Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual ...Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.展开更多
Livestock transportation is a key factor that contributes to the spatial spread of brucellosis.To analyze the impact of sheep transportation on brucellosis transmission,we develop a human–sheep coupled brucellosis mo...Livestock transportation is a key factor that contributes to the spatial spread of brucellosis.To analyze the impact of sheep transportation on brucellosis transmission,we develop a human–sheep coupled brucellosis model within a metapopulation network framework.Theoretically,we examine the positively invariant set,the basic reproduction number,the existence,uniqueness,and stability of disease-free equilibrium and the existence of the endemic equilibrium of the model.For practical application,using Heilongjiang province as a case study,we simulate brucellosis transmission across 12 cities based on data using three network types:the BA network,the ER network,and homogeneous mixing network.The simulation results indicate that the network's average degree plays a role in the spread of brucellosis.For BA and ER networks,the basic reproduction number and cumulative incidence of brucellosis stabilize when the network's average degree reaches 4 or 5.In contrast,sheep transport in a homogeneous mixing network accelerates the cross-regional spread of brucellosis,whereas transportation in a BA network helps to control it effectively.Furthermore,the findings suggest that the movement of sheep is not always detrimental to controlling the spread of brucellosis.For cities with smaller sheep populations,such as Shuangyashan and Qitaihe,increasing the transport of sheep outward amplifies the spatial spread of the disease.In contrast,in cities with larger sheep populations,such as Qiqihar,Daqing,and Suihua,moderate sheep outflow can help reduce the spread.In addition,cities with large livestock populations play a dominant role in the overall transmission dynamics,underscoring the need for stricter supervision in these areas.展开更多
This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disea...This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disease prevalence is established,and the parameter conditions for the existence of equilibria are discussed.The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.By utilizing composite matrices and geometric techniques,the global dynamic behavior of the endemic equilibrium is investigated,and the sufficient conditions for its global asymptotic stability are derived.Furthermore,the disease-free equilibrium is a saddle-node when the basic reproductive number is 1,and tthe transcritical bifurcation in this case is discussed.展开更多
This paper concentrates on the dynamics of a waterborne pathogen periodic PDE model with environmental pollution.For this model,we derive the basic reproduction number R0and establish a threshold type result on its gl...This paper concentrates on the dynamics of a waterborne pathogen periodic PDE model with environmental pollution.For this model,we derive the basic reproduction number R0and establish a threshold type result on its global dynamics in terms of R0,which predicts the extinction or persistence of diseases.More precisely,the disease-free steady state is globally attractive if R_(0)<1,while the system admits at least one positive periodic solution and the disease is uniformly persistent if R_(0)>1.Moreover,we carry out some numerical simulations to illustrate the long-term behaviors of solutions and explore the influence of environmental pollution and seasonality on the spread of waterborne diseases.展开更多
This paper first estimated the infectious capacity of COVID-19 based on the time series evolution data of confirmed cases in multiple countries. Then, a method to infer the cross-regional spread speed of COVID-19 was ...This paper first estimated the infectious capacity of COVID-19 based on the time series evolution data of confirmed cases in multiple countries. Then, a method to infer the cross-regional spread speed of COVID-19 was introduced in this paper, which took the gross domestic product(GDP) of each region as one of the factors that affect the spread speed of COVID-19 and studied the relationship between the GDP and the infection density of each region(China's Mainland, the United States, and EU countries). In addition, the geographic distance between regions was also considered in this method and the effect of geographic distance on the spread speed of COVID-19 was studied. Studies have shown that the probability of mutual infection of these two regions decreases with increasing geographic distance. Therefore, this paper proposed an epidemic disease spread index based on GDP and geographic distance to quantify the spread speed of COVID-19 in a region. The analysis results showed a strong correlation between the epidemic disease spread index in a region and the number of confirmed cases. This finding provides reasonable suggestions for the control of epidemics. Strengthening the control measures in regions with higher epidemic disease spread index can effectively control the spread of epidemics.展开更多
In this paper,a sexually transmitted disease model is proposed on complex networks,where contacts between humans are treated as a scale-free social network.There are three groups in our model,which are dangerous male,...In this paper,a sexually transmitted disease model is proposed on complex networks,where contacts between humans are treated as a scale-free social network.There are three groups in our model,which are dangerous male,non-dangerous male,and female.By mathematical analysis,we obtain the basic reproduction number for the existence of endemic equilibrium and study the effects of various immunization schemes about different groups.Furthermore,numerical simulations are undertaken to verify more conclusions.展开更多
Foot-and-mouth disease is one of the major contagious zoonotic diseases in the world.It is caused by various species of the genus Aphthovirus of the family Picornavirus,and it always brings a large number of infection...Foot-and-mouth disease is one of the major contagious zoonotic diseases in the world.It is caused by various species of the genus Aphthovirus of the family Picornavirus,and it always brings a large number of infections and heavy financial losses.The disease has become a major public health concern.In this paper,we propose a nonlocal foot-and-mouth disease model in a spatially heterogeneous environment,which couples virus-to-animals and animals-to-animals transmission pathways,and investigate the dynamics of the disperal.The basic reproduction number R_(0)is defined as the spectral radius of the next generation operator R(x)by a renewal equation.The relationship between R_(0)and a principal eigenvalue of an operator L_(0)is built.Moreover,the proposed system exhibits threshold dynamics in terms of R_(0),in the sense that R_(0)determines whether or not foot-and-mouth disease invades the hosts.Through numerical simulations,we have found that increasing animals'movements is an effective control measure for preventing prevalence of the disease.展开更多
Investigating the stability of information spreading over SNS helps to understand the principles inherent in the spreading behavior.This paper explores the mechanisms of information spreading including stifling mechan...Investigating the stability of information spreading over SNS helps to understand the principles inherent in the spreading behavior.This paper explores the mechanisms of information spreading including stifling mechanism,latent mechanism and forgetting mechanism,establishes a refined SEIR model,and builds the corresponding mean-field equations.The methods of the differential dynamics and the next generation matrix are used to calculate the equilibriums and the basic reproductive number,and the asymptotical stability of the network equilibriums are proved theoretically.Simulation experiments are carried out to analyze the effect of the spreading mechanisms on the information spreading process and the results support our conclusions.展开更多
Current public-opinion propagation research usually focused on closed network topologies without considering the fluctuation of the number of network users or the impact of social factors on propagation. Thus, it rema...Current public-opinion propagation research usually focused on closed network topologies without considering the fluctuation of the number of network users or the impact of social factors on propagation. Thus, it remains difficult to accurately describe the public-opinion propagation rules of social networks. In order to study the rules of public opinion spread on dynamic social networks, by analyzing the activity of social-network users and the regulatory role of relevant departments in the spread of public opinion, concepts of additional user and offline rates are introduced, and the direct immune-susceptible, contacted, infected, and refractory (DI-SCIR) public-opinion propagation model based on real-time online users is established. The interventional force of relevant departments, credibility of real information, and time of intervention are considered, and a public-opinion propagation control strategy based on direct immunity is proposed. The equilibrium point and the basic reproduction number of the model are theoretically analyzed to obtain boundary conditions for public-opinion propagation. Simulation results show that the new model can accurately reflect the propagation rules of public opinion. When the basic reproduction number is less than 1, public opinion will eventually disappear in the network. Social factors can significantly influence the time and scope of public opinion spread on social networks. By controlling social factors, relevant departments can analyze the rules of public opinion spread on social networks to suppress the propagate of negative public opinion and provide a powerful tool to ensure security and stability of society.展开更多
文摘Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.
基金Project supported by the National Natural Science Foundation of China(Grant No.12101443,12371493)the Natural Science Foundation of Shanxi Province(Grant Nos.20210302124260 and 202303021221024)。
文摘Livestock transportation is a key factor that contributes to the spatial spread of brucellosis.To analyze the impact of sheep transportation on brucellosis transmission,we develop a human–sheep coupled brucellosis model within a metapopulation network framework.Theoretically,we examine the positively invariant set,the basic reproduction number,the existence,uniqueness,and stability of disease-free equilibrium and the existence of the endemic equilibrium of the model.For practical application,using Heilongjiang province as a case study,we simulate brucellosis transmission across 12 cities based on data using three network types:the BA network,the ER network,and homogeneous mixing network.The simulation results indicate that the network's average degree plays a role in the spread of brucellosis.For BA and ER networks,the basic reproduction number and cumulative incidence of brucellosis stabilize when the network's average degree reaches 4 or 5.In contrast,sheep transport in a homogeneous mixing network accelerates the cross-regional spread of brucellosis,whereas transportation in a BA network helps to control it effectively.Furthermore,the findings suggest that the movement of sheep is not always detrimental to controlling the spread of brucellosis.For cities with smaller sheep populations,such as Shuangyashan and Qitaihe,increasing the transport of sheep outward amplifies the spatial spread of the disease.In contrast,in cities with larger sheep populations,such as Qiqihar,Daqing,and Suihua,moderate sheep outflow can help reduce the spread.In addition,cities with large livestock populations play a dominant role in the overall transmission dynamics,underscoring the need for stricter supervision in these areas.
基金supported by the National Natural Science Foundation of China(No.12171337)the Central Government Guided Local Science and Technology Development Projects(No.2024ZYD0059)+1 种基金the Natural Science Foundation of Sichuan Province(No.2022NSFSC0529)the Open Research Fund Program of Data Recovery Key Laboratory of Sichuan Province(No.DRN2405)。
文摘This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disease prevalence is established,and the parameter conditions for the existence of equilibria are discussed.The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.By utilizing composite matrices and geometric techniques,the global dynamic behavior of the endemic equilibrium is investigated,and the sufficient conditions for its global asymptotic stability are derived.Furthermore,the disease-free equilibrium is a saddle-node when the basic reproductive number is 1,and tthe transcritical bifurcation in this case is discussed.
基金supported by the NSFC(12161079)the XSTP(KC2023058)。
文摘This paper concentrates on the dynamics of a waterborne pathogen periodic PDE model with environmental pollution.For this model,we derive the basic reproduction number R0and establish a threshold type result on its global dynamics in terms of R0,which predicts the extinction or persistence of diseases.More precisely,the disease-free steady state is globally attractive if R_(0)<1,while the system admits at least one positive periodic solution and the disease is uniformly persistent if R_(0)>1.Moreover,we carry out some numerical simulations to illustrate the long-term behaviors of solutions and explore the influence of environmental pollution and seasonality on the spread of waterborne diseases.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.62266030 and 61863025)International S & T Cooperation Projects of Gansu province (Grant No.144WCGA166)Longyuan Young Innovation Talents and the Doctoral Foundation of LUT。
文摘This paper first estimated the infectious capacity of COVID-19 based on the time series evolution data of confirmed cases in multiple countries. Then, a method to infer the cross-regional spread speed of COVID-19 was introduced in this paper, which took the gross domestic product(GDP) of each region as one of the factors that affect the spread speed of COVID-19 and studied the relationship between the GDP and the infection density of each region(China's Mainland, the United States, and EU countries). In addition, the geographic distance between regions was also considered in this method and the effect of geographic distance on the spread speed of COVID-19 was studied. Studies have shown that the probability of mutual infection of these two regions decreases with increasing geographic distance. Therefore, this paper proposed an epidemic disease spread index based on GDP and geographic distance to quantify the spread speed of COVID-19 in a region. The analysis results showed a strong correlation between the epidemic disease spread index in a region and the number of confirmed cases. This finding provides reasonable suggestions for the control of epidemics. Strengthening the control measures in regions with higher epidemic disease spread index can effectively control the spread of epidemics.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10901145)the Natural Science Foundation of Shanxi Province,China(Grant Nos. 2009011005-1 and 2012011002-1)the Top Young Academic Leaders of Higher Learning Institutions of Shanxi Province,China
文摘In this paper,a sexually transmitted disease model is proposed on complex networks,where contacts between humans are treated as a scale-free social network.There are three groups in our model,which are dangerous male,non-dangerous male,and female.By mathematical analysis,we obtain the basic reproduction number for the existence of endemic equilibrium and study the effects of various immunization schemes about different groups.Furthermore,numerical simulations are undertaken to verify more conclusions.
基金supported by the National Natural Science Foundation of China(12001339,61573016,11871316)Shanxi Scholarship Council of China(2015-094)+1 种基金the Natural Science Foundation of Shanxi(201801D121006)the Shanxi Province Science Foundation for Youths(201901D211413).
文摘Foot-and-mouth disease is one of the major contagious zoonotic diseases in the world.It is caused by various species of the genus Aphthovirus of the family Picornavirus,and it always brings a large number of infections and heavy financial losses.The disease has become a major public health concern.In this paper,we propose a nonlocal foot-and-mouth disease model in a spatially heterogeneous environment,which couples virus-to-animals and animals-to-animals transmission pathways,and investigate the dynamics of the disperal.The basic reproduction number R_(0)is defined as the spectral radius of the next generation operator R(x)by a renewal equation.The relationship between R_(0)and a principal eigenvalue of an operator L_(0)is built.Moreover,the proposed system exhibits threshold dynamics in terms of R_(0),in the sense that R_(0)determines whether or not foot-and-mouth disease invades the hosts.Through numerical simulations,we have found that increasing animals'movements is an effective control measure for preventing prevalence of the disease.
基金The authors would like to thank the reviewers for their detailed reviews and constructive comments, which have helped improve the quality of this paper. This work was supported in part by Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China under Grant No. IRT1078 Key Program of NSFC-Guangdong Union Foundation under Grant No. U1135002+3 种基金 National Science and Technology Major Project of the Ministry of Science and Technology of China under Grant No. 2011ZX03005- 002 National Natural Science Foundation of China under Grant No.61173135 Natural Science Foundation of Shaanxi Province under Grant No.2014JQ8297 Fundamental Research Funds for the Central Universities of Ministry of Education of China under Grant Nos. JY 10000903001, K5051303007, K5051203012.
文摘Investigating the stability of information spreading over SNS helps to understand the principles inherent in the spreading behavior.This paper explores the mechanisms of information spreading including stifling mechanism,latent mechanism and forgetting mechanism,establishes a refined SEIR model,and builds the corresponding mean-field equations.The methods of the differential dynamics and the next generation matrix are used to calculate the equilibriums and the basic reproductive number,and the asymptotical stability of the network equilibriums are proved theoretically.Simulation experiments are carried out to analyze the effect of the spreading mechanisms on the information spreading process and the results support our conclusions.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61471080)the Equipment Development Department Research Foundation of China (Grant No. 61400010303)+2 种基金the Natural Science Research Project of Liaoning Education Department of China (Grant Nos. JDL2019019 and JDL2020002)the Surface Project for Natural Science Foundation in Guangdong Province of China (Grant No. 2019A1515011164)the Science and Technology Plan Project in Zhanjiang, China (Grant No. 2018A06001)。
文摘Current public-opinion propagation research usually focused on closed network topologies without considering the fluctuation of the number of network users or the impact of social factors on propagation. Thus, it remains difficult to accurately describe the public-opinion propagation rules of social networks. In order to study the rules of public opinion spread on dynamic social networks, by analyzing the activity of social-network users and the regulatory role of relevant departments in the spread of public opinion, concepts of additional user and offline rates are introduced, and the direct immune-susceptible, contacted, infected, and refractory (DI-SCIR) public-opinion propagation model based on real-time online users is established. The interventional force of relevant departments, credibility of real information, and time of intervention are considered, and a public-opinion propagation control strategy based on direct immunity is proposed. The equilibrium point and the basic reproduction number of the model are theoretically analyzed to obtain boundary conditions for public-opinion propagation. Simulation results show that the new model can accurately reflect the propagation rules of public opinion. When the basic reproduction number is less than 1, public opinion will eventually disappear in the network. Social factors can significantly influence the time and scope of public opinion spread on social networks. By controlling social factors, relevant departments can analyze the rules of public opinion spread on social networks to suppress the propagate of negative public opinion and provide a powerful tool to ensure security and stability of society.
