It　was　shown　in　[11]　that　in　an　epidemic　model　with　a　nonlinear　incidence　and　two　compartments　some　complex　dynamics　can　appear,　such　as　the　backward　bifurcation,　codimension　1　Hopf　bifurcation　and　codimension　2　Bogdanov-Takens　bifurcation.　In　this　paper　we　prove　that　for　the　same　model　the　codimension　of　Bogdanov-Takens　bifurcation　can　be　3　and　is　at　most　3.　Hence,　more　complex　new　phenomena,　such　as　codimension　2　Hopf　bifurcation,　codimension　2　homoclinic　bifurcation　and　semi-stable　limit　cycle　bifurcation,　exhibit.　Especially,　the　system　can　have　and　at　most　have　2　limit　cycles　near　the　positive　singularity.