An SEIR epidemic model with a nonconstant vaccination strategy is studied. This SEIR model has two disease transmission rates β1 and β2 which imitate the fact that, for some infectious diseases, a latent person can pass the disease into a susceptible one. Here we study the spread of some childhood infectious diseases as good examples of diseases with infectious latent. We found that our SEIR model has a unique disease free solution (DFS). A lower bound R0inf and an upper bound R0sup of the basic reproductive number, R0 are estimated. We show that, the DFS is globally asymptotically stable when R0sup < 1 and unstable if R0inf > 1. Computer simulations have been conducted to show that non trivial periodic solutions are possible. Moreover the impact of the contact rate between the latent and the susceptibles is simulated. Different periodic solutions with different periods including one, two and three years, are obtained. These results give a clearer view for the decision makers to know how and when they should take action against a possible new wave of these infectious diseases. This action is mainly, applying a suitable dose of vaccination just before a severe peak of infection occurs