title: In the interests of time: improving HIV allocative efficiency modelling via optimal time-varying allocations.
abstract: BACKGROUND
  International investment in the response to HIV and AIDS has plateaued and its future level is uncertain. With many countries committed to ending the epidemic, it is essential to allocate available resources efficiently over different response periods to maximize impact. The objective of this study is to propose a technique to determine the optimal allocation of funds over time across a set of HIV programmes to achieve desirable health outcomes.
  
  
  METHODS
  We developed a technique to determine the optimal time-varying allocation of funds (1) when the future annual HIV budget is pre-defined and (2) when the total budget over a period is pre-defined, but the year-on-year budget is to be optimally determined. We use this methodology with Optima, an HIV transmission model that uses non-linear relationships between programme spending and associated programmatic outcomes to quantify the expected epidemiological impact of spending. We apply these methods to data collected from Zambia to determine the optimal distribution of resources to fund the right programmes, for the right people, at the right time.
  
  
  CONCLUSIONS
  Considering realistic implementation and ethical constraints, we estimate that the optimal time-varying redistribution of the 2014 Zambian HIV budget between 2015 and 2025 will lead to a 7.6% (7.3% to 7.8%) decrease in cumulative new HIV infections compared with a baseline scenario where programme allocations remain at 2014 levels. This compares to a 5.1% (4.6% to 5.6%) reduction in new infections using an optimal allocation with constant programme spending that recommends unrealistic programmatic changes. Contrasting priorities for programme funding arise when assessing outcomes for a five-year funding period over 5-, 10- and 20-year time horizons.
  
  
  CONCLUSIONS
  Countries increasingly face the need to do more with the resources available. The methodology presented here can aid decision-makers in planning as to when to expand or contract programmes and to which coverage levels to maximize impact.
authors.affiliation: The Kirby Institute, University of New South Wales, Sydney, Australia; ashattock@kirby.unsw.edu.au.
authors.forename: Andrew J
authors.initials: AJ
authors.lastname: Shattock
authors.affiliation: The Kirby Institute, University of New South Wales, Sydney, Australia.|The Burnet Institute, Melbourne, Australia.|School of Physics, University of Sydney, Sydney, Australia.
authors.forename: Cliff C
authors.initials: CC
authors.lastname: Kerr
authors.affiliation: The Kirby Institute, University of New South Wales, Sydney, Australia.|The Burnet Institute, Melbourne, Australia.|Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark.
authors.forename: Robyn M
authors.initials: RM
authors.lastname: Stuart
authors.affiliation: The World Bank Group, Washington DC, USA.
authors.forename: Emiko
authors.initials: E
authors.lastname: Masaki
authors.affiliation: The World Bank Group, Washington DC, USA.
authors.forename: Nicole
authors.initials: N
authors.lastname: Fraser
authors.affiliation: The World Bank Group, Washington DC, USA.
authors.forename: Clemens
authors.initials: C
authors.lastname: Benedikt
authors.affiliation: The World Bank Group, Washington DC, USA.
authors.forename: Marelize
authors.initials: M
authors.lastname: Gorgens
authors.affiliation: The Kirby Institute, University of New South Wales, Sydney, Australia.|The Burnet Institute, Melbourne, Australia.
authors.forename: David P
authors.initials: DP
authors.lastname: Wilson
authors.affiliation: The Kirby Institute, University of New South Wales, Sydney, Australia.
authors.forename: Richard T
authors.initials: RT
authors.lastname: Gray
mesh_terms: D015658:HIV Infections / Q000191:economics* / Q000453:epidemiology / Q000517:prevention & control; D006801:Humans; D008962:Models, Theoretical; D040841:Resource Allocation; D015024:Zambia
keywords: HIV/AIDS; Optima; Zambia; allocative efficiency; mathematical modelling; time-varying optimization