This paper studies the global behavior of the spread of HBV using a SEIR model with a constant vaccination rate. The infectivity during the incubation period is considered as a second way of transmission. The basic re...This paper studies the global behavior of the spread of HBV using a SEIR model with a constant vaccination rate. The infectivity during the incubation period is considered as a second way of transmission. The basic reproduction number R0 is derived as a function of the two contact rates?β1?and β2?. There is a disease free equilibrium point (DFE) of our model. When R0 R0 > 1, there is a unique endemic equilibrium. We proved that the endemic equilibrium was globally asymptotically stable when R0 > 1 and that the disease persisted in the population. These results are original for our model with vaccination and two contact rates.展开更多
Traditional compartmental models such as SIR(susceptible,infected,recovered)assume that the epidemic transmits in a homogeneous population,but the real contact patterns in epidemics are heterogeneous.Employing a more ...Traditional compartmental models such as SIR(susceptible,infected,recovered)assume that the epidemic transmits in a homogeneous population,but the real contact patterns in epidemics are heterogeneous.Employing a more realistic model that considers heterogeneous contact is consequently necessary.Here,we use a contact network to reconstruct unprotected,protected contact,and airborne spread to simulate the two-stages outbreak of COVID-19(coronavirus disease 2019)on the‘‘Diamond Princess"cruise ship.We employ Bayesian inference and Metropolis-Hastings sampling to estimate the model parameters and quantify the uncertainties by the ensemble simulation technique.During the early epidemic with intensive social contacts,the results reveal that the average transmissibility t was 0.026 and the basic reproductive number R0 was 6.94,triple that in the WHO report,indicating that all people would be infected in one month.The t and R0 decreased to 0.0007 and 0.2 when quarantine was implemented.The reconstruction suggests that diluting the airborne virus concentration in closed settings is useful in addition to isolation,and high-risk susceptible should follow rigorous prevention measures in case exposed.This study can provide useful implications for control and prevention measures for the other cruise ships and closed settings.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
文摘This paper studies the global behavior of the spread of HBV using a SEIR model with a constant vaccination rate. The infectivity during the incubation period is considered as a second way of transmission. The basic reproduction number R0 is derived as a function of the two contact rates?β1?and β2?. There is a disease free equilibrium point (DFE) of our model. When R0 R0 > 1, there is a unique endemic equilibrium. We proved that the endemic equilibrium was globally asymptotically stable when R0 > 1 and that the disease persisted in the population. These results are original for our model with vaccination and two contact rates.
基金supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDA19070104)13th Five-year Informatization Plan of Chinese Academy of Sciences (XXH13505-06)+1 种基金Foundation for Excellent Youth Scholars of Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences (Y851D41)National Natural Science Foundation of China (41801270)。
文摘Traditional compartmental models such as SIR(susceptible,infected,recovered)assume that the epidemic transmits in a homogeneous population,but the real contact patterns in epidemics are heterogeneous.Employing a more realistic model that considers heterogeneous contact is consequently necessary.Here,we use a contact network to reconstruct unprotected,protected contact,and airborne spread to simulate the two-stages outbreak of COVID-19(coronavirus disease 2019)on the‘‘Diamond Princess"cruise ship.We employ Bayesian inference and Metropolis-Hastings sampling to estimate the model parameters and quantify the uncertainties by the ensemble simulation technique.During the early epidemic with intensive social contacts,the results reveal that the average transmissibility t was 0.026 and the basic reproductive number R0 was 6.94,triple that in the WHO report,indicating that all people would be infected in one month.The t and R0 decreased to 0.0007 and 0.2 when quarantine was implemented.The reconstruction suggests that diluting the airborne virus concentration in closed settings is useful in addition to isolation,and high-risk susceptible should follow rigorous prevention measures in case exposed.This study can provide useful implications for control and prevention measures for the other cruise ships and closed settings.
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.
