Based on the transmission mechanism of seasonal influenza,this paper establishes a SEIMHRS model with hospital-visiting behavior and periodic transmission rate,and then analyzes the existence and stability of disease-...Based on the transmission mechanism of seasonal influenza,this paper establishes a SEIMHRS model with hospital-visiting behavior and periodic transmission rate,and then analyzes the existence and stability of disease-free and endemic periodic solutions theoretically.Taking the epidemic of seasonal infuenza during 2013-2018 in Beijing and conducting parameter estimation,we derive its basic reproduction ratio Ro is 1.0065.Then we concentrate on the correlation between time-varying transmission rate of infuenza and change pattern of three meteorology indices for the first time.The results novelly show that there exists a synchronization phenomenon between the transmission rate and variation pattern of average atmospheric pressure and that there is an anti-synchronism phenomenon between that of the average temperature.Whereas it only shows a normal phase difference with the variation pattern of relative humidity.Finally we advocate emphasis on the effect of variation trend of meteorology on infuenza prediction.展开更多
A nonlinear mathematical model is proposed and analyzed to study the dynamics of 2009 HIN1 flu epidemic in a homogeneous population with constant immigration of susceptibles. The effect of contact tracing and quaranti...A nonlinear mathematical model is proposed and analyzed to study the dynamics of 2009 HIN1 flu epidemic in a homogeneous population with constant immigration of susceptibles. The effect of contact tracing and quarantine （isolation） strategies in reduc- ing the spread of H1N1 flu is incorporated. The model monitors the dynamics of five sub-populations （classes）, namely susceptible with high infection risk, susceptible with reduction of infection risk, infective, quarantined and recovered individuals. The model analysis includes the determination of equilibrium points and carrying out their stability analysis in terms of the threshold parameter R0. Moreover, the numerical simulation of the proposed model is also performed by using fourth order Runge-Kutta method along with the sensitivity analysis of the endemic equilibrium point. The analysis and numeri- cal simulation results demonstrate that the maximum implementation of contact tracing and quarantine strategies help in reducing endemic infective class size and hence act as effective intervention strategy to control the disease. This gives a theoretical interpreta- tion to the practical experiences that the early contact tracing and quarantine strategies are criticMly important to control the outbreak of epidemics.展开更多
Influenza H1N1 has been found to exhibit oscillatory levels of incidence in large pop- ulations. Clear peaks for influenza H1N1 are observed in several countries including Vietnam each year [M. F. Boni, B. H. Manh, P....Influenza H1N1 has been found to exhibit oscillatory levels of incidence in large pop- ulations. Clear peaks for influenza H1N1 are observed in several countries including Vietnam each year [M. F. Boni, B. H. Manh, P. Q. Thai, J. Farrar, T. Hien, N. T. Hien, N. Van Kinh and P. Horby, Modelling the progression of pandemic influenza A （H1N1） in Vietnam and the opportunities for reassortment with other influenza viruses, BMC Med. 7 （2009） 43, Doi： 10.1186/1741-7015-%43]. So it is important to study seasonal forces and factors which can affect the transmission of this disease. This paper studies an SIRS epidemic model with seasonal vaccination rate. This SIRS model has a unique disease-free solution （DFS）. The value Ro, the basic reproduction number is obtained when the vaccination is a periodic function. Stability results for the DFS are obtained when R0 〈 1. The disease persists in the population and remains endemic if R0 〉 1. Also when R0 〉 1 existence of a nonzero periodic solution is proved. These results obtained for our model when the vaccination strategy is a non-constant time-dependent function.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12231012,91846302,12101373,61873154)Shanxi Key Laboratory(No.201705D111006)+2 种基金Key R&D projects of Shanxi Province(No.202003D31011/GZ)Health Commission of Shanxi Province(No.2020XM18)Research of Technological Important Programs in the city of Lvliang,China(No.2022GXYF18).
文摘Based on the transmission mechanism of seasonal influenza,this paper establishes a SEIMHRS model with hospital-visiting behavior and periodic transmission rate,and then analyzes the existence and stability of disease-free and endemic periodic solutions theoretically.Taking the epidemic of seasonal infuenza during 2013-2018 in Beijing and conducting parameter estimation,we derive its basic reproduction ratio Ro is 1.0065.Then we concentrate on the correlation between time-varying transmission rate of infuenza and change pattern of three meteorology indices for the first time.The results novelly show that there exists a synchronization phenomenon between the transmission rate and variation pattern of average atmospheric pressure and that there is an anti-synchronism phenomenon between that of the average temperature.Whereas it only shows a normal phase difference with the variation pattern of relative humidity.Finally we advocate emphasis on the effect of variation trend of meteorology on infuenza prediction.
文摘A nonlinear mathematical model is proposed and analyzed to study the dynamics of 2009 HIN1 flu epidemic in a homogeneous population with constant immigration of susceptibles. The effect of contact tracing and quarantine （isolation） strategies in reduc- ing the spread of H1N1 flu is incorporated. The model monitors the dynamics of five sub-populations （classes）, namely susceptible with high infection risk, susceptible with reduction of infection risk, infective, quarantined and recovered individuals. The model analysis includes the determination of equilibrium points and carrying out their stability analysis in terms of the threshold parameter R0. Moreover, the numerical simulation of the proposed model is also performed by using fourth order Runge-Kutta method along with the sensitivity analysis of the endemic equilibrium point. The analysis and numeri- cal simulation results demonstrate that the maximum implementation of contact tracing and quarantine strategies help in reducing endemic infective class size and hence act as effective intervention strategy to control the disease. This gives a theoretical interpreta- tion to the practical experiences that the early contact tracing and quarantine strategies are criticMly important to control the outbreak of epidemics.
文摘Influenza H1N1 has been found to exhibit oscillatory levels of incidence in large pop- ulations. Clear peaks for influenza H1N1 are observed in several countries including Vietnam each year [M. F. Boni, B. H. Manh, P. Q. Thai, J. Farrar, T. Hien, N. T. Hien, N. Van Kinh and P. Horby, Modelling the progression of pandemic influenza A （H1N1） in Vietnam and the opportunities for reassortment with other influenza viruses, BMC Med. 7 （2009） 43, Doi： 10.1186/1741-7015-%43]. So it is important to study seasonal forces and factors which can affect the transmission of this disease. This paper studies an SIRS epidemic model with seasonal vaccination rate. This SIRS model has a unique disease-free solution （DFS）. The value Ro, the basic reproduction number is obtained when the vaccination is a periodic function. Stability results for the DFS are obtained when R0 〈 1. The disease persists in the population and remains endemic if R0 〉 1. Also when R0 〉 1 existence of a nonzero periodic solution is proved. These results obtained for our model when the vaccination strategy is a non-constant time-dependent function.
