摘要：Vaccination is considered one of the most effective control measures for influenza. However, when a virus mutates and multi-strains appear in a population, implementing a vaccine for one strain may affect the spread of the other strains. In this paper, we propose a two-strain model and investigate the effects of a single-strain vaccine on the dynamics of this two-strain model. The global dynamics of the model are completely determined through suitable Lyapunov functions. We show that if the basic reproduction number is less than one, then both strains die out; but when the number is larger than one, one or both of the strains become endemic depending on the parameter values. The theoretical results provide some useful information on the impact of the vaccination rate of this single-vaccine for one strain on the dynamics of the two strains.
关键词：influenza; epidemics; vaccination; equilibrium; basic reproduction number; global asymptotic stability; Lyapunov function
