On a SIS model with impulsive effects
  This paper is concerned with a SIS (susceptible, infected and susceptible populations) propagation disease model with a nonlinear incidence rate and eventual impulsive (non- necessarily being simultaneous) culling of both populations. The disease transmission does not necessarily take into account the total population as a normalizing effect. In this sense, the considered model is a mixed pseudo-mass. The positivity, stability of both the impulse- free and impulsive under pulse culling variants of the model are investigated in this paper. 
M. De la Sen, A. Ibeas and S. Alonso-Quesada
math.DS