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Matrix expression and vaccination control for epidemic dynamics over dynamic networks

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Control Theory and Technology 2016年第1期14卷 39-48页

作者： Peilian GUO Yuzhen WANG School of Control Science and Engineering Shandong University Jinan Shandong 250061 China

This paper investigates epidemic dynamics over dynamic networks via the approach of semi-tensor product of matrices. First, a formal susceptible-infected-susceptible epidemic dynamic model over dynamic networks （SISED-DN） is given. Second, based on a class of determinate co-evolutionary rule, the matrix expressions are established for the dynamics of individual states and network topologies, respectively. Then, all possible final spreading equilibria are obtained for any given initial epidemic state and network topology by the matrix expression. Third, a sufficient and necessary condition of the existence of state feedback vaccination control is presented to make every individual susceptible. The study of illustrative examples shows the effectiveness of our new results.

关键词： epidemic dynamics dynamic network vaccination control semi-tensor product of matrices

Occurrence and epidemic dynamics and Accurate Prevention and Control of Important Sugarcane Pests and Diseases in the Sugarcane Areas of Yunnan

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Agricultural Biotechnology 2018年第5期7卷 148-152页

作者： Wenfeng LI Rongyue ZHANG Hongli SHAN Xiaoyan WANG Jiong YIN Zhiming LUO Jie LI Xiaoyan CANG Yingkun HUANG Sugarcane Research Institute Yunnan Province Academy of Agricultural Science

Based on investigation and research, according to the current actual production of sugarcane, the occurrence dynamics and outbreak causes of important pests and diseases that seriously affect sugarcane production were summarized, and accurate and efficient green prevention and control technology was put forward according to the occurrence and damage characteristics of important pests and diseases, such as strengthening sugarcane introduction and quarantine, breeding and selecting varieties resistant to diseases and pests, promoting the use of detoxified healthy seedlings vigorously, applying lamp trapping technology on a large scale, scientifically guiding and promoting biological prevention and control technology, practically promoting the precise and efficient application of slow-release long- acting and low toxic pesticides, strengthening field management, spraying pesticides in time at the early stage of a disease, and doing a good job of monitoring and emergency prevention and control of sudden pests.

关键词： Sugarcane areas of Yunnan Sugarcane Pests and diseases epidemic dynamics Accurate prevention and control

An Analysis of the Impact of Stay-at-Home Measures on the Occurrence of Vaccine Shortages

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Advances in Infectious Diseases 2024年第2期14卷 411-441页

作者： Nurunnahar Department of Mathematics Feni University Feni Bangladesh

COVID-19, a contagious respiratory disease, presents immediate and unforeseen challenges to people worldwide. Moreover, its transmission rapidly extends globally due to its viral transmissibility, emergence of novel strains (variants), absence of immunity, and human unawareness. This framework introduces a revised epidemic model, drawing upon mathematical principles. This model incorporates a modified vaccination and lockdown approach to comprehensively depict an epidemics transmission, containment, and decision-making processes within a community. This study aims to provide policymakers with precise information on real-world situations to assist them in making informed decisions about the implementation of lockdown strategies, maintenance variables, and vaccine availability. The suggested model has conducted stability analysis, strength number analysis, and first and second-order derivative analysis of the Lyapunov function and has established the existence and uniqueness of solutions of the proposed models. We examine the combined effects of an effective vaccination campaign and non-pharmaceutical measures such as lockdowns and states of emergency. We rely on the results of this research to assist policymakers in various countries in eradicating the illness by developing more innovative measures to control the outbreak.

关键词： epidemic dynamics Non-Pharmaceuticals Interventions Vaccine Shortage Multi-Waving

epidemic propagation on adaptive coevolutionary networks with preferential local-world reconnecting strategy

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Chinese Physics B 2013年第4期22卷 63-69页

作者：宋玉蓉蒋国平巩永旺 College of Automation Nanjing University of Posts and Telecommunications

In the propagation of an epidemic in a population, individuals adaptively adjust their behavior to avoid the risk of an epidemic. Differently from existing studies where new links are established randomly, a local link is established preferentially in this paper. We propose a new preferentially reconnecting edge strategy depending on spatial distance （PR- SD）. For the PR-SD strategy, the new link is established at random with probability p and in a shortest distance with the probability 1 p. We establish the epidemic model on an adaptive network using Cellular Automata, and demonstrate the effectiveness of the proposed model by numerical simulations. The results show that the smaller the value of parameter p, the more difficult the epidemic spread is. The PR-SD strategy breaks long-range links and establishes as many short-range links as possible, which causes the network efficiency to decrease quickly and the propagation of the epidemic is restrained effectively.

关键词： adaptive networks epidemic dynamics network dynamics cellular automata local-world reconnecting mechanism

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epidemic thresholds in a heterogenous population with competing strains

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Chinese Physics B 2011年第4期20卷 384-390页

作者：吴庆初傅新楚杨孟 Department of Mathematics Shanghai University College of Mathematics and Information Science Jiangxi Normal University

Among many epidemic models, one epidemic disease may transmit with the existence of other pathogens or other strains from the same pathogen. In this paper, we consider the case where all of the strains obey the susceptible-infected- susceptible mechanism and compete with each other at the expense of common susceptible individuals. By using the heterogenous mean-field approach, we discuss the epidemic threshold for one of two strains. We confirm the existence of epidemic threshold in both finite and infinite populations subject to underlying epidemic transmission. Simulations in the Barabasi-Albert （BA） scale-free networks are in good agreement with the analytical results.

关键词： complex network epidemic threshold epidemic dynamics

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Modeling and analysis of epidemic spreading on community network with node's birth and death

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The Journal of China Universities of Posts and Telecommunications 2016年第5期23卷 82-87,96页

作者： Li Chanchan Jiang Guoping School of Computer Nanjing University of Posts and Telecommunications School of Automation Nanjing University of Posts and Telecommunications

In this paper, a modified susceptible infected susceptible （SIS） epidemic model is proposed on community structure networks considering birth and death of node. For the existence of node＇s death would change the topology of global network, the characteristic of network with death rate is discussed. Then we study the epidemiology behavior based on the mean-field theory and derive the relationships between epidemic threshold and other parameters, such as modularity coefficient, birth rate and death rates （caused by disease or other reasons）. In addition, the stability of endemic equilibrium is analyzed. Theoretical analysis and simulations show that the epidemic threshold increases with the increase of two kinds of death rates, while it decreases with the increase of the modularity coefficient and network size.

关键词： community structure epidemic dynamics complex networks mean-field theory

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Simulations of a logistic-type model with delays for Chagas disease with insecticide spraying

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International Journal of Biomathematics 2017年第3期10卷 41-60页

作者： Nofe Al-Asuoad Tyler Pleasant Meir Shillor Hrishikesh Munugala Daniel J. Coffield Jr. Anna Maria Spagnuolo Department of Mathematics and Statistics Oakland University Rochester MI 48309 USA Harrison High School MI USA Novi High School Novi MI 48375 USA Mathematics Department University of Michigan-Flint Flint MI 48502 USA

This work studies and numerically simulates a logistic-type model for the dynamics of Chagas disease, which is caused by the parasite T. cruzi and affects millions of humans and domestic mammals throughout rural areas in Central and South America. A basic model for the disease dynamics that includes insecticide spraying was developed in Spagnuolo et al. （2010） [271 and consists of a delay-differential equation for the vectors and three nonlinear ordinary differential equations for the populations of the infected vectors, infected humans and infected domestic mammals. In this work, the vector equation is modified by using a logistic term with zero, one or two delays or time lags. The aim of this study is three-fold： to numerically study the effects of using different numbers of delays on the model behavior; to find if twice yearly insecticide spraying schedules improve vector control; and to study the sensitivity of the system to the delays in the case of two delays, by introducing randomness in the delays. It is found that the vector equation with different number of delays has very different solutions. The ＂best＂ day of spraying is the middle of Spring and twice annual sprayings cause only minor improvements in disease control. Finally, the model is found to be insensitive to the values of the delays, when the delays are randomly distributed within rather narrow intervals or ranges centered on the parameter values used in Coffield et al. （2014） [8].

关键词： Chagas disease logistic equation with delays epidemic dynamics nonlinear dynamical system simulations.

Dynamic analysis of an SEIRS model with nonlinear infectivity on complex networks

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International Journal of Biomathematics 2016年第1期9卷 165-189页

作者： Shouying Huang Mathematics and Science College Shanghai Normal University Shanghai 200234 P. R. China College of Mathematics and Computer ScienceFuzhou University Fuzhou Fujian 350108 P. R. China

In this paper, we study the spreading of infections on complex heterogeneous networks based on an SEIRS epidemic model with nonlinear infectivity. By mathematical analysis, the basic reproduction number R0 is obtained. When R0 is less than one, the disease-free equilibrium is globally asymptotically stable and the disease dies out, while R0 is greater than one, the disease-free equilibrium becomes unstable and the disease is permanent, and in the meantime there exists a unique endemic equilibrium which is globally attrac- tive under certain conditions. Finally, the effects of various immunization schemes are studied. To verify our theoretical results, the corresponding numerical simulations are also included.

关键词： epidemic dynamics complex network nonlinear infectivity immunization.

Threshold analysis for epidemic models with high-risk immunization on networks

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International Journal of Biomathematics 2015年第3期8卷 73-82页

作者： Qingchu Wu Shufang Chen College of Mathematics and Information ScienceJiangxi Normal University Nanchang 330022 P. R. China College of Physics and Communication Electronics Jiangxi Normal University Nanehang 330022 P. R. China

In this paper, an SIRS epidemic model with high-risk immunization was investigated, where a susceptible neighbor of an infected node is immunized with rate h. Through analyzing the discrete-time model, we found that the epidemic threshold above which an epidemic can prevail and persist in a population is inversely proportional to 1 - h value. We also studied the continuous-time epidemic model and obtained a different result： the epidemic threshold does not depend on the immunization parameter h. Our results suggest that the difference between the discrete-time epidemic model and the continuous-time epidemic model exists in the high-risk immunization.

关键词： Complex network epidemic dynamics model dynamic immunization.