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In this paper we introduce the optimal control of a kinetic model describing agents who migrate on a graph and interact within its nodes exchanging a physical quantity. As a prototype model, we consider the spread of an infectious disease…

Optimization and Control · Mathematics 2026-01-15 Jonathan Franceschi , Nadia Loy

Optimizing the impact on the economy of control strategies aiming at containing the spread of COVID-19 is a critical challenge. We use daily new case counts of COVID-19 patients reported by local health administrations from different…

Populations and Evolution · Quantitative Biology 2021-03-12 Afroza Shirin , Yen Ting Lin , Francesco Sorrentino

In Networked Control Systems (NCS), the absence of physical communication links in the loop leads to relevant issues, such as measurement delays and asynchronous execution of the control commands. These issues may lead to unwanted control…

Systems and Control · Electrical Eng. & Systems 2022-11-16 Luca Nanu , Carlos Perez Montenegro , Luigi Colangelo , Carlo Novara

Exploiting the power of the expectation operator and indicator (or Bernoulli) random variables, we present the exact governing equations for both the SIR and SIS epidemic models on \emph{networks}. Although SIR and SIS are basic epidemic…

Dynamical Systems · Mathematics 2014-02-10 Piet Van Mieghem

Pathogen introduction in plant communities can cause serious impact and biodiversity losses that may take long time to manage and restore. Effective control of epidemic spreading in the wild is a problem of paramount importance, because of…

Populations and Evolution · Quantitative Biology 2022-06-15 Ignacio Taguas , José A. Capitán , Juan C. Nuño

Nonlinear model predictive control (NMPC) is one of the few control methods that can handle multivariable nonlinear controlsystems with constraints. Gaussian processes (GPs) present a powerful tool to identify the required plant model and…

Optimization and Control · Mathematics 2020-05-26 E. Bradford , L. Imsland , D. Zhang , E. A. del Rio-Chanona

Optimal control theory in epidemiology has been used to establish the most effective intervention strategies for managing and mitigating the spread of infectious diseases while considering constraints and costs. Using Pontryagin's Maximum…

Physics and Society · Physics 2025-08-08 Sandra Montes-Olivas , Adam J. Kucharski , Michael B. Gravenor , Simon D. W. Frost

The paper considers continuous-time networked susceptible-infected-susceptible (SIS) diseases spreading over a population. Each agent represents a sub-population and has its own healing rate and infection rate; the state of the agent at a…

Systems and Control · Electrical Eng. & Systems 2022-10-11 Yuan Wang , Sebin Gracy , César A. Uribe , Hideaki Ishii , Karl Henrik Johansson

We consider a behavioral-feedback SIR epidemic model, in which the infection rate depends in feedback on the fractions of susceptible and infected agents, respectively. The considered model allows one to account for endogenous adaptation…

Systems and Control · Electrical Eng. & Systems 2026-02-11 Martina Alutto , Leonardo Cianfanelli , Giacomo Como , Fabio Fagnani , Francesca Parise

This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between…

Probability · Mathematics 2020-03-10 Monia Capanna

Network--based epidemic models that account for heterogeneous contact patterns are extensively used to predict and control the diffusion of infectious diseases. We use census and survey data to reconstruct a geo--referenced and…

Social and Information Networks · Computer Science 2026-05-19 Alessandro Celestini , Francesca Colaiori , Stefano Guarino , Enrico Mastrostefano , Lena Rebecca Zastrow

We present and analyze an actively controlled Susceptible-Infected-Susceptible (actSIS) model of interconnected populations to study how risk aversion strategies, such as social distancing, affect network epidemics. A population using a…

Populations and Evolution · Quantitative Biology 2024-10-18 Anastasia Bizyaeva , Marcela Ordorica Arango , Yunxiu Zhou , Simon Levin , Naomi Ehrich Leonard

Analyzing and controlling spreading processes are challenging problems due to the involved non-linear node (subsystem) dynamics, unknown disturbances, complex interconnections, and the large-scale and multi-level nature of the problems. The…

Systems and Control · Electrical Eng. & Systems 2025-10-13 Shirantha Welikala , Hai Lin , Panos J. Antsaklis

The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the…

Applications · Statistics 2025-05-07 Omar Melikechi , Alexander L. Young , Tao Tang , Trevor Bowman , David Dunson , James Johndrow

To control infection spreading on networks, we investigate the effect of observer nodes that recognize infection in a neighboring node and make the rest of the neighbor nodes immune. We numerically show that random placement of observer…

Physics and Society · Physics 2014-07-15 Taro Takaguchi , Takehisa Hasegawa , Yuichi Yoshida

Background: Recently developed techniques to study the spread of infectious diseases through networks make assumptions that the initial proportion infected is infinitesimal and the population behavior is static throughout the epidemic. The…

Populations and Evolution · Quantitative Biology 2012-08-17 Joel C. Miller

This paper studies efficient algorithms for dynamic curing policies and the corresponding network design problems to guarantee the fast extinction of epidemic spread in a susceptible-infected-susceptible (SIS) model. We consider a Markov…

Data Structures and Algorithms · Computer Science 2024-08-15 Yuhao Yi , Liren Shan , Shijie Wang , Philip E. Paré , Karl H. Johansson

To simplify mathematical models of disease spread, we often assume equal contact rates among hosts, but real-world scenarios differ. Network-based frameworks help capture these complexities and structural variations in actual systems. We…

Dynamical Systems · Mathematics 2024-07-03 Saswata Das , Mohammad Hossein Samaei , Caterina Scoglio

Despite the significant advances in identifying the driver nodes and energy requiring in network control, a framework that incorporates more complicated dynamics remains challenging. Here, we consider the conformity behavior into network…

Physics and Society · Physics 2022-01-26 Zu-Yu Qian , Cheng Yuan , Jie Zhou , Shi-Ming Chen , Sen Nie

Using the continuous-time susceptible-infected-susceptible (SIS) model on networks, we investigate the problem of inferring the class of the underlying network when epidemic data is only available at population-level (i.e. the number of…

Populations and Evolution · Quantitative Biology 2019-12-05 F. Di Lauro , J. -C. Croix , M. Dashti , L. Berthouze , I. Z. Kiss
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