  We enter the details of two recent articles concerning as many chemotaxis
models, one nonlinear and the other linear, and both with produced
chemoattractant and saturated chemorepellent. These works, when properly
analyzed, leave open room for some improvement of their results. We generalize
the outcomes of the mentioned articles, establish other statements and put all
the claims together; in particular, we select the sharpest ones and schematize
them. Moreover, we complement our research also when logistic sources are
considered in the overall study.
