Optimal subscription models to pay for antibiotics.

Novel subscription payment schemes are one of the approaches being explored to tackle the threat of antimicrobial resistance. Under these schemes, some or all of the payment is made via a fixed "subscription" payment, which provides a funder unlimited access to the treatment for a specific duration, rather than relying purely on a price per pill. Subscription-based schemes guarantee pharmaceutical firms income that incentivises investment in developing new antibiotics, and can promote responsible stewardship. From the pharmaceutical perspective, revenue is disassociated from sales, removing benefits from push marketing strategies. We investigate this from the funder perspective, and consider that the funder plays a key role in promoting responsible antibiotic stewardship by choosing the price per pill for providers such that this encourages appropriate antibiotic use. This choice determines the payment structure, and we investigate the impact of this choice through the lens of social welfare. We present a mathematical model of subscription payment schemes, explicitly featuring fixed and volume-based payment components for a given treatment price. Total welfare returned at a societal level is then estimated (incorporating financial costs and monetised benefits). We consider a practical application of the model to development of novel antibiotic treatment for Gonorrhoea, and examine the optimal treatment price under different parameterisations. Specifically, we analyse two contrasting scenarios - one where a new antibiotic's prioritised role is reducing transmission, and one where a more pressing requirement is conserving the antibiotic as an effective last defence. Critically, this analysis demonstrates that effective roll-out of a subscription payment scheme for a new antibiotic requires a comprehensive assessment of the benefits gained from treatment. We discuss the insights this work presents on the nature of these payment schemes, and how these insights can enable decision-makers to take the first steps in determining effective structuring of subscription payment schemes.