Negotiated drug prices by healthcare authorities (HAs) are typically contingent on projected treatment demand and the therapeutic value for specific medical conditions. In a world where chronic ailments are managed with regular therapies, HA’s dilemmas remain fairly consistent over time. However, novel and innovative treatments can disrupt these tradeoffs, particularly when they have the potential to outright cure chronic diseases. This can present a challenge for HAs when setting budgets, as the cost of treating a large number of patients may be prohibitive. This issue is likely to intensify as gene and cell therapies promise revolutionary advancements in healthcare, potentially providing cures for previously incurable chronic diseases that require long-term treatment.

These potentially groundbreaking innovations shed light on the difficulty faced by health authorities to optimally allocate their budget intertemporally when a large stock of patients becomes curable. Even absent credit market imperfections, the health authority problem of optimal intertemporal allocation of its budget depends on the likely decreasing efficiency of treatment with the number of patients to be treated but also on the rate of transmission and infection in the untreated population in the case of communicable diseases. While a myopic budget allocation decision seems suboptimal, value-based pricing, which justifies high prices for pharmaceuticals with lifesaving curative values, can challenge the short term “affordability” of health care budgets (Danzon, 2018).

The question on how to allocate an intertemporal budget when innovative curative medical treatments for a communicable disease become available has not been addressed in the literature even if the smoothing of payments over time based on performance may be useful (Danzon, 2018, Brennan and Wilson, 2014, Hlávka et al., 2020). Hlávka et al. (2020) investigate the impact of intertemporal sequencing of treatment. They analyze the sequencing of current-period budgets expended for curing congestive heart failure (CHF) for Medicare beneficiaries in 2009–2014 in the US. They compare the status quo sequence equalizing budget per period to deferred payment schemes varying by the level of downpayments. They show, as we do, that patients would benefit from deferred payments. The main difference from our setting is their use of detailed micro data, while we use calibrated macro data and the fact that CHF is a non-contagious disease so that a susceptible–infected–recovered (SIR) model is not useful. Neither do the authors attempt to derive the optimal sequence of treatment as we do by using welfare evaluations. The literature on pharmaceutical pricing and spending concentrates on the role of price regulation and price setting (Lakdawalla, 2018) in terms of access and incentives for innovation. Little is known about the intertemporal allocation of curative drug treatments when treatments affect future needs.

In this paper, we establish an SIR model for an epidemic, and in a simple setup, we analyze the optimality conditions of the sequence of cure expenses decided by HAs when a curative drug treatment appears in the market. In most European countries, bargaining over drug prices between health authorities and pharmaceutical firms are annual without long-run commitment. However, long-run optimal planning could generate benefits for all parties (see Alvarez et al., 2021 or Assenza et al., 2020, for a recent application to Covid).

These gains admittedly depend on disease and drug characteristics. We focus in this paper on the case of a grave illness, hepatitis C, whose treatment underwent a major upheaval when decisive curative drugs were introduced in 2014. The case of hepatitis C is informative because the management of the market introduction of therapeutic innovations well illustrates the intertemporal tradeoff between expending money on treating patients with new drugs in the present or waiting and treating them in the future. These new drugs however were quite expensive and gave rise to the question of the optimal policies to be chosen over time to master the epidemic in a cost-efficient way. Health authorities usually manage the budget impact of treating the accumulated patient stock by prioritizing patients at high risk and delaying treatment of stable patients as was done in France (Dessauce et al., 2019). Mouterde et al. (2016) describes how France restricted access to the new drugs called direct acting antiviral agents (DAAs) based on a selection of patients depending on virus genotypes, disease stages and comorbidities despite all these treatments obtaining a European Union marketing authorization regardless of the patient’s profile. Berdud et al. (2018) show how the in-class competition for DAAs had a positive impact on uptake and adoption of DAAs in the top-5 European countries.

The SIR model we consider is standard, although it allows for undetected and asymptomatic infected patients, a common occurrence with hepatitis C. Furthermore, we assume that the transmission rate is low so that the long-run equilibrium is disease free as was the case for hepatitis C in France after the 2000s. The inheritance of a stock of infected in 2010 had built up from the uncontrolled usage of syringes before the 2000s among drug addicts, from unsafe blood transfusion, and from any contact, among medical professionals, between the blood of infected and susceptible persons. Those causes of infection were at least partly under control in 2010.

We further assume that the new drug policy cures the disease with decreasing returns to scale, that is, an additional euro per patient is increasingly less likely to be effective on the rate at which patients are cured. It has various justifications given either by biological or economic reasons that we develop in the text. We also assume that the function describing the impact of new drugs remain constant over time, or at least, this is what is anticipated by the health authorities. We mainly focus on what health authorities decide at the onset of the introduction of a new drug on the market, and we leave to future research the additional tradeoff they may face when they know the available health technology will improve in the future, for example because they have good knowledge of forthcoming novel therapies. This obviously adds an additional aspect to the intertemporal tradeoff that depends on the decision-maker’s information about the future. In the case of hepatitis C, the effect of anticipated future entries of new drugs could add complications that are left to future research. Here, we address what the optimal tradeoff is in 2014 between sequences of dynamic expenses while holding fixed expectations about the future — in particular innovative new drugs.

Our first contribution is to derive analytical results that characterize optimal policies using the calculus of variations in the dynamic problem. We show that moving backward expenses in new drugs while holding constant the intertemporal budget of health authorities reduces infection in the short run although there are rebound effects of the epidemic in the medium run. This rebound effect seems particularly important in the case in which there are many asymptomatic patients who could not be administered the new treatment since they remain undetected.

Our second contribution is to simulate optimal policies using parameters that are calibrated to the epidemiological and economic characteristics of hepatitis C in France. We confirm the conclusions we set out above about the short-run gains as well as the rebound effects. The latter effect questions the intertemporal credibility of awarding health authorities an endowment that they are free to expend in the short run if additional resources can be renegotiated in the medium run. Indeed, the optimal management of an intertemporal budget allocation decided ex ante for the treatment of a disease needs the ability to commit to a hard budget constraint that may be difficult to comply when it means spending less per patient in the future than in the past. This is however the lesson from this optimal allocation, which is optimal given an intertemporal hard budget constraint.

Section 2 sets up the model, states our assumptions and describes how we calibrate parameters in our policy simulations. Section 3 develops analytical results and shows that most are indicative and remain generally inconclusive. Section 4 characterizes optimal policies obtained by simulations of a dynamically controlled SIR model, and the last section concludes the paper.