A new SEIR epidemic model with applications to the theory of eradication and control of diseases, and to the calculation of R0R0

We present a novel SEIR (susceptible–exposure–infective–recovered) model that is suitable for modeling the eradication of diseases by mass vaccination or control of diseases by case isolation combined with contact tracing, incorporating the vaccine efficacy or the control efficacy into the model. Moreover, relying on this novel SEIR model and some probabilistic arguments, we have found four formulas that are suitable for estimating the basic reproductive numbers R0R0 in terms of the ratio of the mean infectious period to the mean latent period of a disease. The ranges of R0R0 for most known diseases, that are calculated by our formulas, coincide very well with the values of R0R0 estimated by the usual method of fitting the models to observed data.