Threshold, Amory Faulkner, oil on canvas 1 The prospects of elimination of HIV with test and treat strategy Mirjam Kretzschmar 1,2 Maarten Schim van der Loeff 3 Daniela de Angelis 4 Roel Coutinho 1,2 1 Centre for Infectious Disease Control, RIVM 2 University Medical Centre Utrecht, NL 3 Municipal Health Service, Amsterdam, NL 4 MRC Biostatistics Unit, Cambridge, UK 26July 2012 AIDS conference Washington DC

Test and treat strategy

Treatment and infectivity Cohen et al. NEJM 2011

From Granich et al. Lancet 2009 Elimination possible? Aims of our study: Modify and generalize the model to include knowledge on natural history Derive and analyze under what conditions elimination is possible

Generalized model structure Variable number of compartments with variable duration Variable infectivity -> better description of natural history including variable infectivity

Epidemic dynamics Exponential growth at the start of the epidemic, growth rate determined by R 0 Exponential decay at elimination, decay rate determined by R e Exponential growth Elimination Transient dynamics Epidemic growth and elimination are threshold phenomena => linear analysis

Analysis Determine explicit expressions for R 0 and R e from model equations Estimate disease progression parameters from data (CASCADE collaboration) Use information about distribution of infectivity (Hollingsworth et al. JID 2008) Relate infectivity to epidemic growth rate r and R 0 via generation interval distribution (Wallinga & Lipsitch 2007) Estimate r from incidence or doubling time at onset of epidemic From R 0 determine transmission parameter λ Elimination threshold is determined as function of coverage and adherence to treatment Assumption: populations and behaviors driving HIV transmission during growth phase also determine transmission dynamics during elimination.

3 infection stages Progression rates from CASCADE Infectivity from Hollingsworth 2008 Relationship r and R 0 :

Elimination threshold  Elimination threshold R e as function of transmission and intervention parameters  Elimination possible if R e < 1  From incidence or doubling time during exponential growth phase estimate r  From r compute R 0  Determine elimination threshold for given R 0  If more recent estimates of R 0 are available these can be used (e.g. from genetic data)

Elimination threshold  For R 0 > 6 elimination not possible  Elimination possible for low risk populations  For the coverage and drop out rate assumed by Granich elimination is feasible if R 0 <5 R 0 =

Estimates from literature Populationr (1/yr)R0R0 d (yrs)Data typeRef South Africa incidenceGranich 2009 France incidenceNishiura 2010 West Germany incidenceNishiura 2010 UK incidenceNishiura 2010 SSAC geneticWalker 2005 High income countries geneticWalker 2005 Albania geneticSalemi 2008 England & Wales incidenceGran 2008 Brazil geneticBello 2007 MSM Netherlands 2.39incidenceBezemer 2008

Conclusions  Elimination is a threshold phenomenon. Information about possible elimination can be obtained from epidemic growth rate and generation interval distribution.  Elimination is only feasible for populations with low basic reproduction numbers or if the reproduction number is lowered significantly as a result of other additional interventions.  High infectivity during primary infection significantly increases the elimination threshold.  If reliable estimates for R 0 could be obtained from phylogenetic analysis prospects of elimination could be quantified more reliably.

Acknowledgements Co-authors: Maarten Schim van der Loeff Infectious Disease Unit, Municipal Health Service Amsterdam, The Netherlands Daniela de Angelis MRC Biostatistics Unit, Cambridge UK Roel Coutinho Center for Infectious Disease Control, RIVM and University Medical Center Utrecht, The Netherlands CASCADE Collaboration Paul Birrell, MRC Biostatistics Unit, Cambridge UK