Influenza H1N1 has been found to exhibit oscillatory levels of incidence in large populations. 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: 10.1186/1741-7015-7-43]. 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 R0, 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.
Extinction and persistence of a stochastic SIRS model with nonlinear incidence rate and transfer from infectious to susceptible
