Test du score pour l'exploration de modèles complexes: Application à la modélisation dynamique du VIH.
Texte intégral
(2)
(3)
(4)
(5) !
(6) " # $%
(7) #&'.
(8) ($)''+*,-../0 12#!
(9) " 3 4 $%
(10) #5./! !
(11) " 67"8($%!9 :<;(= >@?BADCDEFHGJIKAML0N4CDO0P@QRFETSBCDL0AVUWYX.XZL0SB[YL!\^]%_^WK`BWYAMaBbBL/cdbBCMe!fgE@?ih jlknmBoqp4rts2uwvyxBz|{ }~g}2K}/p4}l lg} lg}HoVKD@}2}q4@D!g}l uw~g@}V /m}@D}~ JK}@T @s¡!¢¤£¥R}/¦Vlm§@¨@~@sª©©i«izT£¬JK}@T l}K}JTs J@~¤ l} 1® ¯K°<±w²¯´³7FETSB\AµEX.Wi`¶e!ADCM\EThCDWYS#`BL0\.\IK\Jh·0XZL0\fBCDWYAMWY[YCM¸K?¶L!\!Q`BL!\X.Wi`B·0ADL0\¬`BL|aBAM?B\¬L!S a¶AD?B\dO0WYXZa¶ADL¹iL0\d\WYSh^`Be0º@L!AMWYaBae!\!» ¼¾½¿L0\JhCDXZEThCMWYS`BL0\4agE@GETXZ·hGL0\d`BL/hL0AXZWK`B·0ADLCMXZaBAMCD¸y?BLn`BL!\ hL!X.aB\H`¶LO<ETADO!?¶AD\^agE@GJÀÁW@CD\4ADWYS¶[Y\!»^ÂnS[YGE@S¶`SBWYXfBGL`BLX.WK`B·!AML!\^L!\JhÃL¹iaBAMWYGL0GnCMSBO!AM?gE@Shn`BL!\ LĤLh\HE@ADe!EThWYCMGL0\nETCDSB\JCw¸y?BL2`BL!\^ºTE@GCDE@fBADL0\4L¹iaBADCMO<EThCMº@L!\^\?BG^ADL0\n`BC¨Ä¤e0GL0Syh\HagETGE@X.·0hGL!\0»^¼VL'hL0\Jh `¶?.\JO!WYGJLda§L0?¶h<Q`BE@SB\ÅO0LdO!WYShL¥¹KhL@QKÆ0hGLÇ?ihCDAMLaWY?BGÅCMSBO!AM?BGL`BLÇSBWY?iºYL!AMADL0\ź@ETGCµETfBADL0\`gE@S¶\¾ADLX.WK`iÈ ·0ADLT» UL!aL!SB`gETSyh!QÅA½ÉbIKa§W@hbB·!\JLSy?BAMADL`B?hL!\Jha§L0?¶h2Æ0hGJLO0WYXZa¶ADL¹iLTQÊ`B?ÃtADE aBGJe!\JL!SBO0L1`½ÉL0ħL0h\ ETADe<EhWYCMGL!\V`gETSB\ÊAML X.WK`B·!AML¾L0hÅCMA\L a§L0?¶he0[E@AML!X.L!Shw¸K?¶LAµE4XZEThGJCDO!Lq`½ÉCDSiÀÁWYGXZEThCMWYS/SBLªaB?BCM\\L agE@\ ÆhGJL^O!E@ADO0?BADe0L4L0hª¸y?½¿?¶SBLHETaBaBGW<¹iCDXZEThCDWYS¬fBE@\e0Ln\J?BGqADL!\q\JO!WYGJL!\ª\WYC¨hqSBe!O0L!\\E@CDGJL@»qË^WY?B\qaBGW@a§WY\JWYSB\ A½¿?ihCDAMCD\EThCMWYS`BLO!L0\^hL!\h\H`¶?t\JO!WYGJL2`gETSB\nAML'O!WYShL¥¹KhL`¶LADE.X.WK`Be!AMCD\EhCDW@S`¶IKSgE@X.CD¸y?BL`B?8ÌÍÏÎ ÃagE@GhCDGq`BL^\JIK\h·!X.L!\`½¿e0¸y?gEThCMWYSB\ª`BCMħe!GJL!ShCML!AMADL!\0»ÅË^WY?B\S¶WY?B\ªCDShe0GL!\J\WYS¶\dE@?i¹.\hlEThCD\JhCD¸y?BL0\ `B? hL!\hH`B?t\O0WYGLa§W@?BGdhL!\hL0GnA½¿LĤLhn`¶LºTE@GJCµE@fBAML!\dL¥¹¶a¶ADCDO!EThC¨ºYL0\^LhHADE¬º@ETGCµETSBO!L/`½ÉL0ħL0h\E@AMe<EThWYCDGJL!\0» ÐwWY?BGOlbgETO!?BS7`BL|O!L0\¬hL0\Jh\SBW@?B\e0h?B`BCDW@SB\¬ADL0?BG¬L0GGL0?BG`BL1hIKaLÑ8E@CDSB\JC¸y?BL8ADL0?BGa¶?BCD\J\E@SBO0L@» Ë^WY?B\4E@a¶aBADCM¸K?¶WYSB\ÇO0L!\dhL0\Jh\4ET?i¹|agETGE@X.·0hGL!\d`¤½¿?BS8X.Wi`¶·!ADLn`BL/A½ÉCDShL!GETO0hCMWYS1L0SyhGL/AMLHÌÍÏδLh4ADL \IK\Jh·0XZLCMXZX¬?¶SBCMhE@CDGJLL0\JhCDX.e!\/\?¶G/?BSÒJL!? `BL`BWYS¶SBe!L0\`¶LagEThCML!Sh\/CMS¶ÀÁL!Ohe0\/agE@GAMLÌÍÏÎ)CM\\? `¶LADEUWYADADE@fWYGEThCDWYS1UÓ/ÔBUÓHFÕd» ÖØ×gÙÚ°ÛÜÁ¯i°Z³/cÊL0\Jh4`B?8\O0WYGLTQBbBWYX.WY[Ye0SBe!C¨heTQ¶L0ħL0h\4E@ADe!EThW@CDGL0\!QK`BCD\hGJCDfB?¶hCDWYSE@\JIKX.a¶hWThCD¸y?BLTQ X.WK`B·!AML`¶IKSgE@X.CD¸y?BL Ý1Þ °0ÙßÚàgÛ@Ù³cwWáX.Wi`¶L!AªfBCDWYAMWY[YCMO\JIK\JhL!X.\!QqXZW@GL1ETSB`X.WYGLZO!WYX.aBADL¥¹âXZWK`BL!AM\ETGL`¶L0ºYL0A¨È W@a§L0`»¾ÐETGE@X.L0hL!G\L!\JhCDXZEThCMWYS¬W@ÀR\J?BOlb.XZWK`BL!AM\O!E@Sf§LǺ@L!GJIhCDX.LÈãO!WYS¶\?BX.CDSB[¶»äÓåADW@hW@ÀXZWK`BL!AM\ CMSBO!AM?B`BCMSB[GE@SB`BWYX-LĤL0O0h\4ETSB`|L¹iaBADE@SgEThWYGJIºTE@GCDE@fBAML!\ªXE<I.f§LHL¹iaBADW@GL!`¤»¾ÍS1hbBCM\O!W@SyhL¹Kh<QihbBL \JO!WYGJL^hL!\h\ªO<E@S.f§L4?B\JL0ÀÁ?BARCMS.W@G`BL0GqhW2CMSBO!AM?B`BLdSBLNæºTE@GCDE@fBAML!\¾CDShbBL4XZWK`BL!A»Î^WNLºYL!G0QihbBLnSy?BAMA bIKaW@hbBL0\CM\ O!E@SZfLdO!W@XZaBAML¹¬`B?BL4hW'GE@S¶`BWYX)LĤL0O0h\ E@SB`C¨hqXE<I¬bBE@aBaL!ShbgEThqhbBL4CDS¶ÀÁWYGJXEhCDW@S XZEThGC¨¹|O<E@SBS¶W@hfLO0WYXZa¶?¶hL0`E@SB`ETSáE@aBa¶GW<¹iCDXZEThCMWYStfBE@\L0`áWYShbBL\JO!WYGJL!\CM\nSBL0O!L0\\ETGJIY»nçL a¶GWYaWY\LnhW?B\JL/\O!W@GLhL0\Jh\dCDShbBLO!W@SyhL¹Kh4W@ÀÊÎnÍãÌ´`¶IKSgE@X.CDO!\XZWK`BL!AM\!»çâLL¥¹BETXZCMSBLnhbBL/\O0WYGL hL!\h2\hlEThCD\hCDO0\HÀÁWYGhL!\JhCDSB[|hbBLL0ħL!Oh2WTÀL¥¹¶a¶AµE@SgEhWYGIºTE@GCDE@fBAML!\/E@S¶` hbBL¬ºTE@GCDE@SBO0LW@ÀGE@SB`BW@X LĤL0O0h\4E@SB`N L\Jh?B`¶I.hbBLnhIiaLÍqL!GJGWYGE@SB`hbBLH\hlEThCD\hCDO!E@Aa§WN L!GÇW@À¤hbBCM\\O0WYGLnhL!\hd\JhEThCM\JhCDO!\0» çâLZE@aBaBA¨Ihb¶LZ\JO!WYGJL.hL!\Jh\hW hbBL.L!\JhCDXZEThL0\/WYf¶hE@CDSBL0`#ÀÁGJWYX+E8GL!E@A¾`gEThE@\Lh2WTÀdÎnÍãÌèCMS¶ÀÁL!OhL!` aBEThCML!Sh\dÀÁGW@Xéhb¶LUÓÔBUÓFHÕêUW@ADAµETf§WYGEThCMWYS» Ñ.
(12) ×ßw°³ ÔiO!WYGJL¬hL0\Jh<Qäb¶WYXZW@[YL!SBL0CMhI@QGE@S¶`BWYX. SBE@XZCMO<E@A§XZWK`BL0A. L0ħL!O0h\!QwE@\IiX.a¶hW@hCMO¬`BCD\hGJCDfB?¶hCDWYS¤Q§`¶IÈ.
(13) "! #$&%' ()! %' +* . ,.-/,. 0)13254&687:9;1=<84.<>9;?;<8@:A.?CBD1E25?GFIHJ1. QyWYSZO!WYSB\JCD`B·0GL^?BSX.WK`B·!AML^¸y?BC`BWYS¶SBLnADE`¶CD\JhGCMfB?¶hCMWYS`B?.ºYL!OhL0?BG ÐwWY?BGª?BS1\J?ÒJL0h `¤½¿WYf¶\L!GºTEThCMWYSB\ iYK i == 1,(Y...,, jnL = 1, . . . , n ) L0S#hL!GJXZL`BLagETGE@X.·0hGL!\/CMSB`BC¨ºiCM`B?BL0AD\ ξ = (ξ , l = Q@L!?K¹KÈãXZÆ0XZL0\ÅX.Wi`Be0ADCM\e!\ÊagE@G \WY?¶\¾AµE^ÀÁW@GX.LADCMSBe<ETCDGLNM Q 1, . . . , p) WPO φ L0\Jh/A½¿CMShL!GJO!L0a¶h<Q ω L!\hA½Ée!O!E@GJhÈãhξ˜IKa=L`BψL2(ξA½ÉL0)ħL0hHE@ADe!EThWYCMGLTQ z L0\Jh?¶SºYξ˜L0O0=hL0?BφG+ω `BLºTuE@G+zCDE@fBβADL0\ L¥¹iaBADCMO<EThCMºYL0\ZaWY?BG.ADL lÈCM·!X.L|agE@GETXZ·hGLT» ¼äL!\ β \JWYSh1AML!\.L0ħL0h\#Q¶¹iL!\1LhW@S \?¶aBa§W@\L u ∼ QgRW O u = (u , l = 1, . . . , p) L0\Jh^ADLº@L!OhL!?¶GnCMSB`BCMºKCM`B?BL!A¤`BL!\4L0ħL0h\^E@ADe!EThWYCMGL0\!».SS8SBW@hL N (0, I ) ADL0\dagE@GE@XZ·hGJL!\4`B?8XZWK`B·0ADL@Q¶AD?BC ÈX.Æ!X.LnSBWThe (P θ )θ » θ = (φ , ω , β , l = 1, . . . , p) ÐwWY?BGd?BS8\?ÚÒJL0h i Q¶AµE2ºKGETCD\L0X¬fBADE@SBO!LH`BL!\dWYf¶\L!GºTEThCMWYSB\ÇO0WYSB`BC¨hCDW@SBSBL!AMADL0XZL0SyhE@?i¹1L0ħL0h\4E@ADe!EÈ hWYCDGJL!\¬L0\JhSBWThe!L Lθ (Y |u) Qq¸y?gE@S¶` u aBGJL!SB`ADEtºTE@ADL0?BG u »¼VEáADW@[@ºKGE@CM\L!XfBAµE@S¶O!LaWY?BGADL \J?ÒJL0h i L!\hnE@ADWYGJT\ M Z i. ij. i. i. i l. l. i l. l. i l. i l. l. i l l. i l. l. i. l. i. p l. l. i l. l. ∈Θ. Yi |ui. i. i. Lθ i = log. U. Lθ Yi |ui (Yi |u)φ(u)du. WPO φ L0\Jh^AµE¬`BL0SB\C¨he'`½É?BSBLADWYC§SBWYGJXE@AMLX¬?BA¨hC¨º@ETGCDe0L ,.-WV. i l l. p. N (0, Ip ). »qË^WY?B\4SBW@hWYSB\. L=. n P Lθ i. ». i=1. XY1:Z[H\68]"Z_^`4aBD1cb4.]dBfeA.Bg?;A.h89;1i1`F&bj9;?;^`AkHJ?Ce.1. Ë^WY?B\ºYW@?BADWYS¶\ hL!\hL!G A½¿LĤLh a§WY\J\CMfBADL(`½É?BSBL(ºTE@GJCµE@fBAMLL¹iaBAMCDO!EThC¨ºYL z \?¶G#AML(agE@GE@XZ·hGJL ξ »q¼¾½¿bIKa§WThbB·0\LSK?¶ADADL H L!\J&h l β = 0lH¸y?BCä`B'e QgSBCMh4?¶St\JWY?B\ÈãXZWK`B·0ADL (P θ )θ QgWRO K l =L!\1,h2..., pL AML\WY?¶\ÈL0SB\L0X¬fBAMLZ`BL Θ hL0A¾¸K?¶L β = 0 »¼äL.\JO!WYGJL`BL β Q U (θ) QVL!\Jh | »UW@XZX.L Θ P Q¾L!S7E@aBaBAMCD¸y?gE@ShADLhbBe!WYGJ·!X.L|ADCMXZC¨hLO!L0SyhGE@AQ¾WYS(WYf¶hCDL0Syh¬¸K?¶L \?¶CMh √ U U = ET\JIKXZaihW@hCD¸y?BL!X.L!Sh?BSBLAMWYC¾SBWYGJXETADL@m» SSS¶W@hL θˆ A½ÉL!\hCMXEThL!?BG'`B?XE¹iCMX¬?BX+`BL.ºiGE@CD\JL!XÈ f¶AµE@SBO0LZ`¶L θ aWY?BG (P θ )θ »tÔiC H L!\Jh2ºKGE@CML@QO0L0hL!\JhCDXZEThL0?BG'L!\h¬O!W@SB\CM\JhlETSyha§W@?BG θ L0h L0S E@aBaBAMCD¸y?gE@ShÇAMdL lO0WYShCMSK?¶WY?B\ÇXZE@aBaBCMSB[2hbBL!W@GL!nX llQiWYS8E¬AµE2XZÆ0XZL`¶CD\JhGCMfB?¶hCMWYS1ET\JIKXZaihW@hCD¸y?BL aWY?BGdADE\JhlEhCD\hCM¸K?¶L/`B? hL!\hn`¶?t\JO!WYGJL#M ˆ ) U (θ S=q K ÑY»¨Ñ L i l. 0. l. 0. · βl. l. n. i=1. i l. l. i βl. · βl. ∂L ∂βl θ Uβl (θ∗ ). ∈Θ0. var Uβ· (θ∗ ) l. 0. ∗. ∈Θ0. 0. ∗. · βl. WPO. ˆ0) var d Uβ· l (θ. 0. ˆ0) var d Uβ· l (θ. L!\h^?BStL0\JhCDXZEThL0?BGdO!WYS¶\CD\hlE@Sh^`BL o. ˆ0) var Uβ· l (θ. ».
(14) ä¼ L!\ª\O0WYGL0\ U (θˆ ) \W@Syh O<ETADO!?¶ADe!\¾ÀE@O0CDAML!X.L!ShqÃ'agE@GJhCDG¾`BL0\ \JO!WYGJL!\ WYf¶hL0Sy?B\ `¶?BGE@Sh AµE/aBGJWiO0eÈ `¶?BGL.`½ÉWYa¶hCMXZCM\EThCDWYS¤» SSE U (θˆ ) = z U (θˆ ) a¶?BCD\J¸K?¶LA½¿E@AM[YWYGC¨hbBX.L2E O!E@ADO0?BADeADL[@GE@`BC È L0Sh¬`BL.AµE8ADWY[TºiGE@CD\JL!X¬f¶AµE@SBO0L.à OlbgET¸K?¶L1CMhe!GEhCDW@SQVADL!\ U (θˆ )(i = 1, . . . , n) \WYShADL!\'ºTE@ADL0?BG\ W@f¶hL0SK?¶L!\nÃ.ADE¬`BL!GJSBCD·0GL'CMhe!GEhCDW@S» ¼VEºTE@GJCµE@S¶O!L4`B?\JO!WYGJL U (θˆ ) \W@?B\ H a§L0?¶hÆhGJLHE@\IKXZa¶hW@hCM¸y?BL!X.L!Sh `Be0hL!GX.CDS¶e!L^Ã2agETGJhCMG `¶L#ADEXEhGCMO!Lá`¤½¿CMS¶ÀÁWYGXZEThCDWYS K UW<¹ L0htÎnCMS yADLIYQÑ L » FE@SB\8AML!\8XZWK`B·0ADL!\O!WYX.aBADL¥¹iL!\!QHAµE Î^L!\J\CDL0SBSBL^SBL4a§L0?¶hªagE@\¾hW@?ÒJWY?BGJ\ªÆhGJL^O!E@ADO0?BADe0LdL0hª?BS.L!\hCDXZEThL!?BG¾`BL4ADE/ºTE@GJCµE@S¶O!Ld`B?.\O0WYGL4aL!?¶h ÆhGJL?ihCDAMCD\Je K ?BL!`ÚÒdLhHETA»¨Q o
(15)
(16) L M i βl. 0. i βl. 0. i l. i φl. 0. i φl. · βl. 0. 0. ˆ0) = var d Uβ· l (θ. ,.-. 0. XY1:Z[H\68]"Z_^`4aBD136d4 254.@:<d@:?CHJ@. n X. 2. ˆ0) Uβi l (θ. i=1. ^Ë WY?B\dºYW@?BADWYS¶\ÇhL!\hL0G^ADE¬aBGe0\L0SBO!L`½É?BStLĤLh^E@ADe!EThW@CDGLn\?BG4AMLagE@GE@XZ·hGJL l »q¼¾½ÉbIiaW@hbB·!\JL2Sy?BAMADL L!\Jh l ω = 0l»1Õ¾SS¶WY?B\fgE@\ETSyh2\?¶G2ADE8ÀÁWYGJXZL[@e!SBe0GE@AMLZ`B?#hL0\Jh2`B?\JO!WYGJLZ`½ÉbBWYX.WY[Ye0SBe!C¨he H `¶e0ºYL0ADWYa¶a§e/agETG4UWYX.XZL0SB[YL!\L0h^>YE@O0¸yXZCMSiÈ E@`B`gE K Ñ L QKAµE\hlEThCD\hCD¸y?BLH`B?1hL0\Jh4`B?8\O0WYGL/\JWY?B\ L!\Jh T = U W U−tr(Iˆ W ) QTPW O U L!\hAML¾ºYL!OhL0?BGÅ`BL0\ U = H | E<º@L!O ε = ω u Q Iˆ L!\hADEXZEThGJCDO0Ld`½¿e0ADe0XZL0Syh\ − 0 L h ! L \ h D A ' E Z X T E h G D C 0 O 4 L B ` n L 0 O Y W G J G e!ADEÈ (θˆ ) W hCDWYS8`BL u X.WYCDSB\AµEXEhGCMO!LCM`BL!ShCMheT» ¼äL!\/\JO!WYGJL!\ U \JWYSh'O<E@AMO!?BAMe!\/E<º@L!O M »FETSB\/ADL¬O!E@\/RW O | | = ET?BO!?BS7L0ħL0h.ETADe<EhWYCMGLS¤½¿L0\Jh.aBGe0\L0SyhZ\W@?B\ H QªADEáXEhGCMO!L Iˆ L0\Jh.`BCµET[YWYSgE@AMLLh Tr(Iˆ W ) = »7FE@SB\ADL0\O<E@\O!W@XZaBAML¹iL!\ K aBGe0\L!S¶O!L `½¿LĤLh\ZE@ADe!EThW@CDGL0\¬\W@?B\ H L Q SBW@?B\`BL0º@WYSB\O!E@ADO0?BADL0G 0 ADE`Be!GJCMºYe0Lt\JL!O0WYSB`BL `BL8AµEADW@[@ºKGE@CM\L!XfBAµE@S¶O!L O<E@AMO!?BAd¸y?BCdaL!?ih\0½ E<ºYe0GL0GZO0WYXZa¶ADCD¸y?Be|Lh.¸K?¤½¿WYS \JWY?BbgETCMhL0GE@C¨h4e0ºKCMhL!G0»4UL!aL!SB`BE@Sh<QADL/hL0GX.LCMS¶ÀÁWYGJXEThCMÀV`gETSB\HA½¿L¥¹¶a¶GL!\J\CMWYSt`¶LAµE\hlEThCD\JhCD¸y?BL'`BL hL!\hqL!\Jh U W U XETCD\\JWYSL!\Ja§e0GE@S¶O!L4S½ÉL!\JhqaBE@\ÅSy?BADAMLÇ`gE@S¶\ÅADLÇO!E@\¾O!W@XZaBAML¹iL@»ËnWY?¶\ÅaBGW@a§WY\JWYSB\ `¶L[YE@G`BL0G4O!L/hL0GX.L/L0h^SBWY?B\4O!E@ADO0?BADL0GWYSB\dO0L0hJhL'L!\Ja§e0GE@SBO0L2aBE@G4\CDX?BAµEThCDWYS¶\ M X PW O T = X U U T =U W U= T 0. l. 0. WPC. T. i l l. ij. ∗. ∂ 2 log L ∂εij ∂εi0 j 0. ε. i l. ∂L(εij ,j=1,...,ni ;i=1,...,n) (θˆ0 ) ∂εij. ij l. ∗. . ∗. 0. ∂L(εij ,j=1,...,ni ;i=1,...,n) (θˆ0 ) ∂εij. ij l. 0. ∂L ∂φl (θˆ0 ). ε. ε. ∗. 0. T. ∗. n. T. ∗. i. ij 0 l. j,j 0 ≤ni j 0 6=j. i=1. ¼VE\JhEThCM\JhCD¸y?BL/`BL/hL0\JhnL!\hHETADWYGJ\jM. ij l. i. b H0 [T ] T −E SH = p var d H0 T. PW O Eb [T ] Lh var \JWYShÇ`BL0\dL!\JhCDXZEThL0?BG\ª`BLA½¿L0\ae!GE@SBO!LHL0hÇ`¶LAµE'º@ETGCµETSBO!Ln`BL T \W@?B\ H » d T ULhhL1\JhEThCM\JhCM¸y?BL\J?BCMh¬E@\JIKX.a¶hW@hCD¸y?BL0XZL0Syh?BSBL1AMWYCqSBWYGJXE@AMLO!L!ShGe!L|GJe!`B?¶CMhLT»ÐÊW@?BGWYfihL!S¶CDG O0L!\.L!\hCDXZEThL!?BGJ\!QªSBWY?B\Ge!E@ADCM\WYS¶\?BS fWKW@h\hGETa7aBE@GE@X.e0hGCM¸K?¶LM S¶WY?B\\CMX¬?BADW@SB\ K ÒJL0?i¹`BL `¶WYSBSBe0L!\¬`BL n CMSB`BCMºKCM`B?B\\WY?B\ P θ aWY?BGOlbBE@¸y?BL1GL0aBADCM¸y?BLZS¶WY?B\O!E@ADO0?BADW@SB\2AML!\\JhEThCM\JhCM¸y?BL!\ L0h^SBW@\^L0\JhCDXZEThL0?BG\d\JWYShnADEXZWIYL0SBSBL'L0h^ADEºTE@GJCµE@S¶O!L/L!X.aBCMGCD¸y?BLH`BL'O!L!\4ºTE@ADL0?BG\0» T H0. H0. ˆ. 0. (k). . 0.
(17) ! % ' I "%
(18) T'. VI-/,. 4&6d7:9;1c6I<8A 25?I]81. ^Ë WY?B\2O!WYSB\JCD`Be0GWYS¶\¬?BSX.Wi`¶·!ADLO0AµE@\J\CD¸y?BLZ`½Ée!¸y?gEThCDWYSB\2`BCMħL!GJL!ShCML!AMADL!\WYGJ`BCDSgETCDGL0\ K ÐÊL0GL0AD\W@SL0h ETA»4Ñ L a§WY?¶GdAµE`¶IKSgE@X.CD¸y?BL'`BL0\nO0WYSBO!L0ShGEhCDW@SB\4`BL!\4ºKCDGCMWYSB\dLhH`BL0\nA¨IKXZaBb¶WiOIKhL!\4cØUÇF aWY?BGd?¶St\J?ÒJL0h i `gE@SB\4AML/O!WYShL¥¹KhL`¶LA½¿CMS¶ÀÁL!OhCMWYS1agE@GdAMLÌÍÏλgÍAäCDSBO0AD?¶hdhGWYCM\ÇO!WYX.agE@GhCMXZL0Syh\TM ADL0\ÇO!L0ADAD?¶ADL!\O!CDf¶ADL!8\ MÅAMIKX.aBbBWKO0IyhL0\dc´UÇF L Q I K AML!\ÇO0L!AMAD?BAML!\ÇCMS¶ÀÁL!Ohe!L0\ L Lh V K ADL!\ǺKCMGCDW@SB\ T K O0CDGJO!?BADE@Sh\ L »q¼äLX.WK`B·!AMLa§L0?¶h^\!½Ée!O0GCDGJL'\WY?B\4ADEÀÁW@GX.L\?BC¨ºTE@ShL M i. i. . dT i dt dI i dt dV i dt. i. = λi − γV i T i − µiT T i = γV i T i − µiI I i = π i I i − µV V i. ¼äL0\dO!L!AMAD?BAML!\ O!CDf¶ADL!\L!ShGJL!Sh^`gE@SB\ÇAML\ETSB[O!CMGO!?¶AµE@Sh4ì?BS1hE@?i¹ Q¶L!AMADL0\Ça§L0?¶ºYL0ShnÆhGJL/CDS¶ÀÁL0O0he0L!\ aBE@G?BSáºKCDGJCDWYSÃ?BSáhE@?i¹ γ Lh/X.L!?BGJL!Sh'E@?hE@?i¹ µ »'¼äL!\'UÇF λ8CMS¶ÀÁL!Ohe!\HXZL0?BGL0Syh/Ã?BSáhlET?i¹ L0h.aBGJWi`¶?BCD\JL!Sh`¶LtSBW@?¶ºYL!E@?i¹ºKCDGJCDWYSB\.E@?hlET?i¹ π »æ¼äL!\ºKCDGCMWYSB\X.L!?BGJL!ShE@?7hE@?i¹ µ L0h µ aL!?iºYL!ShHE@ADW@G\ÇCMS¶ÀÁL!OhL!Gd`¤½ E@?ihGL0\4O!L!AMAD?BAML!\dO0CDfBAML!\!»ÅËnWY?B\4\J?BaBaWY\WYS¶\n¸y?BL L0h \JWYSh^O!WYSB\hlE@Sh Lh'O!WYX.X¬?BS Ã1hWY?B\/ADL0\\?ÚÒJL0h\0»¼äL!\/agE@GE@X.·0hGJL!\/CMSB`BCMºKCM`B?BL!AM\H\JWYSh ξ =γ(λ ,µµ , π , µ ) γ L0h \WYSh2\?Ba¶a§WY\Je!\¬O0WYSBSy?B\0»8¼VL0\ \WYSh2ADL!\'WYf¶\L!GºTEThCMWYSB\fBG?BC¨he0L!\`BL Lh »|Ë^WY?B\ µ a¶GL!S¶WYSB\ ξ˜ = log(ξ ) aWY?BGdhWY?¶h lYaWY?BG4E@\J\?BGJL!G^AµE¬aWY\C¨hC¨ºiC¨he`¶L!\4agE@GE@XZT·hGJ+L!\!I» V i. i T i. i I. V. i. V. i. i. i. i l. V i I. i. i. i T i. i l. VI-WV. I?/2E]d9;AaHJ?;4.<8Z. VI-. b8bj9;?;^`AkHJ?;4.<. Ë^WY?B\/E<º@WYSB\/O<ETADO!?¶ADeAML!\L0GGJL!?BGJ\`BL¬hIKa§LÑE@CDSB\JCʸy?BLAML!\naB?BCD\J\E@S¶O!L!\/`¶L!\/`BL0?i¹áhL!\Jh\/L!SáÀÁWYS¶OÈ hCDWYSt`BL¬A½¿LĤLh`BL¬ADE.ºTE@GJCµE@fBAML2L¥¹iaBADCMO<EThCMºYL K fBCMSgE@CMGLWY?áO!W@SyhCDSy?BL L L0hH`BL¬AµEºTE@GCDE@SBO!L2`BL!\/LĤLh\ ETADe<EhWYCMGL!\0»^¼VL0\L!GJGL0?BG\`¶LhIKa§L1Ñ2e0hE@CDL0SyhH`BL¬A½¿WYGJ`BGL`BL2AµE.hE@CDAMADL'SBWYX.CDSBE@ADL/`BL0\HhL0\Jh\ K
(19) »
(20) L » ¼äL0?BG\ÊaB?BCD\J\E@S¶O!L!\ÅE@?B[YX.L!ShlETCDL!ShÊE<ºYL0OÇA½ÉL0ħL0hÊ`BLªAµEdº@ETGCµETfBADLqL¹iaBAMCDO!EThC¨ºYLqL0hAµEdº@ETGCµETSBO!Lq`BL A½ÉL0ħL0h ETADe<EhWYCMGLLhdhL!S¶`gE@CDL0Sh^º@L!GJ\2ÑY» Ë^WY?B\8E<ºYW@SB\ E@aBaBAMCD¸y?BeáO0L!\|hL0\Jh\ E@?K¹åagE@GE@X.·0hGJL!\|L0\JhCMXZe0\|`B? XZWK`B·0ADLa¶Ge!\JL!She#L!S \JL!O0hCDWYS o »MÑ1\J?BG¬?BStÒJL0?(`BL1`BW@SBSBe!L0\`BL iÑagEThCDL0Syh\¬CDSiÀÁL!O0he!\¬aBE@GAMLZÌÍÏÎéCD\\J?(`BL1ADEáUWYAMAµE@fWYGEhCDW@S UÓÔBUÓFHÕ4»ª¼äL|X.Wi`B·0ADLZCDSBO0AD?gE@C¨h`¶L!\L0ħL0h\ZETADe<EhWYCMGL!\2\?BGAML!\agETGE@X.·0hGL!\ λ Lh µ »Ë^WY?B\ E<º@WYSB\¾hL0\Jhe^A½ÉL0ħL0hÅ`BL!\qºTE@GCDE@fBADL0\ª}Ji}4Lh K}4\?BG¾AML!\¾`BC¨Ä¤e0GL0Syh\qagE@GETXZ·hGL0\!»¾¼VEHºTE@GJCµE@fBAML K}^E ehedaBGJCD\JLÇL!S¬ºTE@GJCµE@fBAML O0WYShCMSK?¶LdL0h¾L0S¬º@ETGCµETfBADL fBCDSgETCDGLT»VÓH?BO0?BSL0ħL0hq`BLÇADEnºTE@GCDE@fBAML4}Ji}ÇS½ Eehe X.CD\4L0Se0ºKCD`BL0SBO!LTQ¤`BL2XZÆ0XZLaWY?BG^AµE.ºTE@GJCµE@f¶ADL K}2aBGCM\LL0SáO!W@SyhCDSy?BLT»HË^WY?B\E<º@WYSB\HhGWY?¶º@e?BS LĤLhH`¶LA½ K}/aBGCM\^L0S ºTE@GJCµE@f¶ADLfBCMSgE@CMGL/O!WK`Be0LZÑ'aWY?BG4ADL0\^aBEThCML!Sh!\ @[Ye0\ E@SB\ L0h
(21) aWY?BG AML!\¾aBAM?B\§ÒJL!?¶SBL!\ K
(22) E@SB\¾L!\hªADL ÈCD·0XZL a§L0GO0L!ShCMADL L \J?BG¾ADLagE@GETXZ·hGL µ K KS≥=50−1.99L Q#a "
(23) »
(24) L » i. . I. i I.
(25) U L0AµE\CM[YSBC QgL/¸y?BL'ADL!\daBEThCML!Sh\!@[Ye0\4WYSh4?BSBL/hlE@?K¹8`BL'`Be!O0·!\^`BL!\4O0L!ADAM?BADL0\dCDS¶ÀÁL0O0he!L!\4aBAM?B\ÇÀE@CMfBADLTQ O0L'¸K?¶CwaWY?BGJGE@C¨hdGL ge0hL!G4?BSBL'X.WYCDS¶\df§WYS¶SBL/Ge0a§WYS¶\LCDX.X¬?BSBC¨hlE@CMGL^OlbBL!PO!L0\^aBEThCML!Sh\0» Ë^WY?B\dE<ºYW@SB\Çe![YE@ADL0XZL0SyhE@aBa¶ADCD¸y?Be^ADL4hL0\Jhd`¤½¿bBW@XZWY[@e!SBe0CMhenÃ2O0L!\ÇL0\JhCDXZEThCMWYSB\!»ËnWY?¶\S½¿E<ºYWYSB\ X.CD\L!S.e0ºKCD`BL0SBO!LnE@?BO0?BS.SBWY?¶º@L!AgL0ħL0h E@AMe<EThWYCDGJjL M S = 1.42 K a "
(26) »MÑ L L0h S = 1.55 K #a "
(27) »MÑ o L Q GJL!\Ja§L0O0hC¨ºYL0XZL0SyhnaWY?BG π L0h µ » . H. H. T. . . +% ' . ^Ë WY?B\dE<º@WYSB\d`BeºYL!AMWYaBae/`BL!\ÇhL!\h\Ç`B?|\JO!WYGJL/`gE@SB\?BS|O!WYShL¹KhL'SBWYSKÈ\JhE@SB`gETG`»q¼äL!\\CDX?BAµEThCDWYS¶\ X.WYShGJL!Sh ¸K?¶LHO!L0\ hL!\Jh\ ÀÁWYS¶O0hCMWYSBSBL0ShfBCML!S»¾UL!\ hL!\h\aL!?iºYL!ShdÆhGJLn?¶hCDAMCD\e0\¾a§W@?BG GJe<E@AMCD\JL!Gq?BSBL L¥¹iaBADWYGEThCMWYS(GETaBCD`BL|`¤½¿?BS¶L8ÀETXZCMADADL.`BL8X.Wi`B·0ADL0\O!WYX.aBADL¥¹iL!\L!S7agE@GhCDO0?BADCML!G2a§WY?¶GADL!\X.WK`B·!AML!\ `iIiSBE@XZCM¸y?BL!\0» ?Chj9;?;4aBgA.b 8 ?;1. . Ñ ¾UW¹§QVÓ»§L0hÎ^CDSyADLIYQäF2» K Ñ L TH g}l QäcdbBL0WYGLhCDO!E@AÅ\hlEThCD\JhCDO0\!QVUbgETaBXETS ] ÎnE@ADAQB¼äWYSB`¶WYSQBagET[YL!\ o ÚÈ » o ?BL0`Ò0QR>¶»¨QBcdbBCMe!fgE@?ih<QB_'»¶LhnUWYX.XZL0SB[YL!\0QBF» K o
(28)
(29) L r<Yi-¦Ê } Dg!oq.@~~ T~@ @Rrâ!K} dj¶äQ CMWYXZLhGJCDO!\0Q QÑYÑ ÚÈlÑ o
(30) ¶» }~¤}J@ }.m l} }l4 2K}~¤} ÊUWYX.X.L!SB[YL0\!QgF2»gL0hH>YE@O!¸yX.CDSiÈ ET`B`gE¶Q¶Î2» Ñ . K L ^}7~ { }¨@}#pÇ@~K o }l |r#!K} Q4>@WY?BGJSgE@A^W@Àhb¶Lá_4WÚIYE@AnÔKhlEhCD\hCMO<E@A^ÔiWKO!CML0hI M ÔKL!GCML K L0hbBWK`BWYADW@[YCDO!E@A L Q iQÑ ÚÈÑ iÑY» ¶ÐÊL0GL!AM\WYS¤QÓ»@Ô§»MQYËnL!?¶XE@S¶SQYÓ»@Â2»¨Q E@G @WN4CMhP@Q »MQ¼äL0WYSgE@GJ`Qy>¶» »TLhqÎnWBQYF» Ñ ä@ ~@ l'~tKK.@~K~¤!K} Ç }~¤ ¬¥y ¥g}¡~ <}l ~gQRÔiO0CDL0SBO!LTQ o iÑYQÑ K o ÈÑ L ¶» . . . . . .
(31) . . . . . !. $ $. . . . . . #". &%. ". . . . ". '. ". . .
(32)
Documents relatifs
To test whether the vesicular pool of Atat1 promotes the acetyl- ation of -tubulin in MTs, we isolated subcellular fractions from newborn mouse cortices and then assessed
Néanmoins, la dualité des acides (Lewis et Bronsted) est un système dispendieux, dont le recyclage est une opération complexe et par conséquent difficilement applicable à
Cette mutation familiale du gène MME est une substitution d’une base guanine par une base adenine sur le chromosome 3q25.2, ce qui induit un remplacement d’un acide aminé cystéine
En ouvrant cette page avec Netscape composer, vous verrez que le cadre prévu pour accueillir le panoramique a une taille déterminée, choisie par les concepteurs des hyperpaysages
Chaque séance durera deux heures, mais dans la seconde, seule la première heure sera consacrée à l'expérimentation décrite ici ; durant la seconde, les élèves travailleront sur
A time-varying respiratory elastance model is developed with a negative elastic component (E demand ), to describe the driving pressure generated during a patient initiated
The aim of this study was to assess, in three experimental fields representative of the various topoclimatological zones of Luxembourg, the impact of timing of fungicide
Attention to a relation ontology [...] refocuses security discourses to better reflect and appreciate three forms of interconnection that are not sufficiently attended to