We study the effect of incubation period on epidemic spreading in the Barabasi-Albert scale-free network and the Watts-Strogatz small world network by using a Suspectable-Incubated-Infected-Suspectable model. Our anal...We study the effect of incubation period on epidemic spreading in the Barabasi-Albert scale-free network and the Watts-Strogatz small world network by using a Suspectable-Incubated-Infected-Suspectable model. Our analytical investigations show that the epidemic threshold is independent of incubation period in both networks, which is verified by our large-scale simulation results. We also investigate the effect of incubation period on the epidemic dynamics in a supercritical regime. It is found that with the increase of incubation period Ω, a damped oscillation evolution of ρT (the ratio of persons in incubated state) appears and the time needed to reach a saturation value increases. Moreover, the steady value of ρT increases and approaches to an asymptotic constant with the value of Ω increasing. As a result, the infected ratio ρI decreases with the increase of Ω according to a power law.展开更多
To understand the influence of seasonal periodicity and environmental heterogeneity on the transmission dynamics of an infectious disease, we consider asymptotic periodicity in the fecally-orally epidemic model in a h...To understand the influence of seasonal periodicity and environmental heterogeneity on the transmission dynamics of an infectious disease, we consider asymptotic periodicity in the fecally-orally epidemic model in a heterogeneous environment. By using the next generation operator and the related eigenvalue problems, the basic reproduction number is introduced and shows that it plays an important role in the existence and non-existence of a positive T-periodic solution. The sufficient conditions for the existence and non-existence of a positive T-periodic solution are provided by applying upper and lower solutions method. Our results showed that the fecally-orally epidemic model in a heterogeneous environment admits at least one positive T-periodic solution if the basic reproduction number is greater than one, while no T-periodic solution exists if the basic reproduction number is less than or equal to one. By means of monotone iterative schemes, we construct the true positive solutions. The asymptotic behavior of periodic solutions is presented. To illustrate our theoretical results, some numerical simulations are given. The paper ends with some conclusions and future considerations.展开更多
Objective:The paper was to analyze the investigation and study of the psychological status of children and adolescents during the epidemic period of COVID-19.Methods:From March 5th to 11th,2020,1766 students from 8 to...Objective:The paper was to analyze the investigation and study of the psychological status of children and adolescents during the epidemic period of COVID-19.Methods:From March 5th to 11th,2020,1766 students from 8 to 18 years old in Yan'an area were taken as the research objects,and the psychological characteristics of this group of people during the epidemic period of COVID-19 were analyzed by the online questionnaires.Results:In the questionnaire,all children and adolescents were in good psychological conditions,and they had not shown serious negative psychological emotions,and they attached great importance to COVID-19.Conclusion:The psychological changes of children and adolescents during the epidemic period of COVID-19 are diverse.Most children and adolescents have a good mental state,and a few have negative psychological emotions.It can strengthen the psychological management of children and adolescents during the epidemic,and promote the healthy growth of children and adolescents clinically.展开更多
This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate. A threshold parameter R is identified. If R≤1, the disease-free equilibrium...This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate. A threshold parameter R is identified. If R≤1, the disease-free equilibrium O is globally stable. If R〉1, there is a unique endemic equilibrium and O is unstable. For two important special cases of bilinear and standard incidence ,sufficient conditions for the global stability of this endemic equilibrium are given. The same qualitative results are obtained provided the threshold is more than unity for the corresponding SEIS model with no infectious force in the latent period. Some existing results are extended and improved.展开更多
In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-In</span></span><span style="font-family:Verdana;...In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-In</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">fective</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-Removed), household epidemic model, with false negative and false positive misclassification probabilities. Maximum likelihood based algorithm is then employed for its inference. We then analyzed and compared the estimates of the two dimensional model with those of the three and four dimensional models associated with misclassified final size data over arrange of theoretical parameters, local and global infection rates and corresponding proportion infected in the permissible region, away from its boundaries and misclassification probabilities.</span></span></span><span><span><span style="font-family:""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">The adequacies of the three models to the final size data are examined. The four and three-dimensional models are found to outperform the two dimensional model on misclassified final size data.展开更多
Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptib...Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.展开更多
This paper formulates two stochastic nonautonomous SIRI epidemic systems with nonlinear perturbations.The main aim of this study is to investigate stochastic dynamics of the two SIRI epidemic systems and obtain their ...This paper formulates two stochastic nonautonomous SIRI epidemic systems with nonlinear perturbations.The main aim of this study is to investigate stochastic dynamics of the two SIRI epidemic systems and obtain their thresholds.For the nonautonomous stochastic SIRI epidemic system with white noise,the authors provide analytic results regarding the stochastic boundedness,stochastic permanence and persistence in mean.Moreover,the authors prove that the system has at least one nontrivial positive T-periodic solution by using Lyapunov function and Hasminskii’s theory.For the system with Markov conversion,the authors establish sufficient conditions for positive recurrence and existence of ergodic stationary distribution.In addition,sufficient conditions for the extinction of disease are obtained.Finally,numerical simulations are introduced to illustrate the main results.展开更多
The aim of this paper is first to establish a general prediction framework for turning(period)term structures in COVID-19 epidemic related to the implementation of emergency risk management in the practice,which allow...The aim of this paper is first to establish a general prediction framework for turning(period)term structures in COVID-19 epidemic related to the implementation of emergency risk management in the practice,which allows us to conduct the reliable estimation for the peak period based on the new concept of“Turning Period”(instead of the traditional one with the focus on“Turning Point”)for infectious disease spreading such as the COVID-19 epidemic appeared early in year 2020.By a fact that emergency risk management is necessarily to implement emergency plans quickly,the identification of the Turning Period is a key element to emergency planning as it needs to provide a time line for effective actions and solutions to combat a pandemic by reducing as much unexpected risk as soon as possible.As applications,the paper also discusses how this“Turning Term(Period)Structure”is used to predict the peak phase for COVID-19 epidemic in Wuhan from January/2020 to early March/2020.Our study shows that the predication framework established in this paper is capable to provide the trajectory of COVID-19 cases dynamics for a few weeks starting from Feb.10/2020 to early March/2020,from which we successfully predicted that the turning period of COVID-19 epidemic in Wuhan would arrive within one week after Feb.14/2020,as verified by the true observation in the practice.The method established in this paper for the prediction of“Turning Term(Period)Structures”by applying COVID-19 epidemic in China happened early 2020 seems timely and accurate,providing adequate time for the government,hospitals,essential industry sectors and services to meet peak demands and to prepare aftermath planning,and associated criteria for the Turning Term Structure of COVID-19 epidemic is expected to be a useful and powerful tool to implement the so-called“dynamic zero-COVID-19 policy”ongoing basis in the practice.展开更多
文摘We study the effect of incubation period on epidemic spreading in the Barabasi-Albert scale-free network and the Watts-Strogatz small world network by using a Suspectable-Incubated-Infected-Suspectable model. Our analytical investigations show that the epidemic threshold is independent of incubation period in both networks, which is verified by our large-scale simulation results. We also investigate the effect of incubation period on the epidemic dynamics in a supercritical regime. It is found that with the increase of incubation period Ω, a damped oscillation evolution of ρT (the ratio of persons in incubated state) appears and the time needed to reach a saturation value increases. Moreover, the steady value of ρT increases and approaches to an asymptotic constant with the value of Ω increasing. As a result, the infected ratio ρI decreases with the increase of Ω according to a power law.
文摘To understand the influence of seasonal periodicity and environmental heterogeneity on the transmission dynamics of an infectious disease, we consider asymptotic periodicity in the fecally-orally epidemic model in a heterogeneous environment. By using the next generation operator and the related eigenvalue problems, the basic reproduction number is introduced and shows that it plays an important role in the existence and non-existence of a positive T-periodic solution. The sufficient conditions for the existence and non-existence of a positive T-periodic solution are provided by applying upper and lower solutions method. Our results showed that the fecally-orally epidemic model in a heterogeneous environment admits at least one positive T-periodic solution if the basic reproduction number is greater than one, while no T-periodic solution exists if the basic reproduction number is less than or equal to one. By means of monotone iterative schemes, we construct the true positive solutions. The asymptotic behavior of periodic solutions is presented. To illustrate our theoretical results, some numerical simulations are given. The paper ends with some conclusions and future considerations.
基金Supported by Project Science and Technology Plan Project in Yan'an City No.SL2020ZCSY-004。
文摘Objective:The paper was to analyze the investigation and study of the psychological status of children and adolescents during the epidemic period of COVID-19.Methods:From March 5th to 11th,2020,1766 students from 8 to 18 years old in Yan'an area were taken as the research objects,and the psychological characteristics of this group of people during the epidemic period of COVID-19 were analyzed by the online questionnaires.Results:In the questionnaire,all children and adolescents were in good psychological conditions,and they had not shown serious negative psychological emotions,and they attached great importance to COVID-19.Conclusion:The psychological changes of children and adolescents during the epidemic period of COVID-19 are diverse.Most children and adolescents have a good mental state,and a few have negative psychological emotions.It can strengthen the psychological management of children and adolescents during the epidemic,and promote the healthy growth of children and adolescents clinically.
文摘This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate. A threshold parameter R is identified. If R≤1, the disease-free equilibrium O is globally stable. If R〉1, there is a unique endemic equilibrium and O is unstable. For two important special cases of bilinear and standard incidence ,sufficient conditions for the global stability of this endemic equilibrium are given. The same qualitative results are obtained provided the threshold is more than unity for the corresponding SEIS model with no infectious force in the latent period. Some existing results are extended and improved.
文摘In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-In</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">fective</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-Removed), household epidemic model, with false negative and false positive misclassification probabilities. Maximum likelihood based algorithm is then employed for its inference. We then analyzed and compared the estimates of the two dimensional model with those of the three and four dimensional models associated with misclassified final size data over arrange of theoretical parameters, local and global infection rates and corresponding proportion infected in the permissible region, away from its boundaries and misclassification probabilities.</span></span></span><span><span><span style="font-family:""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">The adequacies of the three models to the final size data are examined. The four and three-dimensional models are found to outperform the two dimensional model on misclassified final size data.
文摘Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.
基金supported by the National Natural Science Foundation of China under Grant No.11371230the Research Fund for the Taishan Scholar Project of Shandong Province of Chinathe SDUST Research Fund under Grant No.2014TDJH102
文摘This paper formulates two stochastic nonautonomous SIRI epidemic systems with nonlinear perturbations.The main aim of this study is to investigate stochastic dynamics of the two SIRI epidemic systems and obtain their thresholds.For the nonautonomous stochastic SIRI epidemic system with white noise,the authors provide analytic results regarding the stochastic boundedness,stochastic permanence and persistence in mean.Moreover,the authors prove that the system has at least one nontrivial positive T-periodic solution by using Lyapunov function and Hasminskii’s theory.For the system with Markov conversion,the authors establish sufficient conditions for positive recurrence and existence of ergodic stationary distribution.In addition,sufficient conditions for the extinction of disease are obtained.Finally,numerical simulations are introduced to illustrate the main results.
基金Supported by the National Natural Science Foundation of China(71971031,U1811462)
文摘The aim of this paper is first to establish a general prediction framework for turning(period)term structures in COVID-19 epidemic related to the implementation of emergency risk management in the practice,which allows us to conduct the reliable estimation for the peak period based on the new concept of“Turning Period”(instead of the traditional one with the focus on“Turning Point”)for infectious disease spreading such as the COVID-19 epidemic appeared early in year 2020.By a fact that emergency risk management is necessarily to implement emergency plans quickly,the identification of the Turning Period is a key element to emergency planning as it needs to provide a time line for effective actions and solutions to combat a pandemic by reducing as much unexpected risk as soon as possible.As applications,the paper also discusses how this“Turning Term(Period)Structure”is used to predict the peak phase for COVID-19 epidemic in Wuhan from January/2020 to early March/2020.Our study shows that the predication framework established in this paper is capable to provide the trajectory of COVID-19 cases dynamics for a few weeks starting from Feb.10/2020 to early March/2020,from which we successfully predicted that the turning period of COVID-19 epidemic in Wuhan would arrive within one week after Feb.14/2020,as verified by the true observation in the practice.The method established in this paper for the prediction of“Turning Term(Period)Structures”by applying COVID-19 epidemic in China happened early 2020 seems timely and accurate,providing adequate time for the government,hospitals,essential industry sectors and services to meet peak demands and to prepare aftermath planning,and associated criteria for the Turning Term Structure of COVID-19 epidemic is expected to be a useful and powerful tool to implement the so-called“dynamic zero-COVID-19 policy”ongoing basis in the practice.