptible model on this network. We theoretically analyze the model, and obtain the basic reproduction number, which is also the generalization of the critical number corresponding to undirected or bipartite networks. And we prove the global stability of disease-free and endemic equilibria via the basic reproduction number as a forward bifurcation parameter. We also give a condition for epidemic prevalence only on a single subnetwork. Furthermore, we carry out numerical simulations, and find that the independence between each nodes in- and out-degrees greatly reduce the impact of the networks topological structure on disease spread.
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