Albert Barnes on Mark 1:45

Began to publish it much. That is, the subject of his own cure. He was so deeply affected with it, and so much rejoiced, that he followed the natural dictates of his own feelings, rather than the command of the Saviour.

Jesus could no more openly enter into the city. The word could, here, does not refer to any natural inability, or to any physical obstacle in his way, but only denotes that there was difficulty, or inconvenience, or impropriety, in his doing it then; that he judged it best not then to enter into the city. The difficulty was, probably, that his being in the city drew such crowds of people as rendered it difficult to accommodate them, or so as to excite the opposition of civil rulers.

The city. The city, or large town, where the leper was cured. The same reason for not entering that city applied also to others; so that he remained in the deserts, where the multitudes could come to him without any difficulty or opposition.

(c) "began to publish" Ps 77:11,12, Tit 1:10 (c) "and they came to him" Mk 2:13