  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.
