How important is the acute phase in HIV epidemiology?

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1 How importat is the acute phase i HIV epidemiology? Bria G. Williams South Africa Cetre for Epidemiological Modellig ad Aalysis (SACEMA), Stellebosch, Wester Cape, South Africa Correspodece should be addressed to BW at BriaGerardWilliams@gmail.com Abstract At preset, the best hope for elimiatig HIV trasmissio ad brigig the epidemic of HIV to a ed lies i the use of ati-retroviral therapy for prevetio, a strategy referred to variously as Test ad Treat (T&T), Treatmet as Prevetio (TasP) or Treatmet cetred Prevetio (TcP). Oe of the key objectios to the use of T&T to stop trasmissio cocers the role of the acute phase i HIV trasmissio. The acute phase of ifectio lasts for oe to three moths after HIVserocoversio durig which time the risk of trasmissio may be te to twety times higher, per sexual ecouter, tha it is durig the chroic phase which lasts for the ext te years. Regular testig for HIV is more likely to miss people who are i the acute phase tha i the chroic phase ad it is essetial to determie the extet to which this might compromise the impact of T&T o HIVtrasmissio. Here we show that ) provided the iitial epidemic doublig time is about.0 to.5 years, as observed i South Africa, radom testig with a average test iterval of oe year will still brig the epidemic close to elimiatio eve if the acute phase lasts for 3 moths durig which time trasmissio is 26 times higher tha i the chroic phase; 2) testig people regularly at yearly itervals is sigificatly more effective the testig them radomly; 3) testig people regularly at six mothly itervals ad startig them o ART immediately, will almost certaily guaratee elimiatio. I geeral it seems ulikely that elevated trasmissio durig the acute phase is likely to chage predictios of the impact of treatmet o trasmissio sigificatly. Other factors, i particular age structure, the structure of sexual etworks ad variatio i set-poit viral load are likely to be more importat ad should be give priority i further aalyses. Itroductio We ca estimate the relative risk of ifectio durig the acute ad chroic stages of ifectio i two ways. We ca estimate it idirectly if we have data o the viral load i the acute ad chroic stages ad data o the probability of a trasmissio evet as a fuctio of viral load. -6 We ca estimate it directly if we have a sero-icidet cohort with a short follow up time ad if we ca measure the umber of ifectio evets i each stage. 8 Both methods require a sero-icidet cohort ad repeated measuremets of the viral load. Cohort data are always difficult to obtai ad cohorts of discordat couples will become icreasigly biased with time as those that are most likely to ifect their parters do so ad are removed from the cohort. Nevertheless, these are the data that we have. Idirect estimates We first ask: how does viral load vary from iitial ifectio through sero-coversio ad the acute phase to the chroic phase ad evetually to the fial phase shortly before death? The most useful data i this regard, based o two sets of archived samples from HIV ifected plasma doors, are from Fiebig et al. 7 Figure shows the observed media values of viral load as a fuctio of time sice ifectio. 7 The fitted (gree) lie is { ( α, δ ) [ β ( β)( α, δ )] } V = N l t + l t 2 2 where V is the viral load, t is the time sice ifectio ad Log0(viral load/mm3) α ( t δ ) e lt ( αδ, ) =. 2 α ( t δ ) + e Time/days Figure. Media values of viral load as a fuctio of time sice ifectio. 7 Error bars are 95% cofidece limits o media values. Gree lies: maximum likelihood fit (see text); red lies 95% cofidece bads. Data for idividuals (ot show) vary by about ±.5 logs. I Equatio 2, N scales overall trasmissio up or dow, the first logistic fuctio l i the curly brackets icreases with time at a rate α reachig half the maximum value at time δ, the secod decreases with time at a rate α 2 reachig half the Acute phase /7 2/0/20

2 maximum value at time δ 2. β is the asymptotic value to which the viral load coverges durig the chroic phase. I short, the viral load icreases at a rate α to a peak value from which it coverges dowwards at a rate α 2 to a asymptote at β. The media value of the log 0 (viral load) durig the chroic phase is 4.09 ± 0.3 ad at the peak of the acute phase is 5.45 ± 0.5. The acute phase lasts from day 8 to day 70 after sero-coversio so that the duratio of the acute phase, D AP = 62 days, durig which time the average value of the media viral load is 4.73 ± 0.02 for a average icrease of 0.7 logs or a factor of = 5.0 ( ) over the value durig the chroic stage of ifectio. T = αρv so that the probability of ifectio per virio per mm 3 is αρ, trasmissio saturates at α trasmissios per year ad we ca defie V*, the viral load time at which trasmissio saturates, as the itercept of the iitial liear icrease with the asymptotic value so that V* =. 4 ρ The fits i Figure 2 give the values i Table. Allowig for the small amout of over-dispersio i the estimates we see that for low viral loads the probability of ifectio is ( ) times the viral load per mm 3 ad at high viral loads trasmissio saturates whe the viral load is 4.37±0.29 logs. We ca ow estimate the probability of trasmissio at the peak of the acute phase, whe the log 0 (media viral load) is 5.45, ad i the chroic phase, whe the log 0 (media viral load), usig each of the three data sets. The ratio of the pairs of estimates gives RR, the relative risk of ifectio, per uit time, i the acute ad the chroic phase as RR = 2. (. 3.9). Table. The viral load at which trasmissio saturates; the probability of ifectio per virio per mm 3 ; ad the relative risk (RR) of ifectio i the acute ad chroic phases. Referece Log0(sat. viral load/mm 3 ) (Prob. ifectio/ virio/mm 3 /yr) 06 RR acute v. chroic phase Attia 4.05 ± ( ).4 ( ) Doell ± ( ) 2.5 ( ) Ligappa ± ( ) 3.4 (.0.3) Average 4.37 ± (.4 5.3) 2. (. 3.9) Figure 2. HIV trasmissio probability per year as a fuctio of viral load. A: Attia et al.; B: Doell et al.; 3 C: Ligappa et al. 6 Sigificace levels for the fitted lies are A: 0.778; B: 0.376; C: 0.0. If we assume a power law relatioship betwee trasmissio ad viral load the sigificace levels for the best fit curves are A: ; B: 0.302; C: There are three sets of data o the risk of ifectio per uit time as a fuctio of viral load,3,6 (Figure 2). The simplest model of the relatioship betwee viral load ad trasmissio assumes that the former icreases liearly with the latter (but see also Appedix ). However, the data suggest that trasmissio saturates at high viral load ad we therefore assume a relatioship of the followig form: ρv ( e ) T = α 3 where T is the probability of trasmissio per year. At low viral loads trasmissio icreases liearly as Direct estimates The most widely cited direct estimates of the relative trasmissio i the acute ad chroic stages of HIV-ifectio are based o the Ugada study of Wawer et al. 8 The most reliable data, i this regard, are those from the icidece cohort i which there were 0 trasmissio evets amog 23 couples who had 22 coital acts i the first six moths after serocoversio ad 2 trasmissio evets amog the remaiig 3 couples who had 33 coital acts i moths 6 to 5 after serocoversio. This gives a relative risk of trasmissio RR = 3.4 ( ). Wawer et al. 8 give a uadjusted estimate of the RR of trasmissio, comparig the acute phase to the prevalet cases, of 8.25 ( ) but sice the risk of trasmissio i prevalet cases is close to half of the risk i icidet cases 6 to 5 moths after sero-coversio, their estimate of the RR, usig those i the icidece cohort who were ifected 6 to 5 moths after sero-coversio, would be 4. (.6 0.). This is still sigificatly higher tha the idirect estimate give above, Acute phase 2/7 2/0/20

3 especially sice the Wawer et al. 8 estimate is averaged over six moths while the estimate made here is averaged over two moths. I order to favour the importace of the acute phase o the epidemic we will use the high estimate from Wawer et al. 8 Now, cosider a cohort of ewly ifected people. Viral load varies cosiderably amog people ifected with HIV. From data o the distributio of viral load i a cross-sectioal study from Orage Farm, South Africa 2 (Bertra Auvert, persoal commuicatio) log 0 (viral load) measuremets rage from 2 to 6 correspodig to a rage i the risk of trasmissio of 00 to 000 times. Allowig for the fact that those with the highest viral load will ifect their parters ad die more quickly, 9 removig them from the pool of sero-discordat couples, the rate of trasmissios will fall by about 50% after five years as show i Figure 4 ad observed by Wawer et al. 8 (See Appedix 2 for details.) Relative risk of trasmissio Time sice ifectio (years) Figure 3. Variatio of ifectiousess as a fuctio of time sice ifectio i a cohort of people. No allowace is made for icreased ifectiousess durig the acute phase but it is assumed that both ifectiousess ad mortality are highest i those with a high set-poit viral load. Holligsworth et al., 0 usig the data provided by Wawer et al., 8 use a modellig approach to determie the relative risk of trasmissio durig the acute ad chroic phases. Their estimate of the duratio of the acute phase is D AP = 2.9 (.2 6.0) moths with RR = 26.2 ( ). At the limits we ca assume that the short estimate of D AP correspods to the high value of RR while the log estimate of D AP correspods to a low value of RR. Assumig that their compariso is with the seroprevalet couples oe might agai reduce the relative risk by a factor of about 2. A ievitable cosequece of these estimates is that R 0 must be close to ad ideed Holligsworth et al. 0 give a estimate of 2.2 uder radom mixig. If this were the case HIV should be much less stable tha it is observed to be ad small improvemets i prevetio should have a substatial impact o the epidemic which is ot see to be the case. Agai, for the purposes of this aalysis, we will use the high estimate from Holligsworth et al. 0 The estimates of D AP ad RR that we will use i this aalysis are give i Table 2. Table 2. Estimates of the duratio of the acute phase, D AP, ad the relative risk of trasmissio, RR, used i this aalysis. D AP (mo.) RR acute/chroic phase This study 2. (. 3.9) Wawer ( ) Holligsworth (.2 6.0) 26.2 ( ) The impact of uiversal testig o trasmissio We ow wish to explore the cosequeces for the differet estimates of the acute phase duratio ad the relative ifectiousess of the acute phase o the impact of T&T o trasmissio. The key poit is this: oe of the few directly observed parameters cocerig the epidemiology of HIV is the iitial doublig time which, i South Africa, is.25 ± Sice the acute phase lasts for cosiderably less time tha the chroic phase, the greater the relative risk of trasmissio i the acute phase the smaller must be the value of R 0 to maitai the same iitial doublig time. Ideed, if we kow the iitial doublig time (the growth rate r i Equatios ad 3 i Appedix 3) ad we kow the relative risk of ifectio i the acute phase ad each of the four chroic phases (β i /β 0 i Equatios 7 to 9 i Appedix 3) ad the duratio of each of the four stages (/ρ i i Equatios 7 to 9 ad 0) i Appedix 3, the we ca determie the values of the each of the idividual ρ i ad hece the value of R 0 (Equatio 0 i Appedix 3). Values of R 0, as a fuctio of the relative risk of trasmissio durig the acute phase ad the duratio of the acute phase i moths, are give i Figure 4A. Without ART the value of R 0 is 5.8 (brow rectagle). With RR = 2. ad D AP = 2 mo. (gree ellipse) R 0 falls to 5.4. With RR = 8.3 ad D AP = 6 mo. (red ellipse) R 0 falls to 3.0. With RR = 26 ad D AP = 6 mo. (blue ellipse) R 0 falls to 2.3. As expected the higher the rate of trasmissio durig the acute phase the lower the value of R 0. The boudaries of the ellipses idicate the ucertaity i the poit estimates which are cosiderable. Assumig, as oted above, that i the Holligsworth et al. 0 study the high values of D AP correspod to low values RR, ad vice versa, we slat the correspodig cofidece ellipse at a appropriate agle. This also serves to show that if we let D AP = 6 mo. The Holligsworth et al. 0 ad the Wawer et al. 8 estimates are ot sigificatly differet. Acute phase 3/7 2/0/20

4 Relative risk Relative risk Relative risk Relative risk Relative risk Relative risk Figure 4. The value of R 0 for a epidemic with a doublig time of 5 moths as a fuctio of the duratio of the acute phase ad the relative trasmissio rate i the acute phase compared to the chroic phase. Colours correspod to differet values of R 0 ad the umbers i circles give the values o differet cotour lies. A without ART; B ad C with radom testig oce a year or twice a year, o average; D ad E with regular testig oce a year or twice a year. Brow rectagle: RR = ; gree ellipse: RR = 2., D AP = mo.; ellipse RR = 8.3, D AP = 6 mo.; blue ellipse: RR = 26, D AP = 3 mo. The size of the ellipse idicates the ucertaity i the estimate. Acute phase 4/7 2/0/20

5 Figure 4B shows what happes if people are tested radomly but oce a year o average. With RR =, the value of R 0 falls to 0.58 (brow rectagle). With RR = 2. ad D AP = 2 mo. R 0 falls to 0.6. With RR = 8.3 ad D AP = 6 mo. R 0 falls to 0.84 ad with RR = 26 ad D AP = 3 mo. R 0 falls to I all three cases R 0 still falls below although with the two higher estimates of RR it is oly 0% to 20% below which allows little margi of error. Figure 4C shows what happes if the average testig iterval is reduced to six moths. With RR =, R 0 falls to 0.29 (brow rectagle). With RR = 2. ad D AP = 2 mo. R 0 falls to With RR = 8.3 ad D AP = 6 mo. R 0 falls to 0.6 ad with RR = 26 ad D AP = 3 mo. R 0 falls to Eve i the worst case (RR = 26, D AP = 3 mo.) R 0 is sigificatly less tha. Figure 4D shows what happes if people are tested regularly oce a year. With RR =, the value of R 0 agai falls to 0.29 (brow rectagle). With RR = 2. ad D AP = 2 mo. R 0 falls to With RR = 8.3 ad D AP = 6 mo. R 0 falls to 0.70 ad with RR = 26 ad D AP = 3 mo. R 0 falls to Agai, eve i the worst case (RR = 26, D AP = 3 mo.) R 0 is sigificatly less tha. Figure 4E shows what happes if people are tested regularly twice a year. With RR =, R 0 falls to 0.4 (brow rectagle). With RR = 2. ad D AP = 2 mo. R 0 falls to 0.2. With RR = 8.3 ad D AP = 6 mo. R 0 falls to 0.45 ad with RR = 26 ad D AP = 3 mo. R 0 falls to Eve i the worst case (RR = 26, D AP = 3 mo.) R 0 is agai sigificatly less tha. Coclusio We have three estimates of RR, the relative risk of ifectio, ad D AP, the duratio of the acute phase ragig from 2. over 2 moths to 26.2 over 3 moths givig values of R 0 ragig from 5.8 to 2.3. The high estimates for RR may well be overestimates. They are both based o the data from Rakai 8 ad discordat couple studies i which oe parter is sero-prevalet will select agaist those couples who are most ifectious ad therefore o loger sero-discordat. Furthermore, the high values of RR with log values of D AP imply values of R 0 2 which seems ulikely; if this were the case HIV should be relatively easy to elimiate through mior chages i behaviour ad the epidemic should be much less stable. However, it is clear from this aalysis that eve if we adopt the most pessimistic view ad assume the relative risk of ifectio is 26 times higher durig a acute phase that lasts for 3 moths aual testig ad immediate treatmet has the potetial to R 0 to less tha ad with ay further cotributio to prevetio will probably guaratee elimiatio i the log term. Testig people regularly, o a aual basis, is cosiderably more effective tha radom testig because uder radom testig some people will be tested very frequetly, which is ot ecessary, while others will be tested very ifrequetly which is ot ideal. With regular testig eve the most pessimistic view reduces R 0 to 0.82 ad will probably lead to elimiatio. As expected, testig people twice a year reduces R 0 eve further ad uder all assumptios about the acute phase would guaratee elimiatio. However, this aalysis raises a possibility that may be eve more importat tha cosideratios of high rates of ifectio durig the acute phase. We kow that the set poit values of the viral load vary by several orders of magitude. I the Fiebig 7 study the log 0 (viral load) varies from about 2.6 to 5.6 i the chroic stage. The data i Figure 4 suggest that variatio i the average viral load i a cohort of people, as a fuctio of time sice ifectio, is likely to have a greater ifluece o the model predictios tha ay differece betwee acute ad chroic phase trasmissio. However, there are two reasos why this is more difficult to allow for. First of all the result show i Figure 4 assumes a relatioship betwee survival ad set-poit viral load based o oly oe small study ad better data are eeded if this is to be made the basis for modellig the epidemic. Secodly, icludig this variatio would probably eed a model that icludes the distributio of set-poit viral loads explicitly ad the structure of the models that are curretly used does ot allow for this. If this were to be explored further, the first priority would be to cosider models i which the variatio i the set-poit viral load is icluded explicitly ad comparisos made with a model i which this variatio is set to zero. We coclude, therefore, that icreased trasmissio durig the acute phase is ulikely to chage the model predictios sigificatly for several reasos:. The acute phase duratio is more likely to be of the order of oe or two moths or about % to 2% of the total disease duratio. 2. If trasmissio durig the acute phase is sufficietly high for trasmissio durig this short time to be importat, the R 0 must be correspodigly low ad the reductio i R 0 eeded for elimiatio is correspodigly less. 3. There is strog evidece that trasmissio saturates above a viral load of about 4 to 5 logs mitigatig the impact of eve very high viral loads durig the acute phase. 4. A more importat limitatio of the curret model structures, is that variatio i the setpoit viral load is ot icluded ad this should be explored further. Acute phase 5/7 2/0/20

6 5. The short duratio of the acute phase meas that it ca oly ever make a sigificat cotributio to trasmissio if the rate of parter chages is much higher tha is geerally observed to be the case. Appedix. Fittig trasmissio as a power-law fuctio of viral load Several authors 3 have fitted the relatioship betwee trasmissio ad viral load to a power law fuctio with the trasmissio icreasig as the viral load to the power of about 0.3. This implies that at all viral loads trasmissio icreases more slowly the liearly so that there is a degree of saturatio i trasmissio as viral load icreases. However, there is o obvious biological basis for this although from a statistical poit of view it is ot possible to choose betwee this power law model ad the liear icrease to a asymptote suggested here. Appedix 2. Reductio i trasmissio Let the relative risk of ifectio vary with time sice ifectio as RR(t) The uder radom testig at a rate ρ year, the reductio i the overall trasmissio will be R = ρt e ( ) 0 RRt dt RR() t dt 0 while uder regular testig at a iterval of τ years the reductio i overall trasmissio will be R = ( t ) τ RR( t) 0 τ RR() t 0 Sice we have estimates of the relative risk of trasmissio, give that a perso is alive, for differet stages of ifectio, we approximate RR(t) with a appropriate step fuctio. Appedix 3. R 0 ad the growth rate for a -stage model We wat to itroduce a acute phase but also keep four chroic stages i order to esure that the survival distributio approximates the observed Weibull distributio with a shape parameter of abut 2 reasoably well. The equatios for this model are (keepig the total populatio costat) I0 = I 0 βiii+ ρi 7 I i = I0 βiii ρi 8 i, i = 2 to 9 Ii = ρi Ii ρ iii where I 0 refers to the proportio of people that are susceptible people ad I i to the proportio i each 5 6 successive stage of ifectio. The ifectiousess of each stage is determied by β i ad the mea duratio of each stage is /ρ i. From Equatios 7 to 9 it follows that R i 0 = β 0 ρi Durig the iitial expoetial growth of the epidemic at a rate r we have I 0 ad i Ii = r, Ii i = 0 to from which it follows that with βii r = 2 ρ i j ri = j= 0 r + ρ j. 3 We ca ow determie the relatioship betwee the relative risk of ifectio i each stage ad R 0 while costraiig the overall growth rate, r, as follows. We first set the duratio of each stage /ρ i ad the relative ifectiousess of each stage β i /β 0, for i = to, ad the vary β 0 to get the required value of the iitial growth rate r. Usig Equatio 0 we the calculate R 0 directly. Refereces Attia, S., Egger, M., Muller, M., Zwahle, M. & Low, N. Sexual trasmissio of HIV accordig to viral load ad atiretroviral therapy: systematic review ad meta-aalysis. AIDS 23, (2009). 2 Baete, J. M. et al. Geital HIV- RNA Predicts Risk of Heterosexual HIV- Trasmissio. Sciece traslatioal medicie 3, 77ra29, doi:0.26/scitraslmed (20). 3 Doell, D. et al. Heterosexual HIV- trasmissio after iitiatio of atiretroviral therapy: a prospective cohort aalysis. Lacet 375, (200). 4 Fideli, U. S. et al. Virologic ad immuologic determiats of heterosexual trasmissio of huma immuodeficiecy virus type i Africa. AIDS Res. Hum. Retroviruses 7, (200). 5 Garcia, P. M. et al. Materal levels of plasma huma immuodeficiecy virus type RNA ad the risk of periatal trasmissio. Wome ad Ifats Trasmissio Study Group. N. Egl. J. Med. 34, (999). Acute phase 6/7 2/0/20

7 6 Ligappa, J. R. et al. Estimatig the impact of plasma HIV- RNA reductios o heterosexual HIV- trasmissio risk. PLoS ONE 5, e2598 (200). 7 Fiebig, E. W. et al. Dyamics of HIV viremia ad atibody serocoversio i plasma doors: implicatios for diagosis ad stagig of primary HIV ifectio. AIDS 7, (2003). 8 Wawer, M. J. et al. Rates of HIV- Trasmissio per Coital Act, by Stage of HIV- Ifectio, i Rakai, Ugada. J. Ifect. Dis. 9, (2005). 9 Araout, R. A. et al. A simple relatioship betwee viral load ad survival time i HIV- ifectio. Proc Natl Acad Sci USA 96, (999). 0 Holligsworth, T. D., Aderso, R. M. & Fraser, C. HIV- Trasmissio, by Stage of Ifectio. J. Ifect. Dis. 98, (2008). Williams, B. G. & Gouws, E. The epidemiology of huma immuodeficiecy virus i South Africa. Philos. Tras. R. Soc. Lod. B. Biol. Sci. 356, (200). 2 Williams, B. G. et al. HIV Ifectio, atiretroviral therapy, ad CD4+ cell cout distributios i Africa populatios. J. Ifect. Dis. 94, (2006). 3 Wilso, D. P., Law, M. G., Grulich, A. E., Cooper, D. A. & Kaldor, J. M. Relatio betwee HIV viral load ad ifectiousess: a model-based aalysis. Lacet 372, (2008). Acute phase 7/7 2/0/20