Article
Mathematics, Applied
Pan Yang, Junbo Jia, Wei Shi, Jianwen Feng, Xinchu Fu
Summary: This paper investigates the stability and optimal control of SIS epidemic systems with birth and death in directed complex networks. A class of epidemic systems are constructed based on SIS models and the topology of the network, introducing a nonlinear incidence rate. The disease-free and the endemic equilibria are derived, and the local and global stability of these equilibria are discussed. The optimal control issue is considered from the perspective of the Pontryagin Minimum Principle, and the corresponding optimal control systems and tactics are obtained. Numerical examples demonstrate the effectiveness of the proposed method.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Madhab Barman, Nachiketa Mishra
Summary: This article considers a time delay networked Susceptible-Infectious-Recovered (SIR) epidemic model with a nonlinear incidence rate on a graph of Laplacian diffusion. The model incorporates population mobility through the graph network. Several stability theorems are established for all possible equilibrium points of the model. In addition, Hopf bifurcation analysis is conducted for the endemic equilibrium. Numerical results are provided to validate the theoretical findings.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
H. I. Alrebdi, Andre Steklain, Edgard P. M. Amorim, Euaggelos Zotos
Summary: The evolution of epidemics based on the SIS model relies on the density of infected individuals rho. Recent research shows that the mean density rho and its variance Sigma 2 can be considered as canonical variables and follow Hamilton's equations. By using the Hamiltonian formulation, the SIS system coupled to a Nose thermal bath is studied. Classical parameters like temperature are reinterpreted in an epidemiological context. Unlike classical epidemiological models, the thermal bath introduces fluctuations that modify the system's dynamical behavior, such as those observed in some infectious waves. The stability is investigated, and it is shown that rho tends to be half of the value predicted by the original SIS model.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Shangzhi Li, Shangjiang Guo
Summary: This paper investigates a stochastic epidemic model with nonlinear incidence rate and Brownian motions, proving the permanence or extinction of the disease under different conditions. Numerical simulations illustrate the results, showing that appropriate intensities of white noises can cause fluctuations in susceptible and infected individuals.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2021)
Article
Mathematics, Applied
Xiao-Bing Zhang, Liang Zheng
Summary: In this paper, we propose a stochastic SIR epidemic model with vertical transmission and varying total population size. We prove the existence and uniqueness of the global positive solution for the stochastic model. We establish three thresholds of the model and study their effects on the disease transmission. Furthermore, we find that stochastic perturbations can either enhance or decrease certain thresholds, resulting in different impacts on disease spread. Finally, we provide numerical examples to illustrate the obtained results.
JOURNAL OF NONLINEAR SCIENCE
(2023)
Article
Mathematics, Applied
Aadil Lahrouz, Adel Settati, Mohamed El Fatini, Abdessamad Tridane
Summary: This paper aims to analyze the classical SIS epidemic model with a generalized force of infection perturbed by white noise. Through Feller's test, it is proven that the disease dies out with probability one without any restriction on the model parameters.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Biology
Carl Corcoran, Alan Hastings
Summary: This study examines a network-based model for simulating the spread of SIS-type diseases, analyzing its epidemiological characteristics, deriving the epidemic threshold and equilibrium point, and assessing the model's sensitivity to network parameters.
BULLETIN OF MATHEMATICAL BIOLOGY
(2021)
Article
Mathematical & Computational Biology
Wenjie Qin, Jiamin Zhang, Zhengjun Dong
Summary: This passage discusses quantifying and evaluating the influence of media coverage on infectious disease control through a mathematical model. It proposes a switching epidemic model that considers the effect of media coverage and incorporates it only when the number of infected cases surpasses a specific threshold. The passage also explores the existence and stability of equilibria within the model and analyzes the impact of key parameters on epidemic outbreaks. The potential benefits of mass media coverage in preventing emerging infectious diseases are discussed as well.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
Review
Mathematics
Florin Avram, Rim Adenane, David I. Ketcheson
Summary: Many mathematical epidemiological models, especially those used in COVID-19 research, can be divided into three groups: susceptible/entrance, diseased, and output. These models have linear ODE dynamics and simple formulas for reproduction number R and first integral. SIR-PH models offer approximate control policies with a probabilistic interpretation.
Article
Automation & Control Systems
Jasmina Dordevic, Bojana Jovanovic
Summary: In this paper, a delayed stochastic SLVIQR epidemic model is derived, which can be applied to model the new coronavirus COVID-19 after calibration. The model assumes that the transmission rate follows a mean-reverting Ornstain-Uhlenbeck process and considers two additional driving processes: a stationary Poisson point process and a continuous finite-state Markov chain. The existence and uniqueness of the positive global solution are proven for the constructed model. Sufficient conditions for disease extinction or persistence in the mean are established, and the model is shown to have a richer dynamic analysis compared to existing models. Numerical simulations are provided to illustrate the theoretical results.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Automation & Control Systems
Nguyen Du, Alexandru Hening, Nhu Nguyen, George Yin
Summary: This paper focuses on realistic hybrid SIR models that consider stochasticity. The proposed systems are applicable to various incidence rates used in the literature. The study analyzes a system of stochastic differential equations that include hidden state individuals and investigates the long-term behavior of the disease based on a threshold A.
NONLINEAR ANALYSIS-HYBRID SYSTEMS
(2023)
Article
Mathematics
Di Liang, Ran Bhamra, Zhongyi Liu, Yucheng Pan
Summary: Risk propagation presents a significant challenge to supply chain management. This study demonstrates the importance of understanding how risks propagate and diffuse in a supply chain network. By using the SIR model, the researchers were able to identify and predict the risk status of the supply chain at different times. The results show a significant relationship between network structure and risk propagation, highlighting the importance of supply network visibility and information extraction for managing risks.
Article
Physics, Multidisciplinary
Sandro M. Reia, Jose F. Fontanari
Summary: The study of citations in scientific literature, also known as the 'science of science,' reveals that citations have a cascading effect and can explain many patterns in citation behavior. By using the SIR epidemic model, researchers can gain insights into the citation dynamics of well-cited papers and their impact on academic communities. There is a good, though not perfect, agreement between journal rankings based on epidemiological parameters and impact factors.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Mathematics, Interdisciplinary Applications
Yassine Chakir
Summary: This paper presents a global semi-analytical method based on two-point Pade approximants for solving the SIR epidemic model of childhood diseases. The method provides an explicit analytical solution over the entire time period, including the peak time, which is crucial for understanding disease spread. The efficiency of the method is demonstrated by comparing the results with classical Pade approximations and the numerical Runge-Kutta-Fehlberg method.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Lasko Basnarkov, Igor Tomovski, Trifce Sandev, Ljupco Kocarev
Summary: We introduce a non-Markovian SIR epidemic spreading model inspired by the characteristics of COVID-19, by considering discrete and continuous-time versions. By selecting appropriate functions, the model can be reduced to the classical Markovian case. The relevance of the model is demonstrated by modeling the first wave of the epidemic in Italy, Spain, and the UK in spring 2020.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Automation & Control Systems
Masako Kishida, Masaki Ogura
Summary: This paper proposes a computational technique to solve discrete-time optimal control problems for nonlinear systems, utilizing deep unfolding and deep learning methods to optimize control inputs that would otherwise be difficult to obtain. Numerical experiments demonstrate the effectiveness of this approach.
IET CONTROL THEORY AND APPLICATIONS
(2022)
Article
Engineering, Electrical & Electronic
Masaya Kumazaki, Masaki Ogura, Takuji Tachibana
Summary: In this paper, a dynamic service chain construction based on model predictive control (MPC) is proposed for beyond 5G era in NFV environments, aiming to simultaneously determine the transmission route of service chains, the placement of VNFs, and the allocation of resources for each VNF to minimize the resource allocation and VNF migration. The method is evaluated through simulation to investigate its effectiveness with different parameter values.
IEICE TRANSACTIONS ON COMMUNICATIONS
(2022)
Article
Robotics
Anna Fujioka, Masaki Ogura, Naoki Wakamiya
Summary: The shepherding problem involves guiding a flock of agents to a destination using repulsion forces exerted by external agents. Most previous studies assume uniform dynamics of the agents to be guided, which may not hold in practical situations. This paper proposes a shepherding method that discriminates normal and variant agents based on their deviation from the predicted behavior of normal agents, using static and dynamic thresholds. Simulation results show the effectiveness of the proposed methods for different types of variant agents.
Article
Automation & Control Systems
Bohao Zhu, James Lam, Masaki Ogura
Summary: This paper investigates the finite-time optimal control problems for positive linear systems with a time-varying control input. The optimization problem with piecewise-constant matrix functions is proven to be log-log convex and can be solved via geometric programming. The log-log convex result is further extended to the optimization problem with continuous functions. An optimal control problem is investigated to verify the effectiveness of the proposed optimization framework.
Article
Engineering, Electrical & Electronic
Chengyan Zhao, Kazunori Sakurama, Masaki Ogura
Summary: This paper focuses on the H-2 and H-8 norm constrained optimization problems of dynamic buffer networks. The extended network model is introduced with independently tunable weights of all edges. Due to the nonconvexity of the extended model, previous results of positive linear systems failed to address this situation. By utilizing the log-log convexity of posynomials, the optimization problems can be reduced to differential convex programming problems. The proposed framework is demonstrated for large-scale networks.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2023)
Article
Automation & Control Systems
Xin Gong, Masaki Ogura, Jun Shen, Tingwen Huang, Yukang Cui
Summary: This work investigates the optimal epidemics policy-seeking problem on networks-of-networks (NoN) in the presence of unknown malicious adding-edge attacks. The conflicts between each network policymaker and the attacker are captured by a series of Stackelberg games, while all network policymakers together compose a Nash game. A Heuristic algorithm based on iterative geometric programming is proposed to seek the gestalt Nash equilibrium (GNE) of the game, with a demonstrated asymptotical convergence. The practicability and validity of the theoretical results and algorithms are illustrated through a simulation example.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Automation & Control Systems
Masaki Ogura, Clyde Martin
Summary: In this study, we analyzed a switched Riccati differential equation driven by a Poisson-like stochastic signal and focused on computing the mean escape time. We found that the mean escape time of the switched Riccati differential equation has a power series expression under the assumption that the subsystems described as deterministic Riccati differential equations escape in finite time regardless of their initial state. Additionally, we presented an approximate formula to compute the escape time of deterministic Riccati differential equations and demonstrated the obtained results through numerical simulations.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Automation & Control Systems
Chengyan Zhao, Bohao Zhu, Masaki Ogura, James Lam
Summary: This letter addresses the optimization problems of discrete-time positive linear systems. It introduces parameterized system coefficient matrices and optimizes system parameters to solve the synthesis problem. By utilizing results from positive linear systems and nonnegative matrix theory, the authors show that the optimization problems of minimizing parameter tuning cost while satisfying certain norm constraints can be reduced to geometric programming problems. Additionally, under reasonable assumptions on system matrices, these geometric programming problems can be further transformed into convex optimization problems. Simulation experiments validate the main results on a numerical example and epidemic spreading process example.
IEEE CONTROL SYSTEMS LETTERS
(2023)
Proceedings Paper
Automation & Control Systems
Yaosheng Deng, Masaki Ogura, Aiyi Li, Naoki Wakamiya
Summary: This paper addresses the problem of controlling a swarm to spatially separate a specific target agent from other agents while maintaining connectivity. The authors propose a movement algorithm for an external agent called a shepherd, which applies repulsive forces to the agents in the swarm. The study has potential applications in manipulating swarms of micro- and nano-particles. The effectiveness of the proposed algorithm is demonstrated through numerical simulations.
Article
Computer Science, Interdisciplinary Applications
Kazuki Nakajima, Ruodan Liu, Kazuyuki Shudo, Naoki Masuda
Summary: Gender imbalance in academia is more severe in East Asian countries, especially in Japan, where the gender imbalance is more pronounced in terms of research career and citation practice.
JOURNAL OF INFORMETRICS
(2023)
Proceedings Paper
Automation & Control Systems
Anna Fujioka, Masaki Ogura, Naoki Wakamiya
Summary: This paper proposes two shepherding methods for guiding a flock of sheep agents, including variant agents. By estimating the trajectory of the sheep agents and discriminating their types based on the degree of deviation, the proposed methods can guide more sheep agents than conventional methods.
2022 61ST ANNUAL CONFERENCE OF THE SOCIETY OF INSTRUMENT AND CONTROL ENGINEERS (SICE)
(2022)
Article
Mathematical & Computational Biology
Ryoto Himo, Masaki Ogura, Naoki Wakamiya
Summary: In this paper, a sheepdog algorithm for guiding unresponsive sheep is proposed, and numerical simulations demonstrate its superiority over the farthest-agent targeting algorithm.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2022)
Article
Automation & Control Systems
Masaaki Nagahara, Masaki Ogura, Yutaka Yamamoto
Summary: In this letter, a novel method is proposed to find matrices that satisfy both sparsity and LMI constraints at the same time. The method is applied in sparse control design and an efficient algorithm based on Dykstra's projection algorithm is introduced. A convergence theorem of the proposed algorithm is proven and some control examples are presented to illustrate the merits and demerits of the method.
IEEE CONTROL SYSTEMS LETTERS
(2022)