Basic Vaccination Control Techniques for a General True -Mass Action   SEIR Model
  This paper presents several simple linear vaccination-based control strategies for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among susceptible and infected. The vaccination control objective is the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously that the remaining populations (i.e. susceptible plus infected plus infectious) tend asymptotically to zero. 
M. De la Sen, S. Alonso-Quesada
math.DS