Vaccination rules for a true-mass action SEIR epidemic model based on an   observer synthesis. Preliminary results
  This paper presents a simple continuous-time linear vaccination-based control strategy 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 control objective is the asymptotically tracking of the removed-byimmunity population to the total population while achieving simultaneously the remaining population (i.e. susceptible plus infected plus infectious) to asymptotically converge to zero. A state observer is used to estimate the true various partial populations of susceptible, infected, infectious and immune which are assumed to be unknown. The model parameters are also assumed to be, in general, unknown. In this case, the parameters are replaced by available estimates to implement the vaccination action. 
M. De la Sen, A. Ibeas and S. Alonso-Quesada
math.DS