E alua ion o he epidemiological ou look o he in luenza A/H3N2 clade
K in England du ing he 2025-26 season
James A Hay*,1, Punya Alahakoon†,1, Alexande G eenshields-Wa son†,1, Michelle Kendall1, Mahan Gha a i1,2,
Ch is Wyman 1, Robe Hinch1, Luca Fe e i1, Jasmina Pano ska-G i i hs1,3,4, Ch is ophe F ase 1
1. Pandemic Sciences Ins i u e, Nu ield Depa men o Medicine, Uni e si y o Ox o d, Ox o d, UK
2. Depa men o Biology, Uni e si y o Ox o d, Ox o d, UK
3. The Queen's College, Uni e si y o Ox o d, Ox o d, UK
4. UK Heal h Secu i y Agency, London, UK
* Co espondence o [email p o ec ed]
† Con ibu ed equally
Key indings
● England is cu en ly expe iencing a high g ow h a e o in ec ions caused by he in luenza
A/H3N2 K clade. An igenic change om he p e iously dominan clade, a apid selec i e
sweep e iden in genomic da a, and an unusually ea ly s a o he season ha e aised
conce ns abou he po en ial se e i y o his yea ’s in luenza season.
● Analysis o publicly a ailable da a sou ces om he cu en season sugges s ha he
e ec i e ep oduc ion numbe has been la gely consis en wi h p e ious se e e seasons.
Howe e , he modelled peak g ow h a e in he cu en season o da e is sligh ly highe han
p e ious peak g ow h a es om he pas 10 yea s when subse ing o A/H3N2 cases, bu
compa able when agg ega ing all in luenza cases.
● Scena io analyses using an age-s a i ied compa men al model compa ed o he p e ious
A/H3N2 season in 2022/23 sugges ha subs an ial immune escape is unlikely gi en
cu en epidemiological ends. Cu en ends a e compa ible wi h small le els o immune
escape in all ages, o sligh ly g ea e immune escape in child en, o a 10-20% highe R0, o
an ea lie seed da e wi h no change in i us i ness o immune escape. In almos all
scena ios, an ea lie and as e epidemic g ow h a e leads o deple ion o suscep ibles
be o e he Ch is mas pe iod wi h a dampening e ec due o he hal e m school holiday.
● To suppo unde s anding and explo a ion o model ou pu s, an in e ac i e isualisa ion ool
was de ised and made a ailable online: h ps://hay-idd.shinyapps.io/ModelFluUk-H3N2/
● This apid analysis is in ended o suppo si ua ional awa eness. I p o ides quan i a i e
compa isons o ea ly epidemic g ow h a es wi h p e ious seasons and quali a i e insigh s
in o plausible epidemic dynamics.
Funding: JAH and PA a e suppo ed by a Wellcome T us Ea ly Ca ee Awa d (g an 225001/Z/22/Z). AGW is suppo ed by a Wellcome
T us di ec ed call (309152/Z/24/Z). MG is suppo ed by a Wellcome T us Ea ly Ca ee Awa d (g an 309205/Z/24/Z). LF acknowledges
suppo om a PSI Ca ee De elopmen Fellowship, he Eu opean REA, Ma ie Skłodowska-Cu ie Ac ions (g an ag eemen no.
101131463 SIMBAD), and UK Resea ch and Inno a ion (UKRI) unde he UK go e nmen ’s Ho izon Eu ope unding gua an ee (g an
numbe EP/Y037375/1). JPG's wo k was suppo ed by unding om he UK Heal h Secu i y Agency and he UK Depa men o Heal h
and Social Ca e (DHSC). The iews exp essed in his a icle a e hose o he au ho s and no necessa ily hose o he UK Heal h
Secu i y Agency o he UK Depa men o Heal h and Social Ca e. RH and CF we e suppo ed by esea ch g an s om CEPI.
Con lic o in e es : JAH, PA, AGW, LF, RH, MK, JPG, CW, MG and CF decla e no compe ing in e es s.
Da a a ailabili y: All code and da a equi ed o ep oduce he analyses a e a ailable a
h ps://gi hub.com/hay-idd/in luenza_H3N2_k_clade
Acknowledgemen s: We hank S e en Riley, Simon Cauchemez, Ben Cowling, Oli e Eales, F eya Shea e , and Julie e Pai eau o
help ul discussion and o p o iding global con ex o he analyses. We also hank Richa d Nehe o help ul discussions a ound g ow h
a e ad an ages es ima ed om genomic da a.
Use o AI: AI ools including Cha GPT and Copilo we e used o li e a u e e iew, sou cing da a and de eloping code.
In oduc ion
The 2025/26 in luenza season in he no he n hemisphe e appea s o be domina ed by an
an igenically d i ed clade o A/H3N2 i uses. This clade—named K (p e iously J.2.4.1)—is
descended om he J.2 clade on which he accine s ain selec ion was based, and has swep o
dominance om a equency o <1% on 2025-07-02 o 99% in Eu ope as o 2025-11-21 [1]. This
sugges s a subs an ial i ness ad an age o e o he J.2 i uses [2]. The combina ion o apid
g ow h, mul iple an igenic subs i u ions in he haemagglu inin (HA) p o ein, an igenic misma ch wi h
he accine s ain, ypically highe mo bidi y and mo ali y amongs he elde ly du ing A/H3N2
seasons [3,4], and an unusually ea ly s a o he season ha e aised conce ns o e he po en ial
o a se e e season in he Uni ed Kingdom and Eu ope mo e b oadly [5–7]. Fu he mo e, he 2025
lu season in Aus alia was one o he wo s on eco d [8,9], and Japan is su e ing om an ea ly
epidemic leading o school closu es and inc eased hospi alisa ions [10]. These indica o s sugges ,
hough no de ini i ely, an unusually se e e in luenza season ahead [11]. The in e ac ion o season
iming, an igenic d i , o he sub ype dynamics, accine e icacy and co e age, non-HA-media ed
immuni y, immune waning om p e ious seasons, clima e ac o s, and con ac pa e n changes
a ound school holidays is complex and leads o highly a ied cumula i e and peak seasonal
bu den [11,12]. The po en ial ou look o he 2025/26 in luenza season is he e o e unce ain,
hough his o ical seasons wi h ea ly onse and peaks ha e o en been se e e [4].
One o he key conce ns a ound clade K is ha i has an es ima ed g ow h a e ad an age o ~20%
o e compe ing s ains based on clade equency da a. Mul inomial logis ic eg ession was used o
es ima e he ela i e i ness o clade K based on i s coe icien in he eg ession model i ed o
clade equencies o e ime [2], gi ing an es ima ed selec ion coe icien o a ound 1.2. How his
g ow h a e ad an age ansla es o an es ima e o he e ec i e ep oduc ion numbe Re depends
on he choice o e e ence s ain and he Re o ha s ain. A sys ema ic e iew ound ha he
median e ec i e ep oduc ion numbe o seasonal in luenza was 1.28 (IQR: 1.19-1.37), wi h he
es ima ed ep oduc ion numbe in 2009 (pandemic H1N1) a 1.46 (IQR: 1.30-1.70) [13].
Real- ime epidemiological assessmen in England is based on weekly in luenza su eillance da a
om he Second Gene a ion Su eillance Sys em (SGSS) [14]. SGSS compiles es esul s o
in ec ious diseases including COVID-19, in luenza, RSV and o he s om mul iple da a s eams: he
Royal College o Gene al P ac i ione s Resea ch & Su eillance Cen e (p ima y ca e), he
Respi a o y Da aMa sys em (hospi al es ing) and o he hospi al es ing. The main su eillance
indica o in he UK Heal h Secu i y Agency weekly su eillance epo s is he pe cen age o es s
ha a e posi i e o in luenza, ou o hose pa ien s p esen ing wi h in luenza-like illness (ILI). This
me ic has inc eased much ea lie han in o he ecen seasons ollowing he decline o a p e ious
COVID-19 wa e, pa icula ly among he 5-14 yea old age g oup. No e ha Sco land, Wales and
No he n I eland ha e sepa a e da a epo ing sys ems and ha e also ecen ly epo ed subs an ial
inc eases in in luenza ac i i y, hough wi h a sligh lag o England [15–17].
Despi e i s widesp ead use, me ics based solely on he pe cen age o es s posi i e o in luenza
a e known o be biased by he dynamics o o he ILI-causing pa hogens which makes in e p e a ion
di icul . I is he e o e ecommended o use an ILI+ indica o which mul iplies ILI cases by he
pe cen age o es s posi i e o in luenza, ideally s a i ied by sub ype [18]. This me ic can be
gene a ed om publicly a ailable da a sou ces om UKHSA. The WHO also p o ides a use ul
global da a sou ce o in luenza dynamics in England, FluNe , which combines samples om
non-sen inel (e.g., ou b eak in es iga ion, POC es ing e c) and sen inel su eillance si es o gi e
sub ype-speci ic case coun s o e ime [19]. We ocus he e on hese sou ces o in luenza case
coun s, ei he o e all o by sub ype, and s a i ied by age o ecen yea s, o unde s and he
ansmission a e o he cu en clade K i uses in he UK based on adi ional measu es o
absolu e g ow h a e and R .
In his epo , we analyse publicly a ailable epidemiological da a om he UK and p esen
modelling analyses using an age-s a i ied Suscep ible-In ec ed-Reco e ed model o add ess wo
main ques ions:
1. Do he epidemiological da a indica e a mo e ansmissible A/H3N2 s ain han p e ious
seasons?
2. Unde plausible scena ios o a i us wi h inc eased ansmissibili y, ea lie seeding, and/o
subs an ial immune e asion, wha is he po en ial impac on cumula i e and peak
heal hca e bu den o he es o he season?
To allow isualisa ion and explo a ion o di e en pa ame e combina ions wi hin he model uns
and cons uc ed analyses, we embedded ou model in o an in e ac i e web ool using a se ice
p o ided by shinyapps.io (h ps://www.shinyapps.io/). The ool (accessible a
h ps://hay-idd.shinyapps.io/ModelFluUk-H3N2/) enables use s o ep oduce ou esul s, bu also
allows explo a ion o di e en pa ame e combina ions.
Resul s
The maximum g ow h a e o in luenza A/H3N2 cases in he cu en season is sligh ly highe
han in p e ious seasons
We calcula ed weekly exponen ial g ow h a es o cases om WHO FluNe , case coun s in
England om he Respi a o y Da aMa sys em, and an ILI+ indica o cons uc ed om he Royal
College o Gene al P ac i ione s Resea ch and Su eillance Cen e da a (Figu e S1-2). We
compa ed aw and modelled g ow h a es om he cu en in luenza season o p e ious seasons,
using bo h gene alised addi i e models (GAMs) and a penalised spline model desc ibed by Eales
e al. (Figu e 1A, Figu e S3-S5) [20].
Using da a om WHO FluNe , and aligning he epidemic cu es o he epidemic peak ac oss
di e en seasons, he 2025/26 season o da e shows an ea lie peak (epidemiological week 40 s.
49, 49, and 47) and a as e A/H3N2 peak weekly g ow h a e (pos e io means and 95% C I: 0.680
[0.503-0.871] s 0.0886 [-0.0577-0.238], 0.388 [0.264-0.515] and 0.592 [0.493-0.708]) compa ed
o he 2024/25, 2023/24 and 2022/23 seasons ( espec i ely) (Figu e 1B). Model i s o e laid on
he empi ical g ow h a es a e shown in Figu e S6. We no e ha he choice o smoo hing model is
has a ela i ely la ge impac on he es ima ed g ow h a es due o he amoun o noise in he da a,
and hus we p esen an al e na i e i using a Gaussian andom walk, no ing ha he peak
es ima ed A/H3N2 g ow h a e o he cu en season is highe unde his model (Figu e S7).
Simila ela i e ends we e obse ed using he RCGP RSC da a (Figu e S8).
Compa ing g ow h a es using all in luenza cases (i.e., agg ega ing A/H3N2, A/H1N1pdm09,
unsub yped in luenza A, and in luenza B) sugges s ha he o e all peak in luenza g ow h a e is
compa able o p e ious seasons (Figu e S9&S10). The 2025/26 season o da e has a peak on
epidemiological week 40 compa ed o weeks 49, 49 and 49 in he 2024/25, 2023/24 and 2024/25
seasons espec i ely. The 2025/26 season a peak weekly g ow h a e o ‘all in luenza’ o 0.482
(pos e io mean; 95% C I: 0.385-0.584) compa ed o 0.528 (0.476-0.582), 0.584 (0.526-0.647) and
0.548 (0.505-0.593) o he 2024/2025, 2023/2024 and 2022/2023 seasons ( espec i ely). The
dominan sub ype om each p io season back o 2014/15 is shown in Table 1.
Figu e 1. G ow h a e es ima es o A/H3N2 cases om he WHO FluNe da abase using he penalised
spline model. Colou ed lines and shaded egions show pos e io mean and 95% c edible in e als o he
model-es ima ed weekly g ow h a e. Colou ing dis inguishes he cu en season om pos , p e and du ing
COVID-19 pandemic seasons. The doubling ime co esponding o he g ow h a e is shown on he igh
hand y-axis.
Table 1. Summa y o dominan in luenza A sub ypes by season (de i ed om UKHSA hospi al yping da a
[21], In luenza | UKHSA da a dashboa d).
Season
Dominan sub ype
2014/15
A/H3N2
2015/16
A/H1N1pdm09
2016/17
A/H3N2
2017/18
A/H3N2
2018/19
A/H1N1pdm09
2019/20
A/H3N2
2020/21
N/A – COVID-19 pandemic
2021/22
A/H3N2
2022/23
A/H3N2
2023/24
A/H1N1pdm09
2024/25
A/H1N1pdm09
2025/26 (cu en )
A/H3N2
Figu e 2. G ow h a e es ima es using a penalised spline model. School holidays a e ma ked wi h e ical
g ey ba s. The au umn hal - e m b eak in 2025 is ma ked in ed. Solid lines and ibbons show pos e io
means and 95% c edible in e als. We no e ha his is he da e o he au umn hal - e m ac oss mos English
schools, bu he e is a sligh a ia ion in some egions and schools Weekly log g ow h a es calcula ed
di ec ly om he da a a e shown in ain colou ed lines o isually e alua e model i .
Age-s a i ied g ow h a es highligh much highe g ow h in child en han adul s
We obse ed subs an ially highe ecen g ow h a es o A/H3N2 cases in he 1-4 and 5-14 yea old
age g oups compa ed o adul s and adolescen s (Figu e 2, Figu e S11). The di e ence in A/H3N2
weekly g ow h a es be ween child en and he 15-44 yea old age g oup was a highe han has
been obse ed in he p io wo in luenza seasons (Table 2, Figu e S12). A subs an ial d op in
g ow h a es was obse ed p eceding and du ing he ecen Au umn hal - e m school b eak,
consis en wi h p e ious yea s and wi h he known ole o school con ac s in d i ing in luenza
sp ead (Figu e 2). Howe e , we ha e so a only been able o ob ain an age-s a i ied ILI+ indica o
o A/H3N2 cases going back o he s a o he 2023/2024 in luenza season, which limi s ou abili y
o compa e age-speci ic ends o p e ious A/H3N2 seasons. Compa ison o hese age-s a i ied
g ow h a es o p e ious seasons should he e o e be in e p e ed cau iously un il his o ical da a can
be included.
Table 2. Values shown a e he absolu e di e ence in he pos e io mean es ima ed peak weekly g ow h a e
be ween he shown age g oup (yea s o age) and he 15-44 yea old age g oup.
Season
1-4
5-14
45-64
65+
2023 o 2024
0.20
0.31
0.10
0.25
2024 o 2025
0.15
0.19
0.10
0.14
2025 o 2026
0.49
0.58
0.11
0.19
Es ima es o he ime a ying ep oduc ion numbe sugges a simila peak in ec ion a e o
p e ious seasons
We used he WHO FluNe da a om 2015 o 2025 o es ima e he ime a ying ep oduc ion
numbe , R . No e ha he e we dis inguish R om he e ec i e ep oduc ion numbe , Re, which we
de ine as he ep oduc ion numbe a he s a o he season. Ac oss he in luenza seasons
2015/16, 2016/17, 2017/18, 2018/19, 2021/22, 2022/23, 2023/24, 2024/25, and 2025/26, he
es ima ed ime- a ying ep oduc ion numbe R gene ally emained close o 1, wi h in e mi en
luc ua ions d opping below 1 and occasionally eaching alues abo e 1.4 (Figu e 3). When
ajec o ies we e aligned ela i e o he p e-Ch is mas pe iod (be o e Decembe 25), peak R
alues consis en ly occu ed be ween ea ly Oc obe and app oxima ely Decembe 20 ac oss all
seasons examined (Figu es 4, Figu e S13). No ably, pos -COVID-19 pandemic seasons exhibi ed
ela i ely s able R ajec o ies, and he 2025/26 season was in line wi h p e ious seasons, wi h R
es ima es no exceeding 1.4 (pos e io mean; 95% c edible in e als: 1.22, 1.47). This sugges s
ha he o e all dynamics o he mos ecen season (2025/26) we e b oadly simila o hose o
p e ious seasons.
Fo compa ison we also es ima ed he cu en Re in Japan, which a ime o w i ing has been
expe iencing a longe pe iod o exponen ial g ow h d i en by clade K han England has. We
ob ained poin es ima es o 9.16 days o he doubling ime and 1.26 o Re.
Figu e 3: Top panel: Daily incidence combining all in luenza sub ypes o in luenza seasons 2015-16,
2016-17, 2017-18, 2018-19, 2022-23, 2023-24, 2024-25, and 2025-26. The daily incidence cu es we e
de i ed by smoo hing he weekly case coun s ob ained om he WHO FluNe dashboa d. Bo om panel:
Es ima ed e ec i e ep oduc ion numbe s o he same seasons using he da a in he op panel wi h he
EpiEs im R package. Ho izon al dashed lines show R =1, 1.2 and 1.4 o e e ence. All lines a e shaded by
he dominan sub ype ha season as shown in Table 1.
Figu e 4: E ec i e ep oduc ion numbe (R ) o each in luenza season a anged ela i e o peak
p e-Ch is mas R . As in Figu e 3, bu aligning he cu es o he da e o peak R iden i ied be ween June and
be o e Decembe 25 o ha yea . All seasons we e aligned ela i e o hei peak da e by calcula ing he
numbe o days since he peak. The da e and es ima ed alue o he peak R a e shown in each subplo .
Plo s a e colou ed by hei iming wi h espec o he COVID-19 pandemic. No e ha we ha e excluded he
COVID-19 pandemic yea s (2019/20 and 2020/21) whe e in luenza ac i i y was se e ely dis up ed.
holidays – he hal - e m holiday can ac as a ci cui b eake , dampening he peak and sp eading
cases o e a longe pe iod o ime. All o ou scena ios place peak incidence p io o he Ch is mas
holiday when inc eased mixing ac oss age g oups is expec ed, educing he oppo uni y o
ansmission in o olde indi iduals.
This wo k p esen ed he e aims o make wo con ibu ions o si ua ional awa eness. Fi s , we aimed
o add ess wo key unknowns ea ly in he in luenza season in England: 1) whe he ea ly
epidemiological da a a e consis en wi h p edic ions om immunological and genomic da a; and 2)
iden i ying he ange o po en ial epidemic dynamics compa ible wi h cu en incidence ends.
These ypes o analyses we e used widely du ing he COVID-19 pandemic [34,35], bu ha e since
become less common o seasonal espi a o y diseases. The analyses pe o med he e a e
ela i ely s aigh o wa d and quick, using da a which a e al eady ou inely collec ed. Second, o
unde s and and suppo he model ou comes, we ha e se ou o design an in e ac i e isualisa ion
ool ha we made a ailable online. Gi en ha he model has a la ge numbe o pa ame e s, a la ge
numbe o scena io analysis can be explo ed. De ising a compac isualisa ion ool o cap u e he
possibili y o di e en model ou comes allows use s o explo e scena ios o in e es ha can enable
insigh s o be d awn on possible p epa edness measu es and in o m policymake s o di e en
esponse op ions.
Regula upda ing o da a analyses o espi a o y i us dynamics would achie e h ee bene i s:
imp o emen s o da a lows and schemas; imp o emen s o analy ical me hods; and mos
impo an ly, easy con ex ualisa ion o sudden change, such as he appea ance o he cu en K
s ain o in luenza. Fo unde s anding he signi icance o such changes o heal h and heal h
sys ems, sys ems and decision making ools such as he Shiny app p esen ed he e should be
main ained egula ly and upda ed ea ly in he season o ule in o ou di e en scena ios.
Main aining he oolki shown he e equi es low- esou ce bu consis en inpu om echnical
specialis s, and eal- ime access o absolu e epo ed case numbe s a he han jus pe cen age o
es s posi i e o in luenza.
Ou analyses ha e a numbe o limi a ions, some due o limi a ions in da a, and some due o he
apid na u e o ou analysis. Fo he epidemiological analyses, we combined da a om mul iple
sou ces (UKHSA epo s, RCGP RSC, WHO FluNe , Respi a o y Da aMa ). These da a sou ces
each ha e hei own limi a ions in ep esen a i eness and epo ing algo i hms [36], and ou
analyses equi ed addi ional assump ions o align age g oups and da es. G ow h a e and R
es ima es a e also possibly biased by changes in es ing in ensi y and epo ing a es be ween age
g oups. When es ima ing g ow h a es, we used a penalised spline model o smoo h he incidence
cu e, which may mask ue sudden changes in g ow h a es. Fo he R analyses, we used WHO
FluNe non-sen inel su eillance da a, which also ha e ca ea s a ound ep esen a i eness and
es ing in ensi y, and used all in luenza posi i e samples, which will mask sub ype-speci ic
ansmission a es. We also smoo hed he incidence da a o help wi h model con e gence, which
again migh mask genuine luc ua ions in ansmission a es. We also no e ha o e con iden
es ima es om small sample sizes a e a known issue wi h EpiEs im. All o he da a used we e
epo ed weekly, which migh obscu e model inely esol ed e ec s. Di ec access o he UKHSA
and RSGP in luenza da a would ha e po en ially gi en us a mo e g anula da ase , and i his we e
a ailable in u u e, ou analyses can be easily epea ed.
The model used o scena io analyses is also hea ily ca ea ed, as we did no pe o m a o mal
model i due o ime cons ain s. Ins ead, we chose ixed pa ame e alues based on commonly
assumed in luenza pa ame e s (R0, in ec ious pe iod, inal size), and hen manually calib a ed
o he pa ame e s (e.g., epo ing a es, age-speci ic symp oma ic ac ion, seed da e and size) o
achie e a easonable isual i o he 2022/23 in luenza incidence da a. Assump ions ega ding
age-speci ic immuni y, immune escape, and all-o -no hing immuni y in wo classes a he han
s a i ied immuni y ([37]) all ha e a la ge impac on he p ojec ed incidence cu es, and we
he e o e ecommend using he ool o in o m a gene al unde s anding o he sys em a he han
p edic ions. A key omission is accina ion, which we did no include due o se e e challenges in
pa ame e ising age-speci ic accine e icacy agains in ec ion and disease. The po en ial
in e ac ion o he ea ly season wi h he ime aken o achie e high accine co e age in high isk
popula ions may be impo an . Ou model is also limi ed by he use o ou da ed con ac da a, and
also s ong assump ions su ounding beha iou changes in school holidays and he Ch is mas
pe iod. Al hough we a e con iden ha hese assump ions cap u e gene al ends, mo e ecen and
well-calib a ed pa ame e alues would likely esul in di e en epidemic ends.
I is impo an o no e ha in his epo we ha e only conside ed da a om England. Sco land,
Wales and No he n I eland ha e all expe ienced a la e s a o he in luenza season, and hus ou
scena ios wi h hal - e m ac ing as a ci cui b eake may be less ele an since he iming o
hal - e m da es di e be ween he ou UK na ions. Fu he mo e, a la e s a o he season wi h
mode a e immune escape o inc eased ansmissibili y may esul in much highe incidence du ing
he Ch is mas pe iod, which may ansla e in o highe bu den in he elde ly. Wi hin he isualisa ion
in e ac i e ool, use s can upload al e na i e da ase s and change he popula ion size as well as
al e di e en model pa ame e s o c ea e he scena io analyses. Hence i is possible o explo e
addi ional scena ios o unde s and possible dynamics in Sco land, Wales and No he n I eland,
which will be impo an o explo e in he u u e h ough collabo a ion wi h policymake s in hese
na ions.
In summa y, we ha e combined publicly a ailable in luenza da a o England wi h an age-s a i ied
Suscep ible-In ec ed-Reco e ed model and an in e ac i e isualisa ion web ool. Ou analysis
shows ha compa ed o p e ious yea s, he epidemic g ow h a e is high bu no excep ional.
Modelling analysis sugges s ha he epidemic ajec o y so a is consis en wi h a mos modes
educ ion in popula ion immuni y compa ed o p e ious yea s. Inc eases in ansmission do no
always ansla e o bigge epidemics because o he in e ac ion be ween epidemic dynamics and
school holidays. We p o ide a ange o scena ios and an in e ac i e scena io-explo e app, ha
show he impac o di e en assump ions on he epidemic cu e o he coming mon hs.
Me hods
Epidemiological analyses
Da a summa y
The ideal da ase o unde s anding in luenza epidemiological ends would be an unbiased
measu e o symp oma ic A/H3N2 in ec ion incidence s a i ied by age. Howe e , i is no possible o
ob ain his exac da ase due o biases in es ing beha iou and co e age, limi a ions o da a
epo ing, and es ic ions on public sha ing. Ins ead, in luenza su eillance in England consis s o
mul iple indica o s om di e en sou ces, anging om p ima y ca e h ough o eme gency
depa men isi s. Following ecommenda ions om [18], ou main aim was o de elop an ILI+
indica o o each age g oup o in e es , calcula ed as:
𝐼𝐿𝐼+=𝐼𝐿𝐼*𝑝+𝑣𝑒*𝑝𝐴/𝐻3𝑁2
Whe e is he p opo ion o all es s done which a e posi i e o in luenza and is he
𝑝+𝑣𝑒 𝑝𝐴/𝐻3𝑁2
p opo ion o all posi i e in luenza es s which a e a ibu ed o A/H3N2.
In he ime ame o his analysis, we we e unable o cons uc one consis en da ase o use in all
analyses and we he e o e pieced oge he di e en da a se s o gene a e as close o an ILI+
indica o by age as possible. We in end o u u e i e a ions o his analysis o simpli y his p ocess.
In b ie , we used da a on in luenza cases by age g oup om he Royal College o Gene al
P ac i ione s (RCGP) Resea ch & Su eillance Cen e (RSC), da a on ILI om he Respi a o y
Da aMa sys em, and da a o he pe cen age o in luenza cases posi i e o A/H3N2 in luenza
om he Second-Gene a ion Su eillance Sys em (SGSS) (Figu e S1). We mul iplied hese
da ase s oge he o ob ain: 1) an ILI+ indica o by age g oup going back o 2023; 2) an es ima e o
absolu e in luenza cases (all sub ypes) o e ime going back o 2009; 3) and an an es ima e o
age-s a i ied in luenza cases (all sub ypes) o he 2022/23 season (see:
h ps://hay-idd.shinyapps.io/ModelFluUk-H3N2/). Fu he de ails on da a p ocessing a e p o ided in
he Supplemen a y Ma e ial.
As a compa a o da ase , we also ob ained weekly coun s o epo ed in luenza specimens
s a i ied by sub ype ob ained om he WHO FluNe pla o m [19]. All da a used a e agg ega ed
weekly and we used he inal da e o he epidemiological week as he epo ed da e.
Fo he calcula ion o Re o Japan, we used weekly cases coun s epo ed a
h ps://wea he news.jp/news/202511/210136/ ex ac ed on 24/11/2025 ( alues ansla ed as “The
numbe o epo s om ixed-poin medical ins i u ions o e he pas week”). We included alues
epo ed as being om 28/09/2025 (be o e which g ow h appea ed sub-exponen ial) un il
16/11/2025 ( he la es a ailable) inclusi e. We ook he gene a ion ime dis ibu ion o be gamma
dis ibu ed wi h he mean and s anda d de ia ion epo ed in (Chan e al. 2024): 3.2 days and 2.1
days espec i ely.
Weekly g ow h a e calcula ions
Weekly g ow h a es we e calcula ed o each in luenza season and aligned by calenda week as:
𝑦=𝑙𝑜𝑔( 𝑖(𝑡)
𝑖(𝑡−1))
Whe e is he epo ed incidence o e week . We hen p oduced smoo hed weekly g ow h a e
𝑖(𝑡)
cu es using wo me hods:
1. Fi ing a penalised smoo hing spline model o epo ed incidence da a using he Bayesian
me hod desc ibed by Eales e al [20]. We used he EpiS ainDynamics package using
penalised splines wi h deg ee 3 and 3 weeks pe kno [38]. We ound ha he model was
uns able wi h low case coun s, and hus o age-s a i ied g ow h a e es ima es we i s
a i icially in la ed he coun s 10- old be o e i ing he model. Thus, unce ain y is likely
un ep esen ed.
2. Fi ing a Gene alised Addi i e Model (GAM) using he mgc R package p edic ing log
weekly g ow h a e as a unc ion o ime, placing a penalised smoo hing spline a basis
dimension o up o 5 [39].
Time- a ying ep oduc ion numbe es ima ion
We es ima ed he ime- a ying e ec i e ep oduc ion numbe (R
) using he EpiEs im package in R,
which implemen s he me hod desc ibed by Co i e al. [40]. We used he o e all weekly in luenza
incidence da a o he pe iod 2015–2025 om he WHO FluNe da abase o his analysis. To
app oxima e daily incidence, weekly coun s we e disagg ega ed by dis ibu ing he cases e enly
ac oss days pe week, ollowed by applica ion o a 14-day olling mean o smoo h sho - e m
luc ua ions.
The se ial in e al dis ibu ion was assumed o ollow a dis ibu ion wi h a mean o 3.6 days and a
s anda d de ia ion o 1.6 days, based on [41]. R was compu ed o e sliding weekly windows o
cap u e empo al a ia ion in ansmission po en ial. The esul ing R ajec o ies we e isualised o
compa e epidemic dynamics ac oss seasons, highligh ing di e ences in ansmissibili y and
po en ial shi s in seasonal pa e ns o e he s udy pe iod. In his analysis, we assumed ha a
ypical lu season s a s on Sep embe 1s each yea .
Fo he es ima ion o Re o Japan, we i s es ima ed he exponen ial g ow h a e using a simple
linea eg ession model o log(cases) agains da e epo ed. We hen es ima ed Re using he
ela ionship implied by he enewal equa ion [42].
𝑅𝑒=1/0
∞
∫ω(τ)𝑒−𝑟τ𝑑τ
Compa men al model and scena io analyses
Model o e iew
We simula ed seasonal in luenza ansmission dynamics o England using an age- and
immuni y-s uc u ed de e minis ic Suscep ible-In ec ed-Reco e ed model. We di ided he
popula ion in o ou age g oups (0-4, 5-18, 19-64 and 65+ yea s; No e ha in an s unde 1 yea
we e excluded, as we did no ha e age-s a i ied A/H3N2 ILI+ da a o his age g oup) and wo
immuni y classes ( ully suscep ible and pa ially immune). Con ac a es wi hin and be ween age
g oups we e de i ed om he POLYMOD s udy using he socialmix R package [43,44]. To accoun
o changes in con ac a es ou side o school e ms, we esampled om he o iginal POLYMOD
da a o scale con ac a es du ing he hal e m holiday, p e-Ch is mas pe iod, and he Ch is mas
school holidays (desc ibed below). Fo each age g oup, we acked he o e all incidence o
in ec ions, symp oma ic cases and in ec ions pe week. We in o mally calib a ed he model o
epo ed o e all in luenza case da a om he 2022/23 season o p o ide a baseline, and pe o med
scena io analyses a ying key model pa ame e s o gene a e plausible scena ios o he 2025/26
season.
Model s uc u e
The o ce o in ec ion in g oup i was de ined as:
λ𝑖(𝑡)=β𝑗=1
𝑚
∑𝐶𝑖,𝑗(𝑡)𝐼𝑗(𝑡)
Whe e β is he o e all ansmission a e (no age-s a i ied), Ci,j is he con ac a e be ween g oup i
and g oup j, and Ij is he numbe o in ec ed indi iduals in g oup j a ime .
T ansi ion a es be ween he h ee compa men s we e de ined by he ollowing se o o dina y
di e en ial equa ions:
𝑑𝑆𝑎,𝑘
𝑑𝑡 =−α𝑘𝑆𝑎,𝑘(𝑡)λ𝑎,𝑘(𝑡)
𝑑𝐼𝑎,𝑘
𝑑𝑡 =α𝑘𝑆𝑎,𝑘(𝑡)λ𝑎,𝑘(𝑡)−𝐼𝑎,𝑘(𝑡)
𝑇𝑔
𝑑𝑅𝑎,𝑘
𝑑𝑡 =𝐼𝑎,𝑘(𝑡)
𝑇𝑔
Whe e ɑk deno es he ela i e suscep ibili y o immune class k and Tg is he in ec ious pe iod. No e
ha ɑk was se o 0 o he immune popula ion, ep esen ing all-o -no hing immuni y. Leaky
immuni y (ɑk>0) leads o e y dynamics. We sol ed he model in daily imes eps using he deSol e
R package [45].
Immuni y, ini ial condi ions and seeding
We se he popula ion size o he model o 60,000,000, co esponding o he popula ion size o
England. We dis ibu ed he popula ion in o age g oups based on he age dis ibu ions e u ned by
he socialmix package using he POLYMOD da a. Each age g oup was hen s a i ied in o he
suscep ible o ully immune class using a ying p opo ions o cap u e di e en le els o immune
escape o pa icula age g oups. An addi ional immune escape mul iplie , δ, was in oduced o
scale he o e all popula ion immune p opo ion (δ=0 co esponds o comple e immune escape,
whe eas δ=1 co esponds o no loss o popula ion immuni y).
The epidemic was seeded by se ing Ia’(0) = s and Sa’(0) = Sa(0) - s, whe e s is he ini ial seed size
and Sa(0) is he numbe o indi iduals o age g oup a who a e ini ially suscep ible. No e ha i is
possible o a y he seed size, da e and age g oup. We kep seeding in he younges age g oup a
1000 ini ial in ec ions in all scena ios, a ying only he ini ial seed size.
Con ac ma ices o e ime
Base con ac ma ices we e calcula ed om he POLYMOD UK da a agg ega ed o he ou age
g oups (0 o 5, 5 o 18, 18 o 65 and 65+ yea s). We gene a ed ou con ac ma ices o di e en
pe iods o ime: 1) egula school e m- ime; 2) hal - e m wi h no school con ac s and educed
school con ac s; 3) p e-Ch is mas shopping pe iod (1-15 Decembe ) wi h an o e all inc ease in
non-school con ac s; and 4) he Ch is mas school holiday pe iod wi h no school con ac s, a
educ ion in all con ac s, and a subs an ial inc ease in a -home con ac s. These ou ma ices we e
cons uc ed by esampling he o iginal POLYMOD con ac dia y en y da a om he socialmix R
package wi h eplacemen and applying mul iplie s o home, wo k and o he con ac ypes. Holiday
da es we e based on he Ox o dshi e school holiday pe iod, hough we no e ha holiday da es a y
o e he coun y, and e en mo e so o e he UK. Fo all non-school con ac s, he ela i e changes
in con ac s o e hal - e m holidays and he Ch is mas pe iod (shopping and holiday) we e
ex apola ed om 2021-2023 da a om Kendall e al. Science 2024 (see Figu es 5A and 7B in he
pape ) [33]. Absolu e changes in o e all non-school con ac a es we e ex apola ed om he same
sou ce (see Figu es 1A, 7A in he pape ).
To ansi ion be ween hese ou di e en con ac ma ices, we gene a ed a single con ac ma ix
o each day, aking a weigh ed a e age o he ou ma ices depending on he ime. Fo example,
con ac s in he middle o he school e m we e en i ely go e ned by he e m- ime ma ix (weigh ing
o 1, all o he ma ices weigh ing 0), whe eas con ac s in he middle o he Ch is mas school
holiday we e go e ned en i ely by he Ch is mas school holiday ma ix. To ensu e smoo h
ansi ions be ween hese con ac pa e ns, we smoo hed he ansi ion o weigh ings o e 7 days
be o e and a e he holiday pe iod using a cosine unc ion.
Baseline model calib a ion
Model pa ame e s we e chosen based on s anda d seasonal in luenza pa ame e alues (R0 o 2,
in ec ious pe iod o 4-5 days, and inal size o a ound 15% [46]), in ui ion and manual calib a ion o
gene a e seasonal dynamics simila o wha was seen in he 2022/23 season. We no e ha his is
a complex model wi h a la ge numbe o pa ame e s, making o mal model i ing ex emely di icul .
Some o he pa ame e s a e ha d o iden i y and in e p e , such as he o e all ac ion o
symp oma ic cases epo ed, he symp oma ic ac ion by age combined wi h age-speci ic epo ing
a es, and he le el o immune escape o he seed i us. Pa ame e alues used o he baseline
scena io a e shown in Table 4.
Scena io analyses
Scena io analyses we e chosen o illus a e po en ial hypo heses o he ea ly and apid g ow h o
A/H3N2 cases in England o he 2025/26 season. We also a ied he immune escape scaling
pa ame e δ, he basic ep oduc ion numbe R0, he p opo ion o he 0-4 and 5-18 yea old
popula ion ini ially immune, and he seed da e we e a ied in a iably o gene a e Figu e 6.
Implemen a ion
All analyses we e implemen ed and un in R e sion 4.2.2. The compa men al model was also
implemen ed as a Shiny app wi h use - iendly slide s o change key pa ame e alues, a ailable
a : h ps://hay-idd.shinyapps.io/ModelFluUk-H3N2/.
Table 4. Model pa ame e s assumed o he baseline scena io. These a e he de aul pa ame e s
in he in e ac i e web ool.
Pa ame e
Assumed alue
R0: basic ep oduc ion numbe
2
Tg: in ec ious pe iod
4 days
γ: immune escape mul iplie
1
Seed da e
10 h Sep embe
Seed size in age g oup 1 (0-4 y s)
1000
Popula ion size
60,000,000
P opo ion o wo k con ac s kep in school holidays
0.75
Mul iplie o home con ac s in school b eaks
1
Mul iplie o non-school and non-wo k con ac s in
school b eaks
1.1
Mul iplie o all non-school con ac s in Ch is mas
pe iod (1-15 Decembe )
1.3
P opo ion o all con ac s kep o e Ch is mas
0.67
Mul iplie o home con ac s o e Ch is mas holiday
3
P opo ion ini ially immune (0-4 y s)
0.3
P opo ion ini ially immune (5-18 y s)
0.6
P opo ion ini ially immune (19-64 y s)
0.7
P opo ion ini ially immune (65+ y s)
0.75
Symp oma ic ac ion and epo ing a e (0-4 y s)
0.05
Symp oma ic ac ion and epo ing a e (5-18 y s)
0.2
Symp oma ic ac ion and epo ing a e (19-64 y s)
0.35
Symp oma ic ac ion and epo ing a e (65+ y s)
0.45
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Figu e S5. Compa ison o weekly g ow h a e es ima es using he EpiS ainDynamics R package
i ed o UKHSA (Respi a o y Da aMa ) and WHO FluNe samples. Shaded ibbons show pos e io
means, 50% and 95% c edible in e als. Es ima es du ing he COVID-19 pandemic a e no shown. The op
panel shows weekly g ow h a es o A/H3N2 samples. The bo om panel shows he weekly g ow h a e o all
in luenza samples.
Figu e S6. Fi s o he penalised spline model o empi ical weekly g ow h a es om he WHO FluNe
da a. Pu ple lines and ibbons show pos e io mean and 95% C I. The blue line shows he aw log weekly
g ow h a es. The yellow line shows he aw log weekly g ow h a es smoo hed o e 4-week in e als ( igh
aligned).
Figu e S7. Fi s o he andom walk model o empi ical weekly g ow h a es om he WHO FluNe da a
using only A/H3N2 cases. Pu ple lines and ibbons show pos e io mean and 95% C I. The blue line shows
he aw log weekly g ow h a es. The yellow line shows he aw log weekly g ow h a es smoo hed o e
4-week in e als ( igh aligned).
Figu e S8. G ow h a e es ima es using a penalised spline model ma ching Figu e 2, bu ins ead aligned by
he week o peak g ow h a e as x=0.
Figu e S9. G ow h a e o all in luenza cases om he WHO FluNe da abase. Colou ed lines and
shaded egions show pos e io mean and 95% c edible in e als o he model-es ima ed weekly g ow h a e.
Colou ing dis inguishes he cu en season om pos , p e and du ing pandemic seasons. Doubling ime is
shown on he igh hand y-axis.
Figu e S10. Fi s o he andom walk model o empi ical weekly g ow h a es om he WHO FluNe
da a using all in luenza cases. Pu ple lines and ibbons show pos e io mean and 95% C I. The blue line
shows he aw log weekly g ow h a es. The yellow line shows he aw log weekly g ow h a es smoo hed
o e 4-week in e als ( igh aligned).
Figu e S11. G ow h a e es ima es o age-s a i ied A/H3N2 cases om he ILI+ indica o ma ching
Figu e 2. Shown a e he empi ical g ow h a es and model i s using he GAM. School holidays a e ma ked
wi h g ey ba s. The au umn hal - e m b eak (i.e., he ecen school holiday) is ma ked in ed. Solid lines and
ibbons show mean es ima es and 95% con idence in e als.
Figu e S12. Compa ison o age-s a i ied g ow h a es om he ILI+ indica o by season. Lines show
he pos e io mean es ima es om he penalised spline model in Figu e 2. Es ima es om each season a e
aligned o he week since he s a o he in luenza season. The g ow h a e di e ence is calcula ed as he
absolu e di e ence be ween he g ow h a e in he ocal age g oup o he 15-44 yea old age g oup, such ha
a line signi ican ly abo e 0 indica es much highe g ow h a es han younge adul s.
Figu e S13. E ec i e ep oduc ion numbe (R
) o each in luenza season a anged ela i e o peak
p e-Ch is mas R . Es ima es shown a e iden ical o Figu e 4, bu plo ed oge he o enable isual
compa ison.
Figu e S14. Compa ison o symp oma ic in luenza incidence in 65+ om he scena io analyses
shown in Figu e 5.
