Needle Exchange for Controlling HIV Spread under Endogenous Infectivity

Losses due to Human immunodeficiency virus (HIV) infections among injection drug users are substantial. Among HIV prevention programmes targeting injection drug users (IDUs), needle and syringe programmes are relatively easy to administrate and are cost-effective. We study the problem of optimally allocating prevention effort over a finite time horizon in a needle and syringe programme by balancing the benefit of infections averted with prevention costs. To maximize the system value, one needs to consider the timing and amount of prevention effort carefully. A key finding of our work is that extreme treatment policies from previous literature are not optimal. Instead, a period of moderate prevention effort is crucial in an optimal policy. We also find that as the time horizon increases, a policy of initial extreme treatment becomes more attractive and such treatment duration grows. Another interesting finding is the nonlinear impact of control effectiveness on the amount of prevention effort: when prevention effort is highly effective, the amount of effort decreases with the effectiveness, contrary to what one might expect. Through policy comparison, optimal policies are found to be most beneficial when the budget is less constrained.