An Age-structured SEIR Epidemic Model With Leaky Vaccination

An age-structured SEIR epidemic model with non-lifelong immunity and leaky vac-cination is modelled in this paper,the well- posedness of the solution to the model isdiscussed.First,the question (P)is changed into the integral equations (H) and by definingoperators ,the question (H)is transformed into the question of existence and uniquenessof an operator fixed point.Second,the existence and uniqueness of local solution to thequestion (H) is proofed by Banach fixed-point theorem and we derive the global existenceand uniqueness of the solution to the integral question (H) , continuous dependence on theinitial value and C1 regularity of the solution,so we get the well-posedness of the solutionto the question (P) ; The existence and uniqueness and the asymptotical stability of thedisease-free equilibrium are discussed ,basing on the other easier model.