Numerical Simulation Of SARS Epidemic In Beijing In 2003 By Differential Equation With Time-Delay

SARS(sever　acute　respiratory　syndrome)　is　the　most　widely-spread　infectious　disease　in　the　recent　decades.　The　study　of　the　development　of　SARS　in　Beijing　has　great　significance,　because　the　SARS　cases　in　Beijing　occupy　a　very　high　proportion　in　China.　This　thesis　analyses　the　observed　statistical　data　of　SARS　in　Beijing.　According　to　the　observed　statistical　data,　a　mathematical　model　is　established　to　simulate　the　SARS　development　in　Beijing　by　differential　equation　with　time-delay.　We　neglect　the　infection　of　SARS　patients　isolated　in　hospitals.　Four　groups　of　people　related　to　the　spread　of　SARS　epidemic　are　discussed.　They　are　the　healthy　people,　the　patients　in　the　latent　period,　the　infectious　patients　outside　hospitals　and　the　patients　who　isolated,　recovered　or　died　in　　hospitals　.　The　model　involves　five　important　parameters　:　the　time　when　the　control　measures　by　the　government　took　effect,　the　infectious　rates　before　and　after　control,　the　average　infectious　period　for　the　infectious　patients　to　stay　outside　hospital　and　the　ratio　of　the　initial　numbers　of　patients　to　the　total　　numbers　of　people　in　Beijing.　Asymptotical　and　numerical　solutions　are　obtained.　The　total　number　of　the　patients　in　Beijing　is　simulated.　The　solution　analysis　shows　that　the　total　patient　number　increases　with　the　average　infectious　period　before　the　infectious　patients　are　isolated　in　hospitals.　That　is,　the　longer　the　patients　stay　outside　hospitals　,the　larger　the　number　of　the　infected　patients　is.　It　would　not　be　impossible　that　all　people　in　Beijing　would　have　been　infected　if　no　control　measures　are　taken　by　the　government.