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

作     者：Islam A. Moneim 

作者机构：Department of Scientific Computing Faculty of Computers and InformaticsBenha University P. O. Box 13518 Benha Egypt 

出 版 物：《International Journal of Biomathematics》 (生物数学学报（英文版）)

年 卷 期：2016年第9卷第1期

页      面：47-63页

核心收录：

学科分类：090603[农学-临床兽医学] 08[工学] 080203[工学-机械设计及理论] 09[农学] 0906[农学-兽医学] 0802[工学-机械工程] 

基　　金：research Deanship Qassim University KSA 

主　　题：Mathematical modeling disease control periodic vaccination rate basicreproduction number R0 periodicity influenza. 

摘      要：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.