After　over　three　years　of　COVID-19,　it　has　become　clear　that　infectious　diseases　are　difficult　to　eradicate,　and　humans　remain　vulnerable　under　their　influence　in　a　long　period.　The　presence　of　presymptomatic　and　asymptomatic　patients　is　a　significant　obstacle　to　preventing　and　eliminating　infectious　diseases.　However,　the　long-term　transmission　of　infectious　diseases　involving　asymptomatic　patients　still　remains　unclear.　To　address　this　issue,　this　paper　develops　a　novel　Markov　process　for　infectious　diseases　with　asymptomatic　patients　by　means　of　a　continuous-time　leveldependent　quasi-birth-and-death　(QBD)　process.　The　model　accurately　captures　the　transmission　of　infectious　diseases　by　specifying　several　key　parameters　(or　factors).　To　analyze　the　role　of　asymptomatic　and　symptomatic　patients　in　the　infectious　disease　transmission　process,　a　simple　sufficient　condition　for　the　stability　of　the　Markov　process　of　infectious　diseases　is　derived　using　the　mean　drift　technique.　Then,　the　stationary　probability　vector　of　the　QBD　process　is　obtained　by　using　RG-factorizations.　A　method　of　using　the　stationary　probability　vector　is　provided　to　obtain　important　performance　measures　of　the　model.　Finally,　some　numerical　experiments　are　presented　to　demonstrate　the　model＇s　feasibility　through　analyzing　COVID-19　as　an　example.　The　impact　of　key　parameters　on　the　system　performance　evaluation　and　the　infectious　disease　transmission　process　are　analyzed.　The　methodology　and　results　of　this　paper　can　provide　theoretical　and　technical　support　for　the　scientific　control　of　the　long-term　transmission　of　infectious　diseases,　and　we　believe　that　they　can　serve　as　a　foundation　for　developing　more　general　models　of　infectious　disease　transmission.