The　prompt　and　massive　detection　of　the　community　population　with　HIV　is　beneficial　to　the　early　diagnosis　and　helps　to　determine　the　main　tendency　of　HIV/AIDS　transmission　from　the　perspective　of　public　health　and　policy　makers.　In　this　study,　an　SIDMA　(Susceptible–Infected–Diagnosed–Monitored–AIDS)　compartmental　model　with　HIV　detection　is　proposed　by　using　Holling　type　II　functional　response.　The　slow　average　handling　time　in　HIV　detection　is　taken　into　account.　We　first　derive　the　basic　reproduction　number　of　the　SIDMA　model　using　the　next　generation　matrix　method.　Then,　the　global　stabilities　for　disease-free　equilibrium　point,　and　boundary　equilibrium　point　are　proved　under　moderate　conditions.　The　research　results　show　that　the　threshold　of　global　stabilities　increases　with　the　monitoring　rate.　Alternatively,　given　that　the　average　handling　time　of　HIV　detection　is　fast　enough,　the　research　results　explore　that　the　underestimation　for　the　threshold　of　the　global　stabilities　usually　exists.　This　study　reveals　that　positive　medical　interventions　for　the　community　population　with　HIV　improve　the　life　quality　through　the　enhancement　of　the　monitoring　rate,　also　finds　that　prevalence　situation　of　the　community　population　with　HIV　is　under　control.　©　2025