Optimal control is an important tool to determine vaccination poli-cies for infectious diseases. For diseases transmitted horizontally, SEIR com-partment models have been used. Most of the literature on SEIR models deals with cost functions that are quadratic with respect to the control variable, the rate of vaccination. In this paper, we consider L 1 –type objectives that are linear with respect to the control variable. Various pure control, mixed control–state and pure state constraints are imposed. For all constraints, we discuss the necessary optimality conditions of the Maximum Principle and determine optimal control strategies that satisfy the necessary optimality con-ditions with high accuracy. Since the control variable appears linearly in the Hamiltonian, the optimal control is a concatenation of bang-bang arcs, singu-lar arcs and boundary arcs. For pure bang-bang controls, we are able to check second-order sufficient conditions.