Author's personal copy
Mathematical and Computer Modelling 52 (2010) 1023–1029
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A network model for the short-term prediction of the evolution ofcocaine consumption in Spain
Francisco-José Santonja a,∗, Iván-C. Lombana b, María Rubio b, Emilio Sánchez c,Javier Villanueva d
a Departamento de Estadística e Investigación Operativa, Universidad de Valencia, Spainb Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Spainc Unidad de Conductas Adictivas de Catarroja, Agencia Valenciana de Salud, Spaind Centro de Estudios Superiores Felipe II, Aranjuez, Madrid, Spain
Cocaine consumption is a social problem with acute consequences and its dependency can
be regarded as a health concern of social transmission. This fact leads us to develop the
Received in revised form 11 February 2010
idea that its transmission dynamics can be studied using epidemiological mathematical
models. Under this point of view, in this paper we propose a network model to studythe short-term evolution of the cocaine consumer subpopulations. The model parameters
are obtained from data source and from an analogue continuous model. Sensitivity of the
model parameters is studied. The parameters are associated with prevention and treatment
policies and the sensitivity study gives us information about which parameters have more
incidence on the future evolution of consumers. Results and discussion are also presented.
2010 Elsevier Ltd. All rights reserved. 1. Introduction
Cocaine consumption is growing at a worrying rate in developed and developing countries [1,2]. In Spain it is becoming
a serious problem not only from an individual health point of view but also from the public socioeconomic one [3,4]. Wenote that cocaine consumption is increasing (see Table 1).
Thus it is in the interest of public health to study the dynamics of cocaine consumption. In this article, we analyze the
evolution of people with habitual cocaine consumption in Spain and simulate some health policy proposals and their effectin reducing this population. Spanish Government strategy on drug abuse appears in the Plan Nacional sobre Drogas (DrugsNational Plan) [3,5], issued by the Spanish Health Ministry. The objectives mentioned in this document are:
1. The prevention of drug consumption, pointing out the health concerns produced by their consumption, delaying the age
of the first contact with drugs, education programs and legal fight against drugs dealing.
2. To improve quantitative and qualitative research, implement new treatments, evaluate current therapy programs and
training to increase professional competence of the people who work with drug abusers.
In this paper, we take cocaine consumption as a socially transmitted epidemic disease. We treat cocaine consumption as a
disease that spreads through social peer pressure or social contact. These social contacts have an influence on the probabilityof transmission of cocaine consumption. The main idea behind this conception is that cocaine consumption can spread
∗ Corresponding address: Instituto de Matemática Multidisciplinar, Edificio 8G, piso 2, Ciudad Politécnica de la Innovación, Universidad Politécnica de
E-mail addresses: email@example.com, firstname.lastname@example.org (F.-J. Santonja).
0895-7177/$ – see front matter 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm.2010.02.032
Author's personal copy F.-J. Santonja et al. / Mathematical and Computer Modelling 52 (2010) 1023–1029
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