Riding the waves from epidemic to endemic: Viral mutations, immunological change and policy responses.

Nonpharmaceutical interventions (NPI) are an important tool for countering pandemics such as COVID-19. Some are cheap; others disrupt economic, educational, and social activity. The latter force governments to balance the health benefits of reduced infection and death against broader lockdown-induced societal costs. A literature has developed modeling how to optimally adjust lockdown intensity as an epidemic evolves. This paper extends that literature by augmenting the classic SIR model with additional states and flows capturing decay over time in vaccine-conferred immunity, the possibility that mutations create variants that erode immunity, and that protection against infection erodes faster than protecting against severe illness. As in past models, we find that small changes in parameter values can tip the optimal response between very different solutions, but the extensions considered here create new types of solutions. In some instances, it can be optimal to incur perpetual epidemic waves even if the uncontrolled infection prevalence would settle down to a stable intermediate level.

The hammer and the jab: Are COVID-19 lockdowns and vaccinations complements or substitutes?

The COVID-19 pandemic has devastated lives and economies around the world. Initially a primary response was locking down parts of the economy to reduce social interactions and, hence, the virus' spread. After vaccines have been developed and produced in sufficient quantity, they can largely replace broad lock downs. This paper explores how lockdown policies should be varied during the year or so gap between when a vaccine is approved and when all who wish have been vaccinated. Are vaccines and lockdowns substitutes during that crucial time, in the sense that lockdowns should be reduced as vaccination rates rise? Or might they be complementary with the prospect of imminent vaccination increasing the value of stricter lockdowns, since hospitalization and death averted then may be permanently prevented, not just delayed? We investigate this question with a simple dynamic optimization model that captures both epidemiological and economic considerations. In this model, increasing the rate of vaccine deployment may increase or reduce the optimal total lockdown intensity and duration, depending on the values of other model parameters. That vaccines and lockdowns can act as either substitutes or complements even in a relatively simple model casts doubt on whether in more complicated models or the real world one should expect them to always be just one or the other. Within our model, for parameter values reflecting conditions in developed countries, the typical finding is to ease lockdown intensity gradually after substantial shares of the population have been vaccinated, but other strategies can be optimal for other parameter values. Reserving vaccines for those who have not yet been infected barely outperforms simpler strategies that ignore prior infection status. For certain parameter combinations, there are instances in which two quite different policies can perform equally well, and sometimes very small increases in vaccine capacity can tip the optimal solution to one that involves much longer and more intense lockdowns.

Drug prices and emergency department mentions for cocaine and heroin.

OBJECTIVES: In this report, the author illustrates the historic relation between retail drug prices and emergency department mentions for cocaine and heroin. METHODS: Price series based on the Drug Enforcement Administration's System to Retrieve Information From Drug Evidence database were correlated with data on emergency department mentions from the DrugAbuse Warning Network for cocaine (1978-1996) and heroin (1981-1996). RESULTS: A simple model in which emergency department mentions are driven by only prices explains more than 95% of the variation in emergency department mentions. CONCLUSIONS: Fluctuations in prices are an important determinant of adverse health outcomes associated with drugs.

A dynamic model of drug initiation: implications for treatment and drug control.

We set up a time-continuous version of the first-order difference equation model of cocaine use introduced by Everingham and Rydell [S.S. Everingham, C.P. Rydell, Modeling the Demand for Cocaine, MR-332-ONDCP/A/DPRC, RAND, Santa Monica, CA, 1994] and extend it by making initiation an endogenous function of prevalence. This function reflects both the epidemic spread of drug use as users 'infect' non-users and Musto's [D.F. Musto, The American Disease: Origins of Narcotic Control, Oxford University, New York, 1987] hypothesis that drug epidemics die out when a new generation is deterred from initiating drug use by observing the ill effects manifest among heavy users. Analyzing the model's dynamics suggests that drug prevention can temper drug prevalence and consumption, but that drug treatment's effectiveness depends critically on the stage in the epidemic in which it is employed. Reducing the number of heavy users in the early stages of an epidemic can be counter-productive if it masks the risks of drug use and, thereby, removes a disincentive to initiation. This strong dependence of an intervention's effectiveness on the state of the dynamic system illustrates the pitfalls of applying a static control policy in a dynamic context.

Setting goals for drug policy: harm reduction or use reduction?

Historically, United States drug policy has focused on use reduction; harm reduction is a prominent alternative. This paper aims to provoke and inform more debate about the relative merits of these two. Since harm is not necessarily proportional to use, use reduction and harm reduction differ. Both terms are somewhat ambiguous; precisely defining them clarifies thinking and policy implications. Measures associated with use reduction goals are poor; those associated with harm reduction are even worse. National goals influence the many decentralized individuals who collectively make drug policy; clearly enunciating goals makes some policy choices transparent and goals serve a variety of purposes besides guiding programmatic decisions. We recommend that the overall objective be to minimize the total harm associated with drug production, distribution, consumption and control. Reducing use should be seen as a principal means of attaining that end.

Is crack cheaper than (powder) cocaine?

AIMS: To compare the prices of cocaine powder and crack cocaine in the United States. DESIGN: Retail prices for crack and powder cocaine are compared for 14 US cities between 1986 and 1991 using regression analysis and t-tests. MEASUREMENTS: Prices are estimated from the United States Drug Enforcement Administration's System to Retrieve Information from Drug Evidence (STRIDE) database. FINDINGS: On average, crack is neither more nor less expensive per pure unit than powder cocaine. Prices are not equal in every city in every year, but crack is equally likely to be more or less expensive, and the differences are not large relative to variation in prices of both forms of cocaine between cities and over time. CONCLUSIONS: Crack has been widely believed to be cheaper than powder cocaine, and this "fact" has been used to help explain why US drug problems worsened in the 1980s. However, crack is not, in fact, cheaper per pure unit than powder cocaine. Other explanations must be sought for why crack spread so rapidly relative to powder cocaine.

What does mathematical modeling tell us about harm reduction?

This paper argues, primarily by example, that mathematical modeling can contribute to harm reduction-orientated drug policy making in three ways: by contributing to quantitative evaluations of effectiveness, by improving data and understanding of the underlying drug-related phenomena, and by encouraging precise thinking about the goals and objectives of harm reduction.

Redefining the goals of national drug policy: recommendations from a working group.

This paper discusses what the goals of national drug policy have been and suggests an alternative set of goals. The past emphasis on use reduction is found wanting. Total harm related to drugs can be viewed as the product of use and harm per use. Thus, reducing use usually serves to reduce harm. However, in some cases, use reduction programs may increase harm per use so much that they increase overall harm even as they succeed in reducing use. Hence, use reduction goals can be usefully augmented with the explicit objective of reducing the total harm created by the production, distribution, consumption, and control of drugs. Numerous programmatic recommendations flow from this approach.

What is the average price of an illicit drug?

Estimates of the total dollar value of the markets for illicit drugs are valuable for policy making. Such estimates are usually produced by multiplying estimated consumption by price. This paper argues that the relevant price for such calculations is not simply the price of one standard unit. There are substantial quantity discounts for illicit drugs, and there is a distribution of retail purchase sizes. Hence, the average price paid per gram need not equal the price of one gram. This concept is illustrated with calculations for heroin and cocaine.