We describe and analyze a simple SIS model with treatment. In particular, we give a completely qualitative analysis by means of the theory of asymptotically autonomous system. It is found that a backward bifurcation o...We describe and analyze a simple SIS model with treatment. In particular, we give a completely qualitative analysis by means of the theory of asymptotically autonomous system. It is found that a backward bifurcation occurs if the adequate contact rate or the capacity is small. It is also found that there exists bistable endemic equilibria. In the case of disease-induced death, it is shown that the backward bifurcation also occurs. Moreover, there is no limit cycle under some conditions, and the subcritical Hopf bifurcation occurs under another conditions.展开更多
Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural birth...Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural births with natural deaths.The incidence term is of the standard incidence.Here the thresholds and equilibria are detemined,and stabilities are examined.The persistence of the infectious disease and disease related deaths can lead to a new equilibrium population size below the carrying capacity.展开更多
The paper analyzes the influence of a susceptible-infectious-susceptible （SIS） infectious disease affecting both fish and broiler species. The paper also considers a joint SIS project of fish and broiler in which th...The paper analyzes the influence of a susceptible-infectious-susceptible （SIS） infectious disease affecting both fish and broiler species. The paper also considers a joint SIS project of fish and broiler in which the growth rates of both species vary with available nutrients and environmental carrying capacities of biomasses. The nutrients for both species are functions of the biomasses of the two species. The harvesting rates of fish and broiler depend linearly on common effort function. It is assumed that the diseases are trans- mitted to the susceptible populations by direct contact with the infected populations. Using the medicine, some portion of the infected populations are transmitted to the sus- ceptible populations. The existence of steady states and their stability are investigated analytically. The joint profit of the SIS model is maximized using Pontryagin＇s max- imum principle and corresponding optimum harvesting rates are also obtained. Using Mathematica software~ the models are illustrated and the optimum results are obtained and presented in tabular and graphical forms.展开更多
A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are in...A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are investigated.展开更多
A simple SI epidemic model with age of vaccination is discussed in this paper.Both vexing birth rate, the mortality rate caused by disease and vaccine waning rate areconsidered in this model. We prove that the global ...A simple SI epidemic model with age of vaccination is discussed in this paper.Both vexing birth rate, the mortality rate caused by disease and vaccine waning rate areconsidered in this model. We prove that the global dynamics is completely determined bythe basic reproductive number R（ψ）（ψ denotes per capita vaccination rate）. If R（0） 〈 1,the disease-free equilibrium is a global attractor; If R（ψ） 〈： 1, the disease-free equilibriumis locally asymptotically stable; If R（ψ） ：〉 1, an unique endemic equilibrium exists and islocally asymptotically stable under certain condition.展开更多
In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction rat...In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model.展开更多
In this paper, we explore the long time behavior of a multigroup Susceptible-Infected Susceptible （SIS） model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also s...In this paper, we explore the long time behavior of a multigroup Susceptible-Infected Susceptible （SIS） model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.展开更多
The aim of this paper is to study the diffusion. We first study the well-posedness of the dynamics of an SIS epidemic model with model. And then, by using linearization method and constructing suitable Lyapunov functi...The aim of this paper is to study the diffusion. We first study the well-posedness of the dynamics of an SIS epidemic model with model. And then, by using linearization method and constructing suitable Lyapunov function, we establish the local and global stability of the disease-free equilibrium and the endemic equilibrium, respectively. Furthermore, in view of Schauder fixed point theorem, we show that the model admits traveling wave solutions con- necting the disease-free equilibrium and the endemic equilibrium when R0 〉 1 and c 〉 c^＊. And also, by virtue of the two-sided Laplace transform, we prove that the model has no traveling wave solution connecting the two equilibria when R0 〉 1 and c ∈（0, c^＊）.展开更多
A diffusive SIS epidemic model with Holling II incidence rate is studied in this paper.We introduce the basic reproduction number R0 first.Then the existence of endemic equilibrium(EE)can be determined by the sizes of...A diffusive SIS epidemic model with Holling II incidence rate is studied in this paper.We introduce the basic reproduction number R0 first.Then the existence of endemic equilibrium(EE)can be determined by the sizes of R0 as well as the diffusion rates of susceptible and infected individuals.We also investigate the effect of diffusion rates on asymptotic profile of EE.Our results conclude that the infected population will die out if the diffusion rate of susceptible individuals is small and the total population N is below a certain level;while the two populations persist eventually if at least one of the diffusion rates of the susceptible and infected individuals is large.展开更多
We study the stability of endemic equilibriums of the deterministic and stochastic SIS epidemic models with vaccination. The deterministic SIS epidemic model with vaccination was proposed by Li and Ma(2004), for which...We study the stability of endemic equilibriums of the deterministic and stochastic SIS epidemic models with vaccination. The deterministic SIS epidemic model with vaccination was proposed by Li and Ma(2004), for which some sufficient conditions for the global stability of the endemic equilibrium were given in some earlier works. In this paper, we first prove by Lyapunov function method that the endemic equilibrium of the deterministic model is globally asymptotically stable whenever the basic reproduction number is larger than one. For the stochastic version, we obtain some sufficient conditions for the global stability of the endemic equilibrium by constructing a class of different Lyapunov functions.展开更多
Malaria infection is a major problem in many countries. The use of the Insecticide-Treated Bed-Nets (ITNs) has been shown to significantly reduce the number of malaria infections;however, the effectiveness is often je...Malaria infection is a major problem in many countries. The use of the Insecticide-Treated Bed-Nets (ITNs) has been shown to significantly reduce the number of malaria infections;however, the effectiveness is often jeopardized by improper handling or human behavior such as inconsistent usage. In this paper, we present a game-theoretical model for ITN usage in communities with malaria infections. We show that it is in the individual’s self interest to use the ITNs as long as the malaria is present in the community. Such an optimal ITN usage will significantly decrease the malaria prevalence and under some conditions may even lead to complete eradication of the disease.展开更多
Microblogs currently play an important role in social communication. Hot topics currently being tweeted can quickly become popular within a very short time as a result of retweeting. Gaining an understanding of the re...Microblogs currently play an important role in social communication. Hot topics currently being tweeted can quickly become popular within a very short time as a result of retweeting. Gaining an understanding of the retweeting behavior is desirable for a number of tasks such as topic detection, personalized message recommendation, and fake information monitoring and prevention. Interestingly, the propagation of tweets bears some similarity to the spread of infectious diseases. We present a method to model the tweets' spread behavior in microblogs based on the classic Susceptible-Infectious-Susceptible (SIS) epidemic model that was developed in the medical field for the spread of infectious diseases. On the basis of this model, future retweeting trends can be predicted. Our experiments on data obtained from the Chinese micro-blogging website Sina Weibo show that the proposed model has lower predictive error compared to the four commonly used prediction methods.展开更多
In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.T...In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.展开更多
In this paper, a stochastic SIS epidemic model on homogeneous networks is considered. The largest Lyapunov exponent is calculated by Oseledec multiplicative ergodic theory, and the stability condition is determined by...In this paper, a stochastic SIS epidemic model on homogeneous networks is considered. The largest Lyapunov exponent is calculated by Oseledec multiplicative ergodic theory, and the stability condition is determined by the largest Lyapunov exponent. The probability density function for the proportion of infected individuals is found explicitly, and the stochastic bifurcation is analysed by a probability density function. In particular, the new basic reproductive number R^＊, that governs whether an epidemic with few initial infections can become an endemic or not, is determined by noise intensity. In the homogeneous networks, despite of the basic productive number R0 〉1, the epidemic will die out as long as noise intensity satisfies a certain condition.展开更多
To study the influence of the moving front of the infected interval and the spatial movement of individuals on the spreading or vanishing of infectious disease, we consider a nonlocal susceptible–infected–susceptibl...To study the influence of the moving front of the infected interval and the spatial movement of individuals on the spreading or vanishing of infectious disease, we consider a nonlocal susceptible–infected–susceptible (SIS) reaction–diffusion model with media coverage, hospital bed numbers and free boundaries. The principal eigenvalue of the integral operator is defined, and the impacts of the diffusion rate of infected individuals and interval length on the principal eigenvalue are analyzed. Furthermore, sufficient conditions for spreading and vanishing of the disease are derived. Our results show that large media coverage and hospital bed numbers are beneficial to the prevention and control of disease. The difference between the model with nonlocal diffusion and that with local diffusion is also discussed and nonlocal diffusion leads to more possibilities.展开更多
Hypergraphs can accurately capture complex higher-order relationships,but it is challenging to identify their important nodes.In this paper,an improved PageRank(ImPageRank)algorithm is designed to identify important n...Hypergraphs can accurately capture complex higher-order relationships,but it is challenging to identify their important nodes.In this paper,an improved PageRank(ImPageRank)algorithm is designed to identify important nodes in a directed hypergraph.The algorithm introduces the Jaccard similarity of directed hypergraphs.By comparing the numbers of common neighbors between nodes with the total number of their neighbors,the Jaccard similarity measure takes into account the similarity between nodes that are not directly connected,and can reflect the potential correlation between nodes.An improved susceptible–infected(SI)model in directed hypergraph is proposed,which considers nonlinear propagation mode and more realistic propagation mechanism.In addition,some important node evaluation methods are transferred from undirected hypergraphs and applied to directed hypergraphs.Finally,the ImPageRank algorithm is used to evaluate the performance of the SI model,network robustness and monotonicity.Simulations of real networks demonstrate the excellent performance of the proposed algorithm and provide a powerful framework for identifying important nodes in directed hypergraphs.展开更多
The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite siz...The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite size networks with complex topological structure is investigated. On the finite size networks, the spreading process of SIS （susceptibleinfected-susceptible） model is a finite Markov chain with an absorbing state. Two parameters, the survival probability and the conditional infecting probability, are introduced to describe the dynamic properties of disease spreading on finite size networks. Our results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks. Also, knowledge about the dynamic character of virus spreading is helpful for adopting immunity policy.展开更多
In this paper, a new susceptible-infected-susceptible （SIS） model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns （the recovered individuals have or have not imm...In this paper, a new susceptible-infected-susceptible （SIS） model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns （the recovered individuals have or have not immunity） on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can spread over a network under vaccination control is determined not only by the network structure but also by the medicine＇s effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence.展开更多
In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the...In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.展开更多
The COVID-19 outbreak has significantly disrupted the lives of individuals worldwide.Following the lifting of COVID-19 interventions,there is a heightened risk of future outbreaks from other circulating respiratory in...The COVID-19 outbreak has significantly disrupted the lives of individuals worldwide.Following the lifting of COVID-19 interventions,there is a heightened risk of future outbreaks from other circulating respiratory infections,such as influenza-like illness(ILI).Accurate prediction models for ILI cases are crucial in enabling governments to implement necessary measures and persuade individuals to adopt personal precautions against the disease.This paper aims to provide a forecasting model for ILI cases with actual cases.We propose a specific model utilizing the partial differential equation(PDE)that will be developed and validated using real-world data obtained from the Chinese National Influenza Center.Our model combines the effects of transboundary spread among regions in China mainland and human activities’impact on ILI transmission dynamics.The simulated results demonstrate that our model achieves excellent predictive performance.Additionally,relevant factors influencing the dissemination are further examined in our analysis.Furthermore,we investigate the effectiveness of travel restrictions on ILI cases.Results can be used to utilize to mitigate the spread of disease.展开更多
基金Supported by the National Natural Science Foundation of China(No.10571143,30770555)
文摘We describe and analyze a simple SIS model with treatment. In particular, we give a completely qualitative analysis by means of the theory of asymptotically autonomous system. It is found that a backward bifurcation occurs if the adequate contact rate or the capacity is small. It is also found that there exists bistable endemic equilibria. In the case of disease-induced death, it is shown that the backward bifurcation also occurs. Moreover, there is no limit cycle under some conditions, and the subcritical Hopf bifurcation occurs under another conditions.
文摘Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural births with natural deaths.The incidence term is of the standard incidence.Here the thresholds and equilibria are detemined,and stabilities are examined.The persistence of the infectious disease and disease related deaths can lead to a new equilibrium population size below the carrying capacity.
文摘The paper analyzes the influence of a susceptible-infectious-susceptible （SIS） infectious disease affecting both fish and broiler species. The paper also considers a joint SIS project of fish and broiler in which the growth rates of both species vary with available nutrients and environmental carrying capacities of biomasses. The nutrients for both species are functions of the biomasses of the two species. The harvesting rates of fish and broiler depend linearly on common effort function. It is assumed that the diseases are trans- mitted to the susceptible populations by direct contact with the infected populations. Using the medicine, some portion of the infected populations are transmitted to the sus- ceptible populations. The existence of steady states and their stability are investigated analytically. The joint profit of the SIS model is maximized using Pontryagin＇s max- imum principle and corresponding optimum harvesting rates are also obtained. Using Mathematica software~ the models are illustrated and the optimum results are obtained and presented in tabular and graphical forms.
基金This work is supported by National Natural Science Foundation of China (10171106)the Special Fund for Major State Basic Research Projects (G1999032805)
文摘A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are investigated.
基金Supported by the NSF of China（10371105） Supported by the Youth Science Foundation of Xinyang Normal University（20060202）
文摘A simple SI epidemic model with age of vaccination is discussed in this paper.Both vexing birth rate, the mortality rate caused by disease and vaccine waning rate areconsidered in this model. We prove that the global dynamics is completely determined bythe basic reproductive number R（ψ）（ψ denotes per capita vaccination rate）. If R（0） 〈 1,the disease-free equilibrium is a global attractor; If R（ψ） 〈： 1, the disease-free equilibriumis locally asymptotically stable; If R（ψ） ：〉 1, an unique endemic equilibrium exists and islocally asymptotically stable under certain condition.
文摘In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model.
基金The authors are grateflfl to tile anonymous referees for carefully reading the manuscript and for important snggestions and comments, which led to the improvement of their manuscript. This research is supported by NSFC grant 11601043, China Postdoctoral Science Foundation （Grant No. 2016M590243）, Jiangsu Province ＂333 High-Level Personnel Training Project＂ （Grant No. BRA2017468） and Qing Lan Project of Jiangsu Province of 2016 and 2017.
文摘In this paper, we explore the long time behavior of a multigroup Susceptible-Infected Susceptible （SIS） model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.
基金Partially supported by the NSF of Guangdong Province(2016A030313426)the HLUCF of South China Normal University(2016YN30)
文摘The aim of this paper is to study the diffusion. We first study the well-posedness of the dynamics of an SIS epidemic model with model. And then, by using linearization method and constructing suitable Lyapunov function, we establish the local and global stability of the disease-free equilibrium and the endemic equilibrium, respectively. Furthermore, in view of Schauder fixed point theorem, we show that the model admits traveling wave solutions con- necting the disease-free equilibrium and the endemic equilibrium when R0 〉 1 and c 〉 c^＊. And also, by virtue of the two-sided Laplace transform, we prove that the model has no traveling wave solution connecting the two equilibria when R0 〉 1 and c ∈（0, c^＊）.
基金the National Natural Science Foundation of China 61472471.
文摘A diffusive SIS epidemic model with Holling II incidence rate is studied in this paper.We introduce the basic reproduction number R0 first.Then the existence of endemic equilibrium(EE)can be determined by the sizes of R0 as well as the diffusion rates of susceptible and infected individuals.We also investigate the effect of diffusion rates on asymptotic profile of EE.Our results conclude that the infected population will die out if the diffusion rate of susceptible individuals is small and the total population N is below a certain level;while the two populations persist eventually if at least one of the diffusion rates of the susceptible and infected individuals is large.
基金Supported by the National Natural Science Foundation of China (Grant No. 12071058)。
文摘We study the stability of endemic equilibriums of the deterministic and stochastic SIS epidemic models with vaccination. The deterministic SIS epidemic model with vaccination was proposed by Li and Ma(2004), for which some sufficient conditions for the global stability of the endemic equilibrium were given in some earlier works. In this paper, we first prove by Lyapunov function method that the endemic equilibrium of the deterministic model is globally asymptotically stable whenever the basic reproduction number is larger than one. For the stochastic version, we obtain some sufficient conditions for the global stability of the endemic equilibrium by constructing a class of different Lyapunov functions.
文摘Malaria infection is a major problem in many countries. The use of the Insecticide-Treated Bed-Nets (ITNs) has been shown to significantly reduce the number of malaria infections;however, the effectiveness is often jeopardized by improper handling or human behavior such as inconsistent usage. In this paper, we present a game-theoretical model for ITN usage in communities with malaria infections. We show that it is in the individual’s self interest to use the ITNs as long as the malaria is present in the community. Such an optimal ITN usage will significantly decrease the malaria prevalence and under some conditions may even lead to complete eradication of the disease.
基金supported by National Natural Science Foundation of China under Grants No. 60773156, No. 61073004Chinese Major State Basic Research Development 973 Program under Grant No. 2011CB302203-2Important National Science &Technology Specific Program under Grant No. 2011ZX01042001-002-2
文摘Microblogs currently play an important role in social communication. Hot topics currently being tweeted can quickly become popular within a very short time as a result of retweeting. Gaining an understanding of the retweeting behavior is desirable for a number of tasks such as topic detection, personalized message recommendation, and fake information monitoring and prevention. Interestingly, the propagation of tweets bears some similarity to the spread of infectious diseases. We present a method to model the tweets' spread behavior in microblogs based on the classic Susceptible-Infectious-Susceptible (SIS) epidemic model that was developed in the medical field for the spread of infectious diseases. On the basis of this model, future retweeting trends can be predicted. Our experiments on data obtained from the Chinese micro-blogging website Sina Weibo show that the proposed model has lower predictive error compared to the four commonly used prediction methods.
文摘In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.
基金Project supported by the Science Foundation of Shanxi Province of China (Grant No 2009011005-1)the Youth Foundation of Shanxi Province of China (Grant No 2007021006)
文摘In this paper, a stochastic SIS epidemic model on homogeneous networks is considered. The largest Lyapunov exponent is calculated by Oseledec multiplicative ergodic theory, and the stability condition is determined by the largest Lyapunov exponent. The probability density function for the proportion of infected individuals is found explicitly, and the stochastic bifurcation is analysed by a probability density function. In particular, the new basic reproductive number R^＊, that governs whether an epidemic with few initial infections can become an endemic or not, is determined by noise intensity. In the homogeneous networks, despite of the basic productive number R0 〉1, the epidemic will die out as long as noise intensity satisfies a certain condition.
基金supported by the Postgraduate Research and Practice Innovation Program of Jiangsu Province(KYCX21-3188)the I.Ahn is supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(NRF-2022R1F1A1063068)the Z.Lin is supported by the National Natural Science Foundation of China(Grant No.12271470).
文摘To study the influence of the moving front of the infected interval and the spatial movement of individuals on the spreading or vanishing of infectious disease, we consider a nonlocal susceptible–infected–susceptible (SIS) reaction–diffusion model with media coverage, hospital bed numbers and free boundaries. The principal eigenvalue of the integral operator is defined, and the impacts of the diffusion rate of infected individuals and interval length on the principal eigenvalue are analyzed. Furthermore, sufficient conditions for spreading and vanishing of the disease are derived. Our results show that large media coverage and hospital bed numbers are beneficial to the prevention and control of disease. The difference between the model with nonlocal diffusion and that with local diffusion is also discussed and nonlocal diffusion leads to more possibilities.
基金Project supported by the National Natural Science Foundation of China(Grant No.62166010)the Guangxi Natural Science Foundation(Grant No.2023GXNSFAA026087).
文摘Hypergraphs can accurately capture complex higher-order relationships,but it is challenging to identify their important nodes.In this paper,an improved PageRank(ImPageRank)algorithm is designed to identify important nodes in a directed hypergraph.The algorithm introduces the Jaccard similarity of directed hypergraphs.By comparing the numbers of common neighbors between nodes with the total number of their neighbors,the Jaccard similarity measure takes into account the similarity between nodes that are not directly connected,and can reflect the potential correlation between nodes.An improved susceptible–infected(SI)model in directed hypergraph is proposed,which considers nonlinear propagation mode and more realistic propagation mechanism.In addition,some important node evaluation methods are transferred from undirected hypergraphs and applied to directed hypergraphs.Finally,the ImPageRank algorithm is used to evaluate the performance of the SI model,network robustness and monotonicity.Simulations of real networks demonstrate the excellent performance of the proposed algorithm and provide a powerful framework for identifying important nodes in directed hypergraphs.
基金Project supported by the National Nature Science Foundation of China （Grant Nos 90204004 and 90304005）.
文摘The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite size networks with complex topological structure is investigated. On the finite size networks, the spreading process of SIS （susceptibleinfected-susceptible） model is a finite Markov chain with an absorbing state. Two parameters, the survival probability and the conditional infecting probability, are introduced to describe the dynamic properties of disease spreading on finite size networks. Our results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks. Also, knowledge about the dynamic character of virus spreading is helpful for adopting immunity policy.
基金supported by the National Natural Science Foundation of China (Grant Nos 60674093,10832006)the Hong Kong Research Grants Council under Grant CityU 1117/08E
文摘In this paper, a new susceptible-infected-susceptible （SIS） model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns （the recovered individuals have or have not immunity） on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can spread over a network under vaccination control is determined not only by the network structure but also by the medicine＇s effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence.
基金supported by the National Natural Science Foundation of China (No.12231008 and No.11971185)。
文摘In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.
基金supported by the National Natural Science Foundation of China(Grant No.62373197)Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX18_0892).
文摘The COVID-19 outbreak has significantly disrupted the lives of individuals worldwide.Following the lifting of COVID-19 interventions,there is a heightened risk of future outbreaks from other circulating respiratory infections,such as influenza-like illness(ILI).Accurate prediction models for ILI cases are crucial in enabling governments to implement necessary measures and persuade individuals to adopt personal precautions against the disease.This paper aims to provide a forecasting model for ILI cases with actual cases.We propose a specific model utilizing the partial differential equation(PDE)that will be developed and validated using real-world data obtained from the Chinese National Influenza Center.Our model combines the effects of transboundary spread among regions in China mainland and human activities’impact on ILI transmission dynamics.The simulated results demonstrate that our model achieves excellent predictive performance.Additionally,relevant factors influencing the dissemination are further examined in our analysis.Furthermore,we investigate the effectiveness of travel restrictions on ILI cases.Results can be used to utilize to mitigate the spread of disease.
