We　analyze　a　time-delayed　SIQR　model　that　considers　transportation-related　infection　and　entry-exit　screening.　This　model　aims　to　determine　the　measures　for　preventing　and　controlling　major　emergent　infectious　diseases　and　the　associated　costs.　We　calculate　the　basic　reproduction　number　(R0)　and　prove　that　the　disease-free　equilibrium　is　locally　and　globally　asymptotically　stable.　We　collect　COVID-19　infection　data　from　two　regions　in　the　United　States　in　2020　for　data　fitting,　obtain　a　set　of　optimal　parameter　values,　and　find　that　transportation-related　infection　rates　increase　the　basic　reproduction　number,　enhancing　the　impact　on　disease　spread.　Entry-exit　screening　effectively　suppresses　the　spread　of　disease　by　reducing　the　basic　reproduction　number.　Furthermore,　we　investigate　the　influence　of　the　incubation　period　on　disease　and　find　that　a　shorter　incubation　period　results　in　a　shorter　duration　but　a　larger　scale　of　infection　and　that　the　peaks　are　reduced.　We　conduct　a　sensitivity　analysis　of　the　R0　and　propose　three　measures　to　prevent　the　spread　of　new　infectious　diseases　based　on　the　most　sensitive　parameters:　wearing　masks,　implementing　urban　closures,　and　administering　medication　to　sick　but　not　yet　hospitalized　patients　promptly.　In　the　case　of　COVID-19,　optimal　control　effectively　controls　the　development　and　deterioration　of　the　disease.　Finally,　several　control　measures　are　compared　through　cost-effectiveness　analysis,　and　the　results　show　that　wearing　masks　is　the　most　cost-effective　measure.