For　understanding　the　influence　of　user　security　awareness　on　the　long-term　spreading　behavior　of　malware　over　mobile　networks,　in　this　paper,　we　intensively　study　the　global　dynamics　of　a　novel　network-based　epidemic　model　with　weakly-protected　and　strongly-protected　susceptible　nodes.　Both　analytical　and　numerical　results　show　that　the　global　dynamics　of　the　model　is　completely　governed　by　a　threshold　value.　Specifically,　we　prove　that　when　the　value　is　lower　than　one,　the　malware-free　equilibrium　is　globally　asymptotically　stable　and　mobile　malware　will　disappear.　When　the　value　is　greater　than　one,　mobile　malware　will　persist　on　the　network,　and　in　the　meantime　there　exists　a　unique　malware　equilibrium　which　is　globally　asymptotically　stable　under　certain　conditions.　The　obtained　results　improve　and　enrich　some　known　ones.　Interestingly,　increasing　the　recovery　rate　of　infected　nodes　can　result　in　the　increase　of　strongly-protected　susceptible　nodes　and　the　decrease　of　the　threshold　value.　The　study　has　valuable　guiding　significance　in　effectively　controlling　mobile　malware　spread.　(C)　2018　Elsevier　B.V.　All　rights　reserved.