Evaluation of three control strategies to limit mpox outbreaks in an agent based model

Mos t o f t he 2022 mpox outbr ea k s in high incom e coun t ri es , w hich pr e domina ntl y affec ted men wh o have sex w ith men, p eake d l es s tha n two months a f ter d etec t io n . To st op the ou tbrea k s , pe ople we r e encou r a ged t o li mit new s ex partn e rs , tak e up a ny o ff er s f or s mal lpox vacc ination , a nd s elf - isola te . The rela t i ve c ont r ib ut i o n s of e ac h of th ese s tr ategi e s to ou tbre ak reduc ti on are ha rd to kno w. To conside r the p o t e n t i al r elative ef fic acy of eac h o f th e se mea s u re s indivi dually , we co nstruct ed a gen t-b a sed mode l s u s ing pl ausibl e par t n e r s hip c ount s , r e a s on able b e havio ur choic e s and publi shed in forma tion ab out smallp ox va cci nation uptak e r ate s in the UK c o ntext during 2022. Compa red to a b as eli ne , no in te r venti on scen a r io , pa rtn er re duction w a s mor e ef f ec t i v e at preve nt i ng ge n era tion o f second a r y ca se s th an the vac cine ro llout at th e spee d t h a t t h e s ma llp ox va cci ne rollout oc cur red in t h e UK in 202 2. Thes e fin di ngs s ug ge st t h at p artn er re d uction by the most a f fect ed communi t y ra ther t h an ph armac eutic al inte rve nt i on was la r g ely to c redit for ca u s ing ca s e numb er s t o p eak a s ea rly a s they di d.

mpox ; UK; s exual ly tran smit te d infec t i on s ; a g ent -ba s ed-mo del s; sel f -i sola tion ; vacc ines . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 3 | Page

Mpox is a smallpox -like zoono tic infec tio n ca us e d by a virus in th e Or t h opoxvi r u s ge nus o rig inally ende mic i n some ar ea s of Af rica. The mo st co mmon mpox s y mpt oms a r e fever an d ly mphadenop a thy wi t h many persi ste nt and pote ntia lly very pa in ful le sion s . Rec o v ery t y pica lly tak es 2-4 w eek s an d con fer s long -l a s ti ng immunity t o r e in fec tion . Tran s mi ssi on to huma ns occu rs a ft er phy s ic al c ont act w ith an i n f e cti ou s individual, contami n at ed mate rial s or a n a nima l 1 . The historic ca s e fa tality ra te wa s th ought to b e abou t 10% , and w as know n to b e hi gher in c hi ldren a nd low e st in h ealthy a dul t s 2 . Although no vac cin e has b een devel oped ag ain s t mpox spec i fi ca lly, smal lpox va cci nes have high e ff i c ac y ag ains t mpox, r ed ucing di sea se ac qui s i t i on by a bou t 8 0% afte r one or two d ose s 3,4 . I t is thoug ht t h at p rote ctio n from th e smal l pox vacc ination may de c line ov er time , but only s l owly 5 . That c es sation o f ro ut i n e co mmunity vacc ination a gain st smallp ox might l ead to recurring mpox ou t b rea k s wa s sugge s ted 5 . Historic ally , mo st mpox outb reak s wer e quic kly contai ned an d s e e med to inv olve r e lativel y short tran s m i ssion c hain s (u nder 7 gen era tion s befor e out bre ak end 2 . H ow ever, a la rge number of mpox ca s e s in n ew c ountri es a nd c ontin ent s w ere ide nt i f i ed in 2 022, c au sing f ea rs t hat the di s ea se m ight bec ome en d emic in many new r e gions . The 2022 m ulti-coun try ou t b rea k ove r w helming ly a f f e cted men who ha ve sex with men ( M S M ) s 6 . Mos t ho spit ali sati on s in hig h inc ome c ou nt rie s in 2022 w ere due t o ne ed f or ana lg esic re lie f 6,7 , a nd relatively fe w dea ths w e re a s s oc ia ted w it h the 202 2 multi - co untr y outb r e ak s 8 . A mode st ob served ca s e fa ta lity ra te ( CF R , probably < 1% ) in 202 2 is thought to relat e i n par t to the speci fi c (mild e r ) c lad e 3 vi r use s t hat the 202 2 out break c a se s mos tly have 9 , a s we ll as und er -a sce rtain me nt o f ca se s whe r e mpox was t r a di tionall y end e mic w hich may h ave skew ed hi s tor ic al e stimat e s of the C FR. Howe ver, to p reve n t onward di s e a se tr a nsmi s s ion , eve n non-ho spi tali s ed c as e s were s tr ong ly a dvised i f no t a l s o lega lly requi r e d t o stric tly s e l f -i s ola t e f or a minim um of thre e we ek s, ca u s i ng ec ono mic and soci al di srup tion for t ho s e a ff ect ed. Mos t o f t he 2022 mpox ou t br ea k s in high incom e coun t ri es p ea ked l ess than tw o months a f t e r detec t i on. To br i ng t he ou tbre ak s und er control, M S Ms w er e e nco ur a ge d to li mit new s ex par tne rs, to take the smallpox vac ci nation , an d to s e l f - i s ola t e if they k new t he y had t h e vir us. The r ela tive co nt ribu tion s o f e ach o f t he se stra tegi es to outb reak r eductio n are ha rd to k now. Co nt a c t tr acing wa s e xpec te d to b e c halle nging beca u se of pr i vac y w or rie s, r ela tiv ely high in ciden c e of a nonymou s p a ir i ng s an d so c i al s t i gm a 10 , mak ing i t d ifficul t to find peo ple who ne e ded t o be warned to b e v i gilant a nd s eek t es ting i f t he y had r e levan t symptom s. I n pa rt beca use o f limite d smal lpox vacc ine suppli e s, va cc ination p rog r a mme s in mo st s e tti ngs w ere not o f fer ed univ ersal ly a nd instea d ini tia lly . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 4 | Page targe ted MS M s thoug ht to be a t grea t e s t ris k of in fec tion du e to beh avi our a l hi s to r y . Pa r t ner reduc t i o n and vacc ination p r og r a mme s h ad a ppar ent s u cce ss, in th at b y mid Aug u s t 20 22, ab ou t 50% of America n MS Ms r e po rt e d r e duc ti ons in t hei r sex ual a c tivity t o pre vent c at ching mpox 11 , and by mid-N o vember 20 22 t ake up o f the s mallp ox v acc ine a mong el igible U K-r esi d ent MSM s wa s ne a r 50% 4 . The level of ad here nce t o self -i so lation guida nc e ha s b een h arde r to a s c e rtai n. Se l f -i s ola t i on for pe r s o n s w ith con fi r me d in fec tion or susp ec t e d exposu re w a s encour ag ed ( for i nsta nce, in B ritain from 22 Ma y 2022 12 ) b ut not leg al ly req uired in many jurisdic tion s. Never thel es s , it seem s like ly tha t be h aviour c hange s (p a r tn er r educ tion and complia nce with gui dance to s e l f - i s ola te ) a s well a s vac cin a t i on pr ogramme s all cont ribut ed to ou t break red uction . To c onside r the p ote ntia l r ela tive e ffica c y o f each of the se mea sur es in i sol ation , w e c ons t ruct ed a ge n t- bas ed m o de ls 13 for mpox tran smi s s ion among MS Ms u sing plau si ble par t ne r ship c ou nt s , rea sona ble beh aviour choi ce s and v ac cin ation up take r a t e s . Th e finding s w er e u s ed to sugge st whi ch of th ree c ommon mpox co nt r ol stra tegie s may have made th e grea te s t contrib uti on to e a rly sub s i d ence o f the ou tbr eak. Sen si tivi t y a nal ys i s w a s under taken by v arying the m ost unc er tain epid emiolog ical pa rame ter s.

Overview Bas eline a nd a lt er n a tive sc e nari o s were c onstruct ed within a gen t ba sed mo d el s (ABM s) u sing Netl ogo ver s ion 6.0.2 . Agen ts in the mo de ls h ad fou r po s s ibl e sta tes tha t oc curre d in t hi s se quenc e : su s c ep tible –e xpo sed −inf ec t ed−r eco ver e d (reco ve red = immune ; S EIR) . All of o ur s i mulati on s co ns id e r t h e cas e o f 6 400 ag ent s w ho ar e a ll MSM s, wi t h no n ew member s adde d or depar ting during each s im ulatio n (a clo sed sy ste m). We us ed a popula tion o f 6400 a gent s in order t o be a bl e to ge nera te many s i mula tion r es ult s i n a rea sona bl e tim e fr ame ( l a rger age n t cou nts woul d h ave take n much longer to a chieve mod e lling re sult s ) . O u tc ome s ar e alw ays moni t or e d from simula ti on sta r t (w hen c ontrol mea su r e s sta rt to be appl ied ) until ou t bre a k end ( w he n no mo r e age n t s a re infec ti ou s or incuba t i ng) . We ide n t i f y plau sibl e par amet er e stim at es an d a s s umption s, sp ecify ing our pr ef e rred e s timat e s and as s u mp t i on s , trea ting the ado pt i o n of th ese plau sible as s ump tion s a s a ba se line a nd rea sona bly pla us i bl e s c ena rio. We t h en ex plore wha t happen s i f w e us e alt erna tive credi ble e stima te s o r as s u mp t i on s i n oth er key epid e miologic parame t e rs . F irst, we con sid er th e p o s it ed control . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 5 | Page strat eg ie s unde r the b a seli n e con dition s. We als o va r i ed epi de miologi cal and c on tr ol par amet er s , to as s e ss sen s i tivity to sel ec ted as s ump t io n s . We c ompar e outb reak cont rol w ith r esp ec t to two h a r mful o utcome s : dura tion a nd number o f n ew ca s e s . Outb reak du r a ti on is d efin ed a s d ur a tion in h o urs or day s f rom simul a t i on s t art (whe n cont rol strat eg y sta r t s to be a ppli ed ) un t il th ere are no more inf ectiou s o r inc ubating age n t s (ou tbre ak end) . Number o f new ca s e s i s de fine d a s the n umber of n e w c ase s tha t o ccur a fte r the s imul a tion st a r t until o ut b rea k en d. We repo rt ou tcome s aft er 1000 s im ul ation s for th e ba se line sc enario a nd sugge st ed pla u s i bl e impl ement atio ns of eac h co nt r ol stra tegy. A s sen si tivity anal y s is , w e run 100 itera tion s for al ter native way s o f implem e nt i ng ea ch c on tr ol s t rat egy with v arying assumpti on s abou t t ran smi s s ion r i s k per con tac t di f fer ent numbe r s of se ed ag en t s . The outco mes do no t ac count f or ho spit ali sati on s or de a t h s be c aus e we were i nte re sted in s c en ario s w hen most symptom s were mi ld, mo rtali ty r a te s very low and most ca s e s stay ed in the c om munity, simil a r t o most o f th e 2022 outb reak s. W e do n o t consid er th e po s s i bility o f a s y mptoma tic tran smis s io n bec au se it se emed unlike ly; a 2022 a udi t of 2917 s p ec imen s f rom MSM s at ten ding s ex ual h e alth cl inics in Engla nd fou nd lo w preva lenc e ( 0.14% , n=4) o f no n -symp t oma tic mpo x i nfec ti on 14 . We do not c on s id er t he po ssibi li ty of ai r born e t r ansmi s s i on b ec au s e o f previou s mod e ls w hic h s ug ges ted that thi s was li kely to b e rel atively r a re fo r mp ox 15 . Fully fixed model parameters ABM s incorpo rat e a blend o f stoch a s tic a nd de t e r mi ni s tic par amet er s. The r e ar e f ixe d (det ermini s tic) a s pec t s of ou r model s ( s a m e in a ll scen a r io s), pa rtly det ermini st i c an d partly stoc ha stic pa r a met er s , a s w ell a s e xplic itl y varied pa r a me ter s (fo r s en s i t i v ity a n alysi s). We full y fix ed a sp ect s o f our mode ll ing e nvironment for pr ag matic re a son s and /o r whe r e t h e e ff ect of varying the a ssump tion wa s predic t a bl e. F ully fixed a s pe c ts of ou r model s in a ll simulati on s are : co unt of ag en ts (6400 ) , popul atio n under s tudy ar e al l MSM s an d the sy stem i s c lo s e d : the re ar e no new member s, no a gen t dep a r tu re s and no new spo radic ca s e in tr odu c tion s. The choic e of 6 400 ag ent s i s not me ant t o be de fi nit ive or a priori know n to be o p t i mal. R ath er, w e u se a f i xed n umber of ag en t s i n the mod el s to st andardi s e th e sce n ario s rel ative to t h e sen sitiv it y an a l yse s , s uc h th at th e fac t o r s tha t s eem t o c ause cha nge s in th e p r ima r y outcom e s (dur ation o f th e out break and new ca s e co unts) should a r i se from varia tion s fu nd amental to th e con t r ol s tra tegie s tried ra ther than va r i ation s in th e popu l ation size . I t is pr e dicta ble that a l arger po pula ti on woul d h av e poten tial f o r long er dura tion ou tbr eak , s o we do not u ndert ake sen sitivi ty anal ys i s by vary ing t he tot al number o f . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 6 | Page ag ent s . 6400 a gen t s fo r the s c en ario s i s also a p rag matic choic e to ena ble ex te n s i ve sen si t i v ity ana lysi s o f oth er facto r s , and ma ny simul ation s an d mod el s to be gen era ted a nd su mmarise d u s i ng our availab le re sour c e s within a f ea sible t i mef r a me . Si milarly, t h e di ff er ence be twee n clo se d a nd open popul atio ns o n ou t b rea k devel opment i s predic ta ble, a n o pen sys tem (n ew age nts enter an d some age n ts depa r t ) is lik ely to have longer duratio n a nd more vari able d ev elop men t. An ou tbre ak or epid em ic in a c los e d s y s t em w ill a lway s co me to an end , a s long as rein fect ion i s not po ssible , as s umi ng t hat n ew s po rad i c c ase s canno t oc cur. We a l s o con fine d our modelli ng t o ac count f or jus t one k ind o f s exu al par t ner s h ip (me n w ho have sex w ith men, MS M s ) ; the 2 022 ou t break s in nov el s et ting s overwhelmi ngly s t ay ed withi n thi s sexua l minori ty c ommunity. Adding oth e r s ex ual pr e fer enc e group s (eg. , wome n who ha ve sex with men or women w ho hav e s ex w ith men who ha ve sex with men) would h ave a dd ed c omplex ity to our ow n model s wi t ho u t increa sing in s i g ht into wh ich mp ox c ontr ol s t rat egie s ha d great es t pot enti al to wo r k well in a pr e domin antly MSM ou tbre ak. Model assumptions that were mixed deterministic and stochastic Asp ect s o f the ag ent in ter action e nviron men t h ad fixe d at tr i bu t e s ( such a s medi a n value for entire popul ati on) bu t the s e val ue s varied f o r i ndividua l ag ent s be t w een sce n ario s , t hu s th e se environmen tal a nd be havioural m od el a s sumpti on s are p artly de t e rmin istic and p a r tly stoc ha s t i c. Homophily in sexual contact network A ke y aspec t of mod el c on st r uc t i on, to m ak e su r e t h e model rep r e s ent ed re a li s tic beha viour c hoice s, wa s to e stabli s h h om ophily within s oc ial netw or k s . H omo p hily i s th e pr i ncipl e tha t peopl e tend to socia li se with oth er pe ople li ke th em selve s 16,17 , a nd in this c a se fo r sex ual pa rtner ship ne tw or k s , wi t h ot h e r per s on s who have s im ilar s exual appe tite s to one s elf . T o ach ieve hom ophily , one thi rd of ag ent s w ere l oc at ed at r andom plac e s in the ag en t world. Mo st ( targe t 67% ) age n t s w e r e loca t e d (s t oc ha s t i call y in individ ual mode l run s) i n 64 c lust e r s with simil ar s ex ual appe tit e s, ini tial ly pla ced on model deve lopme nt t o follow pr oximi t y and d en s i t y rul es u se d in au t h or s’ pr evio u s AB M s 18 t o ac hieve conta c t rat e s and r elati on ship co ntac t simil ar t o tho se r ep o r t ed fo r th e UK i n obser v a tional re sea rch 17,19 . A gamma dist ribution wa s used for exp ected sex act di stribu tion, c or re spo nding with the ‘h e avy t a il’ ob se rved in s ome MSM s exu al c ont a ct n etw or k s 15 . How stro ng homophi ly (on sex ual a p peti te dimen sion ) i s w ithin th e MSM commu nity was no t fea sibl e fo r u s to pa r a met eri se with emp i r ic al data , rat her we cr eat ed varie ty i n homophil y (simil arity f or i ndividua l ag e nt s w ith ot he rs i n t heir con ta ct ci r c le s ) t h a t wa s plau si ble . Clu s ter s ha d . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 7 | Page dime ns i on s tha t w ere ap proxi mat ely 12.2 dist anc e unit s diam et er. The med i an n umbe r of ag ent s wi t hi n a 6.1 radiu s o f eac h ag ent wa s ab ou t 144 in m ost mode l run s (rang e appro x imately 42-242). Within thi s 6 .1 rad iu s circle , abou t 67 % of ag ent s h ad an averag e of h alf o f t h e ir c ontac t s w ith s i milar sexua l app eti te s; remain ing ag en t s w ithi n 6.1 dis t a nce u ni ts ha d a di ver s i ty (stoc h astic ally plac ed ) of sexua l app eti te s . In t hi s w ay, some agen ts ended up wi t h high hom op hily in their loc al a r ea ; oth er s had high variation i n s e xual ap peti te / lo w homophily among their s o cial cont ac ts . U ltima te ly, w e as s e ss ed th e pe rforma nc e of o ur mod el s and ag ent s ’ b ehavi our within o ur model s, aga in st pre speci fi ed an d p lau sible targe t s abou t ho w many unique partn er s a nd uniqu e sex ac t s t hat a g ent s typic ally exp er i ence d in mod e l run s (s ee T able 1). Calibration and partner seeking behaviour Anoth er impor tan t obje ctive o f the cl u st er plac emen t a nd indic a tor s that the mo dels we re repr ese nti ng pa r tn er ship be ha viour a s in tende d, wa s to e n s u re th at mo st ag e nts ha d low part n e r co unts (≤ 1 ove r a t h ree wee k moni torin g period), and t ha t mo s t sex act s wer e w ith a l imited numbe r o f ot h e r agen t s, re s ul t i ng in the pr e s pec i fied ta r g e t count s o f unique sex ac ts an d unique partn er s (se e Table 1 ). D en sity of ag ent plac ement a n d di st a nc e s move d eac h ho ur (wh en th ey co uld pla usibl y enc ount er new agen t s) , a s wel l a s s e arch radiu s f rom w hich to sel e ct a po ten t i a l partn er, w ere empiric ally cal ibra te d in mode l developm ent, a s a functi on of sex ual a ppeti te. Adjus tment o f t r a vel and se arch d i s tanc e s allow ing fo r sexua l appe t i te was to en s ure tha t th e s exua l ac tivity (i n te r m s of un iqu e sex a ct s and pa r tn er c ount s) o f a gent s fell on the ta r g et di st ri butio n over 3 w eek period s (me dian p ar t ne r c ount = 1 , media n se x ac t s = 3-6 ), and tha t high er uniq ue par tner and sex ac t count s would r e s ul t f or th e a gent s with hig he st sex app etit e. The mo de ls h ad a f u rth er targe t tha t th e ma ximum s ex ac ts ac hieved sh ould te nd t o hav e medi an abou t 32 a cts/we ek, a nd uniqu e par tne r count w ith medi a n max imum ≤ 24. T hese t arge t s guiding model develo pmen t and ca librati on a r e me ant to be plau sibl e n ot defini tive . The t a r g et for me dian ( 1 ) uni que p artner c oun t s wa s c ho sen wi t h ref e renc e to em pirical U K data c ollec te d abou t pa rtne r c ount s o ver thr e e wee k period s, w hich d a ta ove rsampl e d from MSMs u s ing digi ta l appli ca tion s de signe d to faci li tat e ca s ua l sexua l enc ount ers, in Augu st-S e pte mber 2022 20 . For c ompari son, 53% o f 5193 America n MSMs in 2009 re ported tha t t h ey ha d s e x wi t h a male partn er le s s o fte n than o nc e every th ree we eks, whi le 14 .1 % repor ted h aving sex with a noth er male at le a st twi ce a wee k. W e thought i t w a s pref e r a bl e tha t ag en ts i n o ur model s w e r e cal ibra te d to be m or e s ex uall y ac t i ve th an t h e gene ra l popula t i on of MS M s , beca u se we w ante d to in clude more hig h ris k individual s, and t h u s our a ge nt s had targe t s of medi a n 3-6 sexu al ac t s pe r 3 week monitoring pe riod. . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 8 | Page All a gent s re t ur n to a ‘h ome’ loca tio n a t end o f each 16 hour w aking period , thi s l ea d s t o highe r co nt a ct r ate s with the same ag ent s . A ma jor i t y of ag e nt s ( targe t 6 0-70% ) ha ve a sing le pre fer red partn er who is in cl o se pr ox imity t o hom e-loc a tion (within 1.48 di s t anc e uni ts o f home locatio n), t he “ste ady ”, a nd thu s s houl d be en count er e d oft en. The t arge t (60 - 7 0%) c or r es pond ed with an obs erved 6 6% (106 / 161 ) MSM s survey ed from th e ge ner al popu la tion w ho re por ted havi ng a partn er in a public ly a vail able d ata se t o f gay, bisexual and o the r MSM s sur v eye d i n Se pt e mb er 2022 21 . Eac h w aking hour (16x/day ) eac h in fec t i o us a gen t i s queri ed fo r t h e ir willi ngne s s to have sex , whi ch wi llingne ss i s a func tion o f th eir fix ed sex ua l appe tite a ttribut e. Empiric ally, th e model s are d e s ig ned such th at th e median numb er o f s ex a ct s in a thre e w eek perio d sh ould be 4 -6 an d t he media n numbe r o f unique pa r tn er s (du ring the in fecti ou s perio d, whic h als o ha s medi an d uration o f ab out thre e w eek s 15 ) s h ou ld u s ua l l y b e 1 . M os t age n ts s tr o n g l y p r e f e r t o h a ve s e x w i th t h e ir s te a d y i f they have one , rat her than o ther pa r tn er s who might be avai labl e. The st eady do es no t cha nge during t he pe riod w hen an agent i s in fe ct ious . The stea d y relati on ship i s 10 0% rec iprocal , bu t the inc lination to have more than on e conc u r ren t pa rtner , to se ek partn er s i n addi tio n t o t he stea dy (“st r a y. thre s h old”) i s not r ec iprocal . The population me dian str ay.th re shold wa s se t to ab o ut 11%. Tha t t hr e shold % wa s d e t e rmin ed empi ri c ally to creat e severa l targ et mode l ou tc ome s: tha t > 50% of al l s e xual act s for all p erson s who have a s t e ady, shoul d be wi t h t h e ste a dy; th at ma ximum partn er co unt (for a ny ind ividua l age n t ) d ur i ng infec tiou s pe riod should ≤ 24 and maximu m s e x ac ts during infec tiou s pe riod be ≤ 3 2 . Duration of period when infectious Mos t source s a gr ee that the in fe cti ou s p eriod (w hich e n ds whe n sca b s h ave ful ly dried and dr opped of f) t end s to h ave 2-4 w eek du ratio n af te r s y mptom on s et 15,22 . U S A CD C guida nc e i s t hat sca b s form on da ys 7 -14 da ys o f mpox illne ss and te nd to ta ke abo ut a we ek to c r u st ove r a n d sta r t d roppin g o ff, but inf ec tiou sn e ss is no t c on s ide r e d like l y to ha ve e nded un til ski n has comp l et el y he aled over a ft er the sca b f ell of f 23 . Mpox pati ent s have t es t ed po s i t ive on P CR a s la te a s da y 39 of illnes s 24 . However, P CR c on firm s pre s enc e o f at le ast s ome viral D NA f r a gmen ts r a t h e r tha n confirm s tha t th e DN A i s a c tiva t e d (can r e plica te and i s the ref ore in fec tiou s); t e sting po s itiv e on PC R aft er th e infec ti ou s peri od ha s end e d is common 25 . W i t h t h e se dat a in m ind, simil a r to o th e r mo del s 15 , we as s u med tha t the in fe c tiou s pe riod ha d media n dura tion 21 day s (504 h ours ), wi th r a nge 14 -28 day s . The infec tiou s pe r i od fo r indivi dual a gen t s i s s tocha stic within tha t ran ge , w ith a G aus s i a n dist r i buti on aro und th e median. Full im munity fol low s af te r inf ec t i ou s p e r i od fin ishe s . . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 9 | Page Daily contact cycles Model s al way s s tar t a t b eginn ing of da y ( nomina lly 7am) wi t h 16 ac tive ho urs c on s id e r e d for di s e a s e tran s m i ssion opp o r tuni tie s, thi s mea n s t he maximu m number of sex act s per d ay that coul d h appe n is 16. To c onfi r m t h a t model s we r e con s tr uc t ed a s sp ecifi e d, we monit ore d s ever al parame ter s s uc h as how many unique p a r tn e rs and uniqu e s ex acts wer e t y pica lly a chie ved by inf e c t io u s a gent s during t he ir in fec tiou s pe riod ( approxim a t e ly thr ee w e eks ). Epidemiologic assumptions varied in sensitivity analysis We unde r took s en si tivi t y ana ly si s v arying s om e model a ssump tion s and e ach of th e con t rol s tr a t e gy option s. I n our ba se line p lau sibl e mod el at simul atio n star t, th e numb er o f in fect ed agent s (able t o tran s m it di se a s e t o oth er s ) numb e r e d 16, w hich could corre s po nd t o a de tec t ed c ase count o f 8 and undet ec ted c a ses n umb er i ng 8. A s a l t e rna t i ve sta rt poin t s fo r outb reak con trol, w e c ons i de r e d the ca s e o f 8, 32 or 64 initi a lly i nfec ted a ge nt s in sen s i t i vi ty a nalysi s . Rema ining agen t s were a ssum ed to be su sce ptibl e with n o rel eva nt vac cina t i on his t o r y . The r e al ri sk o f mpox tran s mi s si on pe r s e x act (or per type of s ex a ct) i s unknow n. Ea r l y (data co llec t e d 1981 -198 6) e stim at e s o f s ec o n dary a t t ac k rate s (SAR ) f or mpox were a s l ow as 3% 26 . However, mpox SAR e stima ted sinc e 201 5 f o r p e r s on s in s ame h ou s eh o ld s with in de x c as e s ( not nec e ssarily be twee n s e xual pa rtn ers) h ave bee n much higher , 50 -60% 27,28 . In s e n s itivity an a lysi s to se e if fin ding s abou t c ontrol stra tegie s w ere de pend e nt on the t ran smi s s ion ri sk a ssumpti on s, we co ns id e r six fixed tr a n s mi s s i on ri s k s ( pe r sex ual e nc ount er) : 6%, 12%, 24%, 36%, 48% a nd 60%. In our pre fe rred b as eline mod el we ap ply t he e xpec ta tion th at t her e w as a 24% ri s k of tra n s mi ssi on eac h s ex a ct fr om infec tiou s t o s u scep t ib l e. Our model s d on’ t all ow for vari ation i n tr a n s mi s sion ri sk that may dep en d on speci fi c s exua l ac ts. Control Strategies Three fu ndamen tal con trol strat eg ie s ar e com pared. Ea ch c ont rol s tr at egy wa s c onsid ered indi vidual ly (not in combin a tion wi t h o t h e r contr ol s t ra teg ie s). The c on trol s t rat e gi es w er e desc ribed and a pplied w ith va r i a t i on s for sen si tivity analy s i s in a ss es s ing t heir inh erit po ten tia l . It wa s o bviou s tha t co mbined s tr a t e gie s w oul d be more e ffe c tive t ha n any s t rat egy in isola tion s o w e did not gene rat e mo del s to de scribe the o bvious adv an tage s o f de ploying multipl e control s tr a teg ie s . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 10 | Page in c ombina t i on . Rath er, ou r int ere s t was in consid ering plau sible i n dividua l pot ent ial of eac h co n t rol strat eg y. T able 1 s umm a r i s e s th e sc en ari o desc riptio ns to ac compa ny th e de s c r ip tion s b e low. Table 1. Scenario Descriptions Control strateg y Scenario description Details Ca sual p a r t ne rs hi p reduc t i o n High Plausible Lo w 50% of age nts c ea s e ca sua l par tne rshi p s 50% of agents cease 50% of casual partnerships, ie., 50% of such opportunities still happen 50% of age nts c ea s e a sma ll % (20 %) of c a s u a l partn er s hi p s Vac cina t i on programme Lo w : 25 % Plausible 50% High : 75% Spe ed o f va cc ine del ivery; % of hig hly a t - risk t arget group tha t rec eive vac cin a tion by day 1 20 % who S elf- isola te a fter dia gnosi s Lo w 11 % Plausible 22% High er 33% Max imal 44% % o f infec ted agen t s who heed ad vice to s t op all sexua l con tac t when in fec tiou s (a f ter po t ential d elay to real is e ow n c ase s ta tu s) Not e: A ssumed up take o f vac cine is con s tant ( s am e numbe r of do se s deli ver ed da ily) ac cum ulating to 50% of th e group o ffe r e d the va cci ne, by 120 da ys aft er vac cina t i on programm e s tar ts. Scenario 1: Partner reduction In thi s scena r i o, th ere i s a r educ tio n in th e pr op ortion o f s ex ac ts tha t ar e ca sual ( c asual me a n s no ste ady pa rtne r to c on side r) o r conc urren t ( stra ys fr om a ste ady pa rtne r). A bou t 5 0% of Ame r ic an MSMs s u rveyed i n 2022 r e ported b ehavi our t o re duce t h e ir s ex par tne r coun t in order to prev e nt ca tching mpox 11 . It wa s u nclea r h ow to r eflec t thi s r epo rted b e havio ur chang e in a gent int erac t i on s . We opt ed f or th ree d i f f e re nt in ter p re tati ons, en abling s en s i tivit y ana lysi s in the e valuation s o f a partn er re duc t io n s t ra tegy . A max imal interp r e ta t io n is t h at 50% of all a gent s s t o pped all c a sual and/o r s t ray ing sex during the o u t br ea k duratio n, w hic h is very mu ch li ke our sel f -i sola tion sce na rio s (below ) s o we d o n’t mod el thi s max imal interp r e ta t i o n a s par t of Sc en ario 1. A not her po ssible interp re tati on mig ht be if 5 0% o f a gent s consi s t ently r educe d t heir ca s ua l /st r a yin g p art ne r s hip c ount by 50%, a nd the oth er 50 % beha ved a s n o r ma l. A mor e w ides pre ad but l e ss co n s i st ent p artn er reduc t i o n stra tegy whic h we tr e a t a s our mos t p l au sible a nd p re fer r e d in terp r e t a t i on, cou ld be i f ag ent s rand o mly reduc ed their c a su al/ st raying partn er s hip s by 50% (50% of suc h opport uniti es still happ ene d) . A third po s sibili ty is tha t 50 % of a gent s beh aved a s normal , while ca sual / stray ing partn er s h ip s re du ced f or 50 % of ag en t s , b ut t he reduct ion was s m all a n d ef f ected by random agent s (80% of such event s stil l h appen ed but 2 0% d id not). . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 11 | Page Scenario 2: Vaccination only In thi s scena r i o, vac cin ation up tak e i s hig h a nd ef fec t i ve, bu t the re are no beh avio ur c hange s . T he model a ssume s tha t th e vacc ination pro tec tion i s imme dia te but o nl y if rec eiv e d befo re ex po s ur e: va cci nating a n alre a dy infec ted ag en t do es no t re duce s ub sequ e nt in fec tiou sne s s. O the rwi se, t h e lev el of pr otec t i on fr o m vac cina tion in th e model s was s table (doe s no t de clin e over time ). Rec e nt data indic a ted that a singl e va cci ne do s e ca use d 78% of r e cipi e nts t o be come i mm une to mpox 4 . Vac cina t i on in th e mo del i s deli v er ed a s a s ing le do s e, t arge te d a t individual s w ho have the hig he st risk o f c atching mpox. Deci ding ho w many of our ag ent s should be of fer ed th e vacc ine w as a trick y dec is ion. Ac t u al o f fer in Britain w a s pr obably t o only a bou t 15% of re s id ent MS Ms. W e e s tima t e 15% beca us e t he re wa s alm ost 50% uptake t o tho s e o f f e re d, r ep ort e d as 55,00 0 firs t do se s o f the smallp ox vac cin e that we r e admini st ered to MSM s in B ritain in the 4 month p eriod le ading up to 3 N ov 2 022 11 , whi ch co mpare s t o a n e stima ted 75 4,000 Bri ti s h men w ho ide nt i f i ed a s ga y or bi sexu al i n 2 019 29 , an d an unc lear numbe r o f B r i t i sh me n who i de nt ify as h ete ro sexua l bu t are a lso M S M s . O nly about 1 0% of ag ent s i n our ba s eline mod el fini s h w ith z e r o pa rt n e rs over a t hre e we ek mo nito ring period. Thi s co mpare s t o a bout 35% of > 20 00 gen era l popul ation MSM s in a Sep tembe r 20 22 sur vey 30 w ho repor ted they had ze ro par tne r s in the pr ece ding thr ee w eek s . How ever, r eal wor ld pa r tn er c ount s repor ted by M S M s i n 2022 may ha ve be e n muc h dimini s hed bec a u s e o f conc urren t mp ox aw arene s s (rea l l ife scen ario 1 dec i s i on s), ma king t h e real -wo r ld s urve y par tne r co unts al s o u n r ep re sent ativ e o f unc ontr ol l ed beh a vioural pre fe r e nce s. We c ame to the pra gmatic deci s ion t h at i n our pre fe rred bas elin e mod el, abou t 30% of our ag ent s (tho se at hig he s t ri sk) w ould be o ff ere d the va cc ine. W e va r i ed the p ac e o f de livery , howe ve r, suc h that t he acc umula ted d elive r y was 25% , 50% or 75% of targe t popu la tion by day 120 of stra te gy imp lementa tion . W e d eemed a s mo s t pl a us i bl e scena r i o , that 50% of the g r oup of f e r e d th e va cci ne had uptak e b y day 120. High risk i ndividu al s were d e f i ned a s ag e nts w ho a re A ) s till su s c ep tible and B ) e i the r / both amo ng the a gen t s with hig he s t sex app eti te a nd / or a gen t s with hig he s t tend e ncy t o pr a c tic e par tner co ncurrency ( s t rayi ng at tribu te; some ag ent s w ere in b o t h group s). The se hig h r i sk agents rece ived at rand om a single s ma llp ox vac cina t io n. This mea n f or in sta nce, wher e 50 % we r e vac cina t e d by d ay 120, that 39% of the en tir e hig h ri s k targ et group w ould no long er be s u sce p t i ble to mpox , bec au se of th eir vacc inatio n. In prac t i ce, b ecau s e the mod el s tar t e d with e xac t l y 6400 agen ts, th e hi gh ri sk group ten d ed to numb er a bo ut 1920 a nd the numb er who should b e e ff ectively p r otec ted by . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 12 | Page va cci nation if 50% de livery ta r g et ach ieved af ter four mon th s w a s abou t 749 (~39 % of 1920): w e monitor ed mo del pa rame te rs t o mak e su r e thi s ou t c ome w a s ach ieved . Scenario 3: Some self isolation We have no t foun d data d e scribi ng ac t u a l adhe r e nce to sel f -i sola tion adv ic e a ft er mpox diag nos i s in 2022 in the UK. 44% of Du tc h MSM s s ur vey ed in J u ly 202 2 31 indic ated hig h will ingnes s t o se lf - isola te i f t h e y had mpox, at lea s t until a ll lesi on s were gone . G iven t hat st at ed int ention s t o co mply wi t h public health a dvic e tend to be muc h s t ronger than a c tual compli ance 32 , t h e percent ag e o f per son s w ith co n fir me d mpox diagn o s i s who have actual ly full y sel f-i so lat ed ha s probabl y bee n muc h lowe r t ha n 44% . In sen si tivity anal y s is we te s t ed t h e s c enari os whe r e ei the r 11%, 22%, 33% o r 44% of infec tiou s agen t s iso lat ed af te r th eir sympt oms s t a rt. W e cho s e 22% as th e mos t plau sible va lue. How ever, sel f -i sola tion st art wa s as s um ed to o ft en be del aye d to r efl ec t l i kely dela yed recog nition /acc e ptanc e of ow n ca se st at us . Fo r tho se who s e lf -i sola te a t all, del a y t o s t art se lf - isola tion fol low s a g amma d istribu tion (l ong right tail ) a f t e r fi rs t s ig n s o f inf ectio n , median delay i s abou t 7 2 hour s, and rang e 0 to 40 0 hour s . Othe r a gent s don ’t sel f -i s ol a te at all when infec tiou s.

Tab le 2 show s mode l targe t s and v alue s ac hieve d, with r eg ard t o age nt b ehavi ou r s a nd outcome s . The model a chie ved mo st o f th e be h aviours an d a gent s ha d qua liti e s con sis ten t with the mod el design objec tive s . Table 3 show s out bre a k ou t c ome s (media ns a nd I QR s) fo r the b a seli ne and pref err ed al tern ative scena rio s. T able s S 1-S 4 in S uppleme n t a r y Mate rial show ou t b r e a k outc ome s va r y ing e pidemiol ogic parame te r s with e ac h of th e candi da te con trol st r a te gy a ss umption s. Monito ring o f mode l be haviou r, p aram et er a s s ig nment s and som e outc ome s all i n dica t e t h a t th e model s p e rforme d a s d e s ig ned . F or in sta nce (T abl e 3) 67% of a gen t s are s t rong ly in contac t clu ste rs, so t hey w ill tend to encou n t e r the s am e other age nts mo st commo nly. Simila rly , inc ubation p e r i od s , recovery/in fec tiou s pe riod s an d o ther p a ramet er s ar e a s s ig ned to a g ent s on the d esi red dist r i buti on s (T abl e 1 ) . The medi an n um ber of p art ner s i s 1 in mos t s imu latio ns , whil e the tran s m i ssion c hain s (co un ts o f ge ner atio ns in th e mpo x outbr eak ) ar e < 10 con si s t e nt l y (T abl e 3) . . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 13 | Page Table 2. Verifying model performance in baseline scenario: stochastic assignments Parameter Tar get s: Distribution Range Mean or median Values realised in baseline model runs (no control strategy) Inc ubati on pe r io d (day s ela p sed f r om ex pos ur e t o s tar t of in fec t i ou s p er i od) o f ag ent s L og Normal 33 Ran ge: 3 -21 days 6,33-35 Medi an: 8 6,33,34 Rang e: 3.4 -21. 1 M e d i a n: 8. 5 Inf ec tiou s pe riod ( day s du rati on) o f agen ts Normal Ran ge: 7 - 2 8 day s 35 Mea n: 20 -21 da ys 36 Rang e: 10 -30 Mean: 20.xx x S ex u a l a p p e ti t e ( fo r s e x ac ts pe r w ee k) Gamma 15,2 0 Ran ge: > 0 t o 32 15,20 Medi an: 3 -6 37 Rang e: 0.2 – 29 .5 M e d i a n: 4. 3 % of agen ts wi t h a pr e fer r e d par tne r (“st eady ”) 60 - 7 0% 21,38 Rang e: 64 -65 Median : 64 .4 Inc linatio n t o try part n e rs no t one ’ s st ea dy, “str ay.thr e shold” a s % risk pe r oppo rtuni ty Gamma 39,4 0 Ran ge: 0 -10 0 Medi an: 10 -12 Rang e: 0 -100 Median : 10 .5 In a dditi on to be h aviour ou tc ome s, Tabl e s 3 and S 1 -S4 repo rt t he k ey epi demic ou tcome s unde r pref err ed plau sibl e ba selin e and c ont r ol s c en ario a s sumpti on s: ou tbr e ak dura tion and tot al c as e s gen era ted a ft er s i mula tion sta rt for ba se l ine a nd unde r s ome pla u s ib l e co nt ro l s tr ategy imple menta tion s . In Ta ble 3, re ducing ca s ual enco unte rs par tne r co ncurr ency (Sce nario 3, 5 0% of such i ncide n ts don’ t ha ppe n) le a d s to th e most i mpr oved (l ow e s t ) c ount o f s econ da r y ca ses and re sult s in t h e s h orte st du rati on, f rom me di an 83.4 days (ba seli ne ) t o 55.5 da y s. T he s c e nario that i s nex t be s t a t r e ducing new ca se s i s when 2 2% of a gent s s e l f i s o la te a fte r inf ec tiou s period st a r t s (65 day duration o utbr eak ) . The vac cina t i on s c en ario ( d e livery to 50% o f most hi gh ri sk 30% of target group) pro duc ed ne gligi ble impr ove ment s over ba s eline , from 83.4 to 8 0.5 da y s a nd alm ost no reduc t i o n in new ca se s (17 t o 16 medi a n) . The s e n s i tivity ana ly se s ( T a ble s S1-S 4 ) sup por t the primary r e sult s . . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 14 | Page . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 15 | Page Table 3. Model performance and outbreak outcomes observed in each simulation, under baseline conditions and plausible control strategies; without sensitivity analysis Out break O utc omes Baseline Ta r g et Baseline media n: IQ R Par tner reduction media n: IQ R Vacc ination median: IQ R S o m e s e l f - is o la t io n median: IQR D u r at i o n of o u t br e a k f r om s eed i n g t o f inis h day s week s no ta r g e t 83.4 : 62.2 -118 .1 13.9 : 8.9 -16.9 55. 5: 43.1 -72. 5 8.9 : 6.2 -10.4 80.5: 61-104 11.5: 8.7 -14.9 65.0: 49 -8 7 9.3 : 6. 9-12 .4 Number o f add i t i onal a ge nt s in fect ed (s econda r y ca ses ) by time ou tbre ak fi ni she d no ta r g e t 17: 10-29 8: 5 -12 16: 1 0-25 11: 6-18 Model perform ance metr i cs % of s e x ac t s w ith the pr ef erre d par tne r % of casu al sex ac t s (no st eady fo r initia t or) % of s e x ac t s in s pit e o f havi ng a st eady > 50% no ta r g e t no ta r g e t 64% : 54-73% 29% : 19-40% 6.7% : 4.8-8 .8 % 79% : 70-86% 17% : 9-26% 4.0 %: 2.1-5 . 9% 62% : 52-72% 31% : 20-42% 6.3% : 4.4-8 .5% 63%: 5 1-74% 30%: 1 7-44% 6.3%: 3 .8-8 .9% Media n # uni q ue pa rtne r s dur i ng inf ec tio us period ( ~3 we ek s) 1 1: 1 -2 1: 1 -1 1: 1-2 1: 1-1 Max imum # u nique pa rtner s du ring i nfec tiou s period (~ 3 wee k s) ≤ 24 8: 4 - 1 2 3: 2 -5 7: 4-12 5: 2-9 #s exa ct s (p er agen t) duri ng infec t io u s pe r io d (~3 w eek s lon g) Media n 3 -6 Max . 32 5: 3 -6 19: 14-26 6: 4 -8.5 19: 14-26 5: 3. 5-6 18: 1 3-24 3: 2-5 15: 10-21 Le ngth tran s m i ssion c hain (c oun t of ag e n ts inc luding but not be fo re se ed s, only cou nted for age nts inf ec t ed af te r s eeding ) Media n ≤ 3 Max . < 10 1: 1 -2 4: 3 -6 1: 1 -1 2: 1 -3 1: 1-2 3: 2-5 1: 1-2 3: 2-4 Not e: A ssumpti on s and conditi on s fo r ba selin e and w ith judge d t o be mo st plau si ble ver sion s of con trol s tr a t e gie s a s de scr ibed in text . 1 000 simula tio n s ea ch . . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 16 | Page Table S1. Sensitivity Analysis for Baseline scenario starting with 8, 16, 32 or 64 agents Simul ation O utc omes Median: I Q R 8 cases at star t 6 x 1000 simulations 16 cases at star t 6 x 1000 simulations 32 cases at star t 6 x 1000 simulations 64 cases at star t 6 x 1000 simulations 8, 16, 32, 64 agent s 24,000 simulations Dura tion o f outb reak fr o m se eding to fini sh day s we eks 66.0: 39-141 9.4: 5.6 -20.1 97.3 : 53-207 13.9 : 7.6 -29.7 132.0: 6 7-267 18.9: 9. 6 -38.1 170.0: 81-312 24.3: 1 1.5 -44.6 99 . 2 : 5 2 -23 4 1 4.1: 7-33 Number o f add i t i onal a ge nt s infec t ed ( se conda r y ca se s ) by t i m e o ut br e ak f i n is h e d 8: 2-36 22: 6-103 56: 13-23 2 122: 28 -476 2 8: 6-173 Not e: Val ue s a re median : I Q R . 6 t ran s m i ssion r ate risk s pe r enc oun ter are : 6% , 12%, 24%, 36%, 48% or 6 0%. 1000 simul ation s wer e run f or ea ch o f th e se 5 opti o ns in th e bas elin e s c en ario condi tion s. Table S2. Sensitivity analysis for partner reduction scenarios (1), starting with 8, 16, 32 or 64 agents Simul ation O utc omes Median: I Q R 8 c as e s a t s t ar t 6 x 3 x 10 0 s i mulations 16 cases at s tar t 6 x 3 x 100 simulations 32 c ases at s tar t 6 x 3 x 100 simulations 6 4 c a se s a t s t a r t 6 x 3 x 1 00 simulations Dura tion o f outb reak fr o m s e e ding to fini sh days wee ks 45.0: 3 4-72 6.5: 4.9 -1 0.3 58. 0: 40-93 8.3 : 5.8 -13.4 73.7 : 49-118 10.5 : 6.9 -16.8 89.1: 60-146 12.6: 8.6 -20.9 Number o f add i t i onal a ge nt s infec t ed ( se conda r y ca se s ) by time outbr eak fini sh ed 4: 2-9 9: 4-22 19: 8-44 41: 17 -96 Not e: 5 v alue s te sted for r i sk o f t r an smis s i on p er enc oun te r are : 6% , 12%, 24%, 36%, 48% or 60 %. Pl eas e s ee mai n text f o r de sc riptio n of pa rt n e r redu ction o ption s (n =3) . 100 s imu lati on s were run for ea ch pe r m uta t i o n and a re pool ed fo r thi s ta ble. . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 17 | Page Table S3. Sensitivity analysis for vaccination delivery rate scenarios (2), starting with 8, 16, 32 or 64 agents Simul ation O utc omes Median: I Q R 8 c ases a t s tar t 6 x 3 x 100 simulations 16 ca s es at st a rt 6 x 3 x 100 s imul at i ons 32 c ases a t s tar t 6 x 3 x 1 00 simulations 64 cases at st ar t 6 x 3 x 100 simula t ions Dura tion o f outb reak fr o m se eding to fini sh day s we eks 63.5 : 38-121 9.1: 5.5 -17.3 8 7 . 3 : 5 1-15 7 12.5: 7.4 -2 2.4 116.0 : 65-195 16.4: 9.3 -27.8 27 1.4: 234 -323 38 .6: 33.5 -4 6.1 Number o f add i t i onal a ge nt s infec t ed ( se conda r y ca se s ) by t i m e o ut br e ak f i n is h e d 7 : 2-29 19: 6-65 46: 1 3-144 50 4: 401-63 6 Not e: V alue s ar e median : I Q R . 6 tr a n s mi s sion r ate risk s ar e: 6% , 12%, 24%, 36%, 48% or 60 %. 3 vac cina t i on roll out ra te s are: 25 %, 50% or 75% of ta rget po pul ati o n by d ay 120. 100 simul ati on s were run for ea ch permuta tion . Table S4. Sensitivity analysis for self isolation scenarios (3), starting with 8, 16, 32 or 64 agents Simul ation O utc omes Median : IQ R 8 ca s es at st a rt 6 x 4 x 10 0 s i mulations 16 cases at s tar t 6 x 4 x 100 simulations 32 c ases at s tar t 6 x 4 x 100 simulations 6 4 c a se s a t s t a r t 6 x 4 x 1 00 simulations Dura tion o f outb reak fr o m se eding to fini sh days week s 48.0: 3 4-83 6.9 : 4 .9-11 .9 62. 5: 40-115 9.9 : 5.7 -16.5 86.3 : 53-147 12.4 : 7.6 -21.1 107.0 : 63-184 15.4: 9.0 -26.3 Number o f add i t i onal a ge nt s infec t ed ( se conda r y ca se s ) by t i m e o ut br e ak f i n is h e d 4: 1-13 9: 3-33 26: 8-75 59: 15 -159 Not e: 6 tr an smission rat e r i sks are : 6% , 12% , 24% , 36% , 48% or 60%. 4 proportion s o f popula tio n th at s e l f i s o la te a ft er illn e s s on se t: 11% , 22%, 33% or 4 4%. 100 simula tion s w er e r u n fo r eac h pe rmuta ti on. . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 18 | Page . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 19 | Page

All of t h e s tr ategi e s c onsi der ed in o ur m odel s (pa rtn er r e duction , v acc ination , s e l f- i s o la t i o n af ter illn e ss on se t) could be v ery ef fec t ive to sto p mpox outbre aks if de ployed fully. H ow eve r, rea li ty is tha t beh aviour c ha nge or vac cine uptake i s o fte n imper fec t an d take s t ime to impleme n t . With re s p ec t to ou tbr eak duration a nd new c as e s a fte r simula tion s ta rt, un der pla us i b le a s s u mp t i on s , our mod ellin g sugge s t s tha t red uc ing part n e r conc ur r enc y a nd ca s u al partn er s hi p s w er e likely t o have had the most b ene fi ts in r edu cing mpox spr ead ( sce n ario 1) . I t m ay be s urp ri sing that smallpo x va cc ination h a d negli gible ef fect s on o utbr eak lengt h a nd to tal num be r of sec ondary in fecti on s in o ur model ling ( sce na rio 2) . T his fi nding l ikely aro se bec au se of the pa c e of v acc ine d e l ivery : only 50% a dministe r e d to targe t group a fte r fou r m ont h s (in r e a lity an d in the mo del s ) . Fa s ter vac cin ati on d eli very w ould ha ve ma de th e rea l- world vac cina t i on s tr ategy more ef fec t i ve. Fre e text c ommen t s abou t mpox col lected a s par t of a 202 2 sur v ey o f MSMs in the UK 30 indi cated t ha t many r esp onden t s we r e f ru s tr a t e d abo ut or h a d encou nte r ed many di fficul tie s in obtaini ng a s mal lpox v acc ine. Se lf - i s ola t i on ( s c enario 3 ) was muc h mor e bene f i cial th an va cc ination , bu t le ss e f f ec t i ve than r e duc tion s in c a sual partn er s h ip s ( sce nario 1 ) in our model s . Info rmatio n abou t ac t u al sel f -i s o la tion a dh er e nc e b ehavi ou r when infec ti ou s during th e mpo x epi demic is st ill e merging. Given t he well docume n t e d cha llenge s ma ny pe ople h a d in adhe r i ng t o s elf -i s o la tion r equir emen t s d uring t he C ovid1 9 pande mic 32 , a dher enc e t o mpox sel f -i sola tion recom menda tion s seem s like ly to h a ve b ee n low , pe rhap s much lower th an our b as eline choic e o f 22% . Howe ver, bec au se cl o s e con tac t i s g ene rally requi r ed to t ran smit mpox , th e s elf -i s ol ation u ndert aken in re a lity may hav e been ade qua te i f not i d eal: pe ople r ef rain ed from physica l contac t alth oug h they di dn’ t s el f - i sola te in th eir home s en t ir el y. The W o r ld H e alth Or g aniza tion al e r t ed gl obal auth oriti e s t o the 2022 mpox outbr eak in l ate M ay 2 022 41 . The model ling h er e p rovide s ev idenc e fo r a c ommon hy pot h e s i s 42 that t he pe a k in case c oun t s (e s timat ed Jul y 9 i n U K 43 not long af te r thi s anno unc emen t and ca se c oun t dec lin e sinc e, should be cr edit e d mostly to b ehavi our choic e s by membe rs of the MS M communi t y rath er than va cc ination p rogramm e s. Inde ed, smal lpox v acc ination t o MSM s a t hig h ris k of ac quiring mpo x in the U K was not wi dely o ffe red be for e ea rly July 20 22 4 . Our modell ing ma y be h elp ful in c onfirming t h e like ly v aluabl e con tribu tion t ha t pe rsonal beh av iour cho ice s hav e made and c an c on tinue t o ma ke in b r ing ing mp ox outbreaks u nde r contr o l. T he importanc e of p er sona l be havi our choic es can b e vita l to s h a r e in publi c hea lth ca mpaign s . T his s t atem ent i s not i n t e nd ed to und e r mi n e the hug e v al ue of v acc ina tion p r og r a mme s ; va cci nes can con fer la sting immunity a nd resi stanc e to di sea s e, a nd thu s are a mo re r el i able popul atio n p r ot ec tion mea s u re t han r e lying on indiv idual b eha v iour choi ces . Pr otec tiv e s exua l behav io ural c hoic e s are of ten no t su s tain e d ove r long time pe riod s 44 . O n going s mal l pox v acc ination for B r iti sh MS Ms wa s su gge s t ed a s a key rea so n the re wa s no l arge re su r g ence in new mpox cas e s i n the UK i n 2023 45 . . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 20 | Page Se ns i tiv ity ana ly si s (Tabl es S1 - S 4 ) whi ch al lowed fo r dif fe r e n t number s o f inf ect e d agent s at b as elin e (8, 16, 32 or 64) and dif fer ent t ran s mi s s i on ri s ks ( from 6 - 60% per c ontact ), do no t chang e th e ov e rall find ing t hat r educ ing c a sual partn er s h ip s w a s rela tive ly more e ffe ctiv e as a epid emic cont rol ac ti on than v acc i nation o r s elf -i sola tion b ehavi our. Howev er, comp ar ed to the ba s eli ne and p lausi ble a l ter n ative sce na rio s , ou r large r simula tion s e t s hav e wid er interqu ar tile r a ng e s fo r t he key epid em ic ha r m outcome s: a ddi t i o nal c a se s a nd du ration o f th e out br e aks . Highe r unc ert a inty abo u t e pid emic prot ection, e s pe ci al ly ov er a long er time peri od, can b e ex pected to a ssoci a te mor e wi t h beha vioural stra tegie s ( par tner reduc t i o n or s om e sel f - i s ol a t i on ) tha n wi t h vac cina t i on .

and Strengths It wa s n ot fe a s i bl e to t e st ou r model s aga inst rea l world d ata . We a r e unawa re o f any r e al w or ld s itu a t io n that we co uld co mpare wi t h, whe re on ly one o f t he s t ra teg ie s d es c ribed h ere wa s appl i ed to co nt rol mpox in MSM s in 2022. We al s o no te t h a t a mpox epide mic w oul d not l a s t pe r pe tua lly i n a c lo s e d s y stem model such a s t hi s one ; the re i s some po s s i bili ty tha t de pl etion o f th e mo s t a c tive susc eptib l e popula t i on al s o hel p ed to ha s ten th e de clin e of mpox ca s e s in B r i t a in in 2 022 . Model s ar e simpl i fie d ve rsion s of a c omplic ated a nd com pl ex w orld. Our model s c ons i d er a re lativ ely sex ually activ e popul ati on; in re a lity, a la rge nu mber o f people have rela tive ly low cou nts of sex event s and p a r tn er s in th ei r l ive s (low er tha n our mod el s sugge st 30 ). Po s t - e xpo sur e small pox vac cina tion i s though t to o ff er some pr otec tion agai n st dev eloping inf ec t i ou s i lln e ss; ou r m od el s don’t all ow for t his p ossi bil ity. W e de s ig ned our mode l s to re fle c t plau sible beha viour bu t la ck inform ation to c onfi d ently k now h ow repre s ent ative all o f th e se ma ny beh a viour a s sumptio ns we r e of mo s t MS Ms in Br i t a in or el sewh e r e . For in stanc e, alt houg h we modelle d vac cine deploy ment a t a sp ee d in ac cordanc e w ith publi sh ed i n f o r ma t io n a bout th e a ctual U K p rog r a mme, we did n ot c on sider i f beh a viour c hange wa s i tsel f a l s o slow ly i mplemen ted . It i s possibl e t h a t chan ge in beh avi our in Eng land w as much s low er t han our model s a ssum ed, a nd a s a r e sult n eith er sel f -i sola tion no r p a r tn e r r educ tion b ut r athe r oth er unme a s u red fa cto r s we r e r e s p on sible for t h e decl in e in new E nglish mpox ca s e s a ft er J uly 2022. Our model s a tt empt to ex amine e ach s t r ategy in isol atio n a nd doe s no t c on s id e r poten tial synergi s tic e f fect s . Nor d o we allow for varyi ng impl emen tati on of a ny sce nari o. F or in stanc e, in re ali ty, the vac cina t i on progr amme l ikely had a slow sta rt, the av era ge pa ce o f delive r y at s t a rt of p e r i od wa s slowe r tha n by the e nd, bec au se in fra s t ruc t u r e t a ke s a little w hile t o cre ate . The c on s tan t ra te of vac cina t io n d eliv ery tha t our mod e l s a pplied will have s lig h tly ov er- es timat e ra ted o f e a rly dos e de livery. Our appr oac h i s novel in tha t we ar e not aw are o f oth er AB Ms t h a t addr es s mp ox spre ad amo ng MSM s . ABM s can be rel a tively more f lex ible a nd na tur alis ti c compared t o o the r modelli ng appr oac h es 46 , expl icitly inco r po rating hete roge n eity of a g ent a tt ribut e s and be ha viour c hoice s 47 . ABM s ar e de signe d t o revea l eme rge nt p henome na 46 . CC-BY-NC 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 6, 2024. ; https://doi.org/10.1101/2024.02.06.24302176doi: medRxiv preprint 21 | Page and t hu s ma y provid e nove l in sight s to e pidemi c dy namic s . Our model s in h er e n tl y inc orpor a te d a s s or tive mixin g whi ch is a well -rec ogni sed fea t ur e of ac t ual s oc ial n etworks 48,49 , possib le c onta ct rate s a nd pl au s i ble b eha viour ch oices . We u s ed pu bli shed in forma tion t o cons tr uc t all o f t he con trol sce na rio s , t w o of th e scen ari o s e mulat ed publi s h ed da ta ab ou t par t ne r count r edu c t i on s a nd va cci nation d el ivery. The s e ABM a dvant ag e s come with a pr ic e in tha t the y are c ompu ta tional ly ex hau sti ve 47 and with our so ftwar e pl at fo r m, me ant tha t th e a gen t popul a tion nee de d to be r e st r i cted (to 640 0 age n ts) to gen era te many s t rat egy and sc en ario outcome s i n a re a sonabl e timef rame . In rea li ty, MSM s in c ommuniti es a f fec t ed by mpox in 2022 d oubtle ss unde rtook a ble nd of b eha viour c hoic e s tha t help ed t o reduc e tr a ns mi s sion . We h a ve not tri ed to e s tima te what the op tima l mix of multiple s tr at egie s w ould be . Clea r l y, c ombined str at egie s are mo r e e f fective than any st r at egy in isola t i on; d e ploy ing a variety of con trol strat eg ie s f or a ny fu tur e mpox outbre aks is c learly wis e in th e r ea l wo r l d.

1. ECD C. F act sh ee t fo r heal t h pr o fe s sio nal s on mpo x (monkeypox ). Jun 1 20 23. http s : / /www .ecdc .eur opa. e u / en /all - top i c s-z/monkey pox /fac t she et -hea lth -pro fe s s ion a ls (acc e ssed Jan 5 2024 ). 2. Sk lenov s ká N, Van R an st M . Eme r g ence o f monkey pox a s the mo s t i mportan t o rth opox virus In fec tion in huma ns. Fr ont ie rs in Pu b l ic H e a lt h 2 018; 6 . 3. Pola nd GA, Kenn edy RB, To sh PK . Preve n tion of monkey pox w ith va cci nes: a r apid r ev iew. The Lanc et Inf ec tiou s D is e a s e s 202 2. 4. Maha se E . M onkey pox: S ingle do se o f sm allpox vac cin e off er s 7 8% protec tio n, UK H S A r e port s. Bri tish Medic al Jo urn al 2022; 379 . 5. Rey nold s MG , Da mon IK . Out bre aks o f h uma n monke ypox afte r ce s s a t i o n of smal lpox vac cin ation. Trend s Mic r ob iol 201 2; 20 (2 ): 80 -7 . 6. Thornhil l J P, Barka t i S, W alm s l ey S, et al . 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