In　this　paper,　a　single-species　logistic　model　with　both　fear　effect-type　feedback　control　and　additive　Allee　effect　is　developed　and　investigated　using　the　new　coronavirus　as　a　feedback　control　variable.　When　the　system　introduces　additive　Allee　effect　and　fear　effect-type　feedback　control,　more　complicated　dynamical　behavior　is　obtained.　The　system　can　undergo　transcritical　bifurcation,　saddle-node　bifurcation,　degenerate　Hopf　bifurcation　and　Bogdanov–Takens　bifurcation.　By　numerical　simulations,　the　system　exhibits　homoclinic　bifurcation　and　saddle-node　bifurcation　of　limit　cycles　as　parameters　are　altered.　Remarkably,　it　is　the　first　time　that　two　limit　cycles　have　been　discovered　in　a　single-species　logistic　model　with　the　Allee　effect.　Further,　stronger　Allee　effect　or　stronger　fear　effect　can　lead　to　the　extinction　of　the　species　population.　©　World　Scientific　Publishing　Company.