The　tumour　suppressor　gene　p53　plays　a　key　role　in　cell　response　to　DNA　damage,　and　the　p53–Mdm2　regulation　relationship　is　crucial　for　the　expression　of　p53.　In　this　paper,　based　on　gene　expression　time-series　data　of　human　leukaemia　cells　after　exposure　to　ionising　radiation,　with　ionising　radiation　as　input,　a　nonlinear　continuous　time-delay　dynamic　stochastic　mathematical　model　of　a　p53–Mdm2　network　is　established　using　a　continuous–discrete　extended　Kalman　filter　algorithm.　The　accuracy　of　the　established　model　is　then　validated.　Numerical　simulation　is　used　to　simulate　the　dynamic　regulation　in　p53–Mdm2　networks　for　low,　medium,　and　high　ionising　radiation　doses.　The　results　show　that　the　proposed　algorithm　is　convergent　and　that　the　error　rate　of　the　model　is　only　1.19%.　In　addition,　the　model　can　simulate　accurately　the　response　of　the　p53–Mdm2　network　to　different　doses　of　ionising　radiation.　The　methods　proposed　in　this　paper　can　supply　the　foundation　for　research　on　the　dynamics　of　the　p53–Mdm2　gene　regulation　relationship　and　play　a　guiding　role　in　research　on　the　p53–Mdm2　response　process　after　DNA　damage　under　different　doses　of　ionising　radiation.　©　2017　Elsevier　B.V.