The　2019　coronavirus　pandemic　exudes　public　health　and　socio-economic　burden　globally,　raising　an　unprecedented　concern　for　infectious　diseases.　Thus,　describing　the　infectious　disease　transmission　process　to　design　effective　intervention　measures　and　restrict　its　spread　is　a　critical　scientific　issue.　We　propose　a　level-dependent　Markov　model　with　infinite　state　space　to　characterize　viral　disorders　like　COVID-19.　The　levels　and　states　in　this　model　represent　the　stages　of　outbreak　development　and　the　possible　number　of　infectious　disease　patients.　The　transfer　of　states　between　levels　reflects　the　explosive　transmission　process　of　infectious　disease.　A　simulation　method　with　heterogeneous　infection　is　proposed　to　solve　the　model　rapidly.　After　that,　simulation　experiments　were　conducted　using　MATLAB　according　to　the　reported　data　on　COVID-19　published　by　Johns　Hopkins.　Comparing　the　simulation　results　with　the　actual　situation　shows　that　our　proposed　model　can　well　capture　the　transmission　dynamics　of　infectious　diseases　with　and　without　imposed　interventions　and　evaluate　the　effectiveness　of　intervention　strategies.　Further,　the　influence　of　model　parameters　on　transmission　dynamics　is　analyzed,　which　helps　to　develop　reasonable　intervention　strategies.　The　proposed　approach　extends　the　theoretical　study　of　mathematical　modeling　of　infectious　diseases　and　contributes　to　developing　models　that　can　describe　an　infinite　number　of　infected　persons.