The dynamic process of dynamic modelling: the cocaine epidemic in the United States of America

In the present article, the authors review several recent dynamic models of the current cocaine epidemic in the United States of America (both uncontrolled and optimally controlled), which differentiate between two levels of use (“light” and “heavy”). Even though all the models have their origin in a study carried out at the RAND Corporation's Drug Policy Research Center in the early 1990s, each has been developed by extending or refining another. In addition to pointing to interesting policy conclusions drawn from the analysis of those models, the authors also demonstrate that the development of dynamic models of illicit drug consumption is itself a dynamic process where subsequent refinements lead to increased quality and reliability of the resulting policy conclusions

The dynamic process of dynamic modelling: the cocaine epidemic in the United States of America

In the present article, the authors review several recent dynamic models of the current cocaine epidemic in the United States of America (both uncontrolled and optimally controlled), which differentiate between two levels of use (“light” and “heavy”). Even though all the models have their origin in a study carried out at the RAND Corporation's Drug Policy Research Center in the early 1990s, each has been developed by extending or refining another. In addition to pointing to interesting policy conclusions drawn from the analysis of those models, the authors also demonstrate that the development of dynamic models of illicit drug consumption is itself a dynamic process where subsequent refinements lead to increased quality and reliability of the resulting policy conclusions

Optimal Resource Exploitations May Be Chaotic

Tragler G, Feichtinger G, Dawid H. Optimal Resource Exploitations May Be Chaotic. Central European Journal of Operations Research and Economics. 1994;3:111-122

Optimal control of interacting systems with DNSS property: The case of illicit drug use

Abstract In this paper we generalize a one-dimensional optimal control problem with DNSS property to a two-dimensional optimal control problem. This is done by taking the direct product of the model with itself, i.e. we combine two similar system dynamics under a joint objective functional that is separable in both states and controls. This framework can be applied to the construction of various optimal control problems, such as optimal marketing of related products, optimal growth of separate but interacting economies, or optimal control of two related capital stocks. We study such a system for a particular case drawn from the domain of drug control. The main result of this paper is that in this domain even a modest amount of interaction can sometimes make a very big difference. Hence, drawing conclusions by simplifying the real world into two independent, one-dimensional models may be problematic. Methodologically the combination of two systems with DNSS property leads to a fascinating series of situations with multiple optimal steady states and associated threshold behavior. These instances reflect some important recent developments in optimal dynamic control theory.Optimal control Indifference points Multiple equilibria DNSS points Illicit drug use Interacting systems

Optimal Control of Interacting Systems with DNSS Property: The Case of Illicit Drug Use

International audienceIn this paper we generalize a one-dimensional optimal control problem with DNSS property to a two-dimensional optimal control problem. This is done by taking the direct product of the model with itself, i.e. we combine two similar system dynamics under a joint objective functional that is separable in both states and controls. This framework can be applied to the construction of various optimal control problems, such as optimal marketing of related products, optimal growth of separate but interacting economies, or optimal control of two related capital stocks

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

Dynamic models of the firm with green energy and goodwill

This paper considers the effect of investment in solar panels on optimal dynamic firm behavior. To do so, an optimal control model is analyzed that has as state variables goodwill and green capital stock. Following current practice in companies like Tesla and Google, we take into account that the use of green energy has positive goodwill effects. As a solution, we find an optimal trajectory that overshoots before reaching a stable steady state