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.
