Modeling and simulation of the spread of H1N1 flu with periodic vaccination

Abstract

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.