Hep B vnon of en who hve ex wh en n he eheln: houl we vne oe en younge en o hgh-k en? M ou Robn vn Hou Sun Hhné Roel ounho J vn Seenbegen Mj Kezh APPEDI A.. Moel equon The oel w evelope by Kezh e l ] o ebe he non of HBV n he eheln fo he whole populon heeoexul n MSM. The uboel fo he MSM populon ebe by he followng ye of pl ffeenl equon n e n ge ] ] ] ] ] ] ] V V V w p w Z p Z Z H H v u H H v u z e e whee he ubp =... 6 enoe exul vy goup. enoe he eny of unnfee nvul H he eny of nvul wh len nfeon he eny of nvul wh ue HBV he eny of e hon HBV Z he eny of une nvul n V he eny of vne nvul of vy goup ge e. The ze of vy goup V Z H n he ol populon ze. The foe of nfeon gven by ] whee we ue popoone xng by ge n vy l.
Bh no he populon wee ue o blne he eh e uh h he populon ze en onn. Deh o eovl fo he populon ue o ou ge 65 uh h he ge buon ove he populon unfo. Men e ue o beoe exully ve he ge of 5. The fon of nfee nvul of ge who beoe e gven by he funon x p exp x wh x = 0.645 n x = 0.455 ]. The populon ze onn ung h bh no he populon blne eh n en of exul vy. Invul ene he populon n pef exul k goup n en n h goup fo lfe. The buon ove he k goup onn n e. Vne nvul e une o nfeon fo lfe. Defnon of pee n eful vlue e ebe n he followng n uze n Tble. The oel equon wee olve nuelly ung he Elo Box Tn eho pleene n he pkge EBT ool 4]. A.. Pne hnge e n oel lbon The e of foon of new pnehp fo en of ge n exul vy goup wee nlly ee fo fo he uy Sexul Helh n he eheln e ou by Ruge WPF n 006 5]. Th w populon uy wh wo phe of euen v nene pnel. Fo he f phe he eponen wee noly elee whle fo he eon phe he eponen wee elee non-noly o heve epeenve ple wh epe o he eogph of he Duh populon ge gene euon n ehny. The eponen oplee n nene-be queonne bou eogph he n exul behvou. Fo 470 eponen 76 wee egoe MSM ong o he epoe nwe. The ol nube of pne h eponen epoe o hve h n he pevou x onh w eue by one f he lo epoe hvng ey pne fo oe hn x onh n he e peo; fo hee he nube of new pne n he pevou x onh w lule. Pnehp fo whh onen ono ue w epoe wee no ken no oun. Subequenly Webull buon w fe o he by he xu lkelhoo eho fo eh of he egh ge egoe 5 9 0 4... 45 49 n 50+ hown n Tble. The uulve buon wee hen ubve no x nevl efne by he fon w = 0.450.50.50.060.00.00 ee Tble A n A. Th ubvon efne he ze of he x exul vy goup fo exple goup 45.% of he populon n goup 5.% of he populon. Th ubvon by bu hoen o efle kewe buon of nube of pne n efne n 6]. The vege pne hnge e e hen lule fo eh vy goup n eh ge goup hown n Tble A.
Wh hee ee e he oel genee ey e nene of 6 pe 00000. Th oel ee w ope o he ee nene fo he follow. In he ye 00 o 005 when vnon w noue HBV nene w elvely ble ppoxely 05 ue HBV e ong MSM pe ye beng epoe he nonl nofon. Aung h h of he e e lnl n h hee 50% uneepong ple h he epoe nube of ue HBV e houl be ulple by fo of 6 o gve he ul nube of new HBV e. Th en h hee wee 05*6 =60 new e of HBV n MSM pe ye. The ol nube of MSM n he eheln w ee o be n he nevl 78000-9000 expole 95% onfene nevl be on he populon uvey of Ruge WPF n 006 5]. Dvng he 60 new e by h ee of he MSM populon ze eul n n nene beween 60 n 7 new nfeon pe 00000. Theefoe fo he nene of HBV he ee fo he oel w hghe hn h fo he. Moeove opng he ge buon of nen nfeon lule fo he oel n he ge buon of he nofe e of ue HBV we fn h he foe oe hfe o younge ge. In ohe wo he fon of new nfeon oung young ge n he oel hghe hn h n he n he fon oung ol ge lowe n he oel hn h n he eul no hown. To oun fo hee nonene beween he oel n he we lbe he oel by jung he pne hnge e uh h he nene n he ge buon of nen e fo he oel woul h hoe fo he. The jue pne hnge e e hown n Tble A. Wh hee e he b epouon nube lule R 0 =.6 n he nene 90 new nfeon pe 00000. The ge buon of nen nfeon fo he oel he ey e whou vnon n he ge buon of he nofe ue HBV e n he l ye befoe he nouon of vnon: nofon 99 00 e hown n Fgue A. Moeove he pevlene of HBV nfeon fo he oel lo n one wh h fo he. Aong en ge 5 60 ye ol he pevlene of une % n he pevlene of e oun % fo he oel. In he uen onl HBV Vnon pgn en who wn o be vne eeve he f vne oe n he e e ge ee fo HBV nfeon ubequenly only hoe unnfee eeve he ohe wo oe. Aong hoe peenng o be vne n 00 he f ye of he vnon pgn 6% w n- HB pove n.% w HBAg pove fo he onl HBV Vnon pgn. Howeve beleve h he en ppng n he vnon pog hve on vege hghe k level hn he genel MSM populon.
A.. Vnon e The vnon e epeen unvel vnon n gven by he followng funon u P whee enoe he D funon u he vne fon n P he ge of vnon pubey. The e of vnng hlen of gn gven by l funon ee ] fo el. The e of k-goup vnon wee lule follow. The ze of he MSM populon n he eheln w ue o be 0000 he pon of he nevl 78000-9000 obne fo he populon uvey of Ruge WPF 5]. A he of he vnon pgn 85% of he e uepble fo HBV n hene elgble fo vnon. Theefoe n evey ge egoy he nube of en elgble fo vnon gven by he pou of he ol nube of MSM n he fon foun uepble ve by he nube of ge egoe: 0000*0.85/=75. Dung he even ye of he vnon pgn 00 009 7 en eeve one oe of HBV vne 4574 eeve wo oe n 08 eeve hee oe of he vne. The nnul vnon e n ln 7* 75 pe ge egoy wee ee whee n he nube of vnon of nhb negve peon n ge egoy ung he oue of he vnon pgn ee Tble A4. Fo he eful eno w ue h h vnon e he e fo ll vy goup enng fo ll ge n ge egoy =... ee Tble A4 n ll vy goup =... 6. The effeve unzon e hen gven he pou of vnon e n vne effy v. 4
REFEREES. Kezh M e W G S L n vn e L M. Vnon gn hep B n low ene oune Epeol. Infe. 00 8: 9 44.. Kezh M Mngen M vn e L M n e W A. Moel be nly of hep B vnon ege n he eheln Vne 009 7: 54 60.. Eun W Meley G oke D Hll A n Whle H. The nfluene of ge on he evelopen of he hep B e e Po. R. So. Lon. B 99 5: 97 0. 4. De Roo A. A genle nouon o oel of phyologlly uue populon n S. Tuljpuk n H. well. e Suue-populon oel n ne eel n fehwe ye hp n Hll ew ok pp. 9 04 997. 5. Ruge o Goup. Sexul helh n he eheln 006 Ebuon Delf 006. 6. Wll J oke D Meley G n Aneon R. The non yn of hep B n he UK: hel oel fo evlung o n effevene of unzon poge Epeol. Infe. 996 6: 7 89. 7. Boo H Shoul L Hhne S Bebe G vn e L M n Kn T. Vnon gn peuoo n hep B n he Duh onl Iunzon Poge e. Tjh. Geneek. 007 5: 7 6. In Duh. 5
Tble A: Moel pee n belne vlue Sybol Defnon Vlue Soue Pobbly of non: pe pnehp wh uely nfee n 0.46 6] pe pnehp wh e 0. 6] hozonl fo houehol on ge 5 0.0 7] Re of pogeon: 5 0 7] fo len o ue HBV 8.667 6] fo ue o hon HBV.467 6] fo hon o une HBV 0.05 6] p Popoon of ue e ge beong e 0.455 exp 0.645 ] Vnon e fo en of ge vy l Tble A4 v Vne effy fo ul vnon 0.75 Tble A5 v Vne effy fo hlen e 0.9 k Fon of hlen elgble fo k goup vnon 0.5 7] u Fon of elgble gn hlen vne 0.9 7] u Popoon of eu o exully ve populon beng vne 0.85 ] Pevlene of hon e ong gn 0.047 7] z Pevlene of une peon ong gn 0. 7] Pe p gon e 0.004 Fon of le ong gn 0.5 Age buon of gn ] v Fely of ge ] 6
Tble A: Re of foon of exul pnehp ee fo fo Ruge WPF Popoon n l w Sexul vy goup 4 5 6 Avege 0.45 0.5 0.5 0.060 0.00 0.00 Age nge Pne hnge e 5-9 0.0 0.64.7.48 6.89.5 0.78 0-4 0.07 0.67.8 5.47.80 7.0.04 5-9 0..08.64 8.66 0.0 4.0.65 0-4 0.4.5 4.76.7 8.0 60.59.8 5-9 0..08.77 9..97 47.0.7 40-44 0.08 0.96.66 9.6 4.48 55.79.7 45-49.9 7.05 8.7 5.6 68.5 0.76 8.5 50+ 0.7 5.08 4.50 0.8 6.50 7.48 6.50 Tble A: Ajue e of foon of exul pnehp* Popoon n l w Sexul vy goup 4 5 6 Avege 0.45 0.5 0.5 0.060 0.00 0.00 Age nge Pne hnge e 5-9 0.0 0. 0.5 0.45 0.79.9 0. 0-4 0.0 0.5 0.87. 5.05 0.78 0.40 5-9 0.07 0.5.56.4 7. 4. 0.70 0-4 0. 0.88.7 6.05.0 6.5. 5-9 0.07 0.64.4 5.0.58 4.07 0.97 40-44 0.05 0.50.8 4.64.40 5.6 0.85 45-49 0.06 0.9 0.67.0..48 0. 50+ 0.0 0.5 0.40 0.8.6.97 0.8 * The e fo Tble A fo Ruge WPF wee jue uh h he nene n he ge buon of nen nfeon woul h hoe fo he ee eho fo el. 7
Tble A4: Age-epenen nnul vnon e ong MSM n he eheln 00-009 Goup Age ube wh f vnon ll ye* Dbuon Annul vnon e < 5 0 0.00 0.00000 5-9 750 0.08 0.00905 0-4 808 0.7 0.0980 4 5-9 654 0.6 0.0899 5 0-4 89 0.5 0.0708 6 5-9 66 0.4 0.064 7 40-44 75 0.06 0.007 8 45-49 86 0.06 0.007 9 50-54 6 0.04 0.0047 0 55-59 770 0.04 0.0047 60-64 40 0.0 0.0000 65-69 78 0.0 0.0000 70+ 94 0.05 0.00609 Tol 860.00 75 * D fo he onl HBV Vnon pgn 00-009. The nube of vnon w jue fo he nube of MSM eevng he f vne oe o oun fo he ol nube of expee vnon ung he even ye of he pgn. Fuheoe w ue h 5% of MSM wee nhb+ n hene no elgble fo vnon. Tble A5: Vne effy: peenge beng 00% poee gn HBV nfeon ong hoe eevng one wo o hee oe of HBV vne Doe vne eeve oplne % unze fe oe % effevely unze fe oe 00% 40% 0% 75% 70% 9% 6% 90% 75% 8
Tble A6: Age-epenen nnul vnon e ong MSM n he eheln 00-009* Annul vnon e fo hypohel eno Age ube Only k Only k Only k goup Vne Double wh f goup 654 goup 654 65 & hlf of 4 5 ye vnon vnon* vne vne vne younge < 5 0 0.00000 0.00000 0.00000 0.00000 0.00000 5-9 750 0.04706 0.57 0.485 0.0868 0.088 0-4 808 0.059 0.6 0.65045 0.0876 0.04000 5-9 654 0.009 0.0785 0.6406 0.0687 0.085 0-4 89 0.0906 0.747 0.576 0.064 0.0445 5-9 66 0.0868 0.608 0.50679 0.040 0.04 40-44 75 0.068 0.05 0.8970 0.009 0.047 45-49 86 0.068 0.05 0.8970 0.0059 0.047 50-54 6 0.048 0.06850 0.77 0.009 0.00945 55-59 770 0.048 0.06850 0.77 0.0009 0.00945 60-64 40 0.059 0.0408 0.0758 0.0009 0.0060 65-69 78 0.059 0.0408 0.0758 0.00048 0.0060 70+ 94 0.049 0.08945 0.608 0.00000 0.0 * D fo he onl HBV Vnon pgn 00-009. Tble A7: Annul nube of MSM who eeve HBV vne n he eheln 00-009 fo he onl HBV Vnon pgn. ube of MSM vne gn HBV e ube wh vne oe ube wh vne oe ov-de 00 59 6 00 0 407 004 5 6 005 977 96 006 058 6 007 468 50 008 74 64 Jn-ov 009 6 0 9
peenge new nfeon 0 5 0 5 0 5 0 0-4 5-9 0-4 5-9 0-4 5-9 0-4 5-9 40-44 45-49 50-54 55-59 60-64 65-69 70+ ge ofon Moel: pe-vnon ey e Fgue A: Age buon of new hep B nfeon fo he oel n fo befoe he nouon of vnon. Geen olun: he ge buon of epoe ue hep B nfeon ong en who hve ex wh en n he eheln n he ye 99 00 fo he onl ofon D. Blue olun: he ge buon of new nfeon lule fo he oel he ey e whou vnon; fo hee eul he jue pne hnge e wee ue Tble A n he pee hown n Tble A. 0