Mathematical models applied to the prediction of doping in male athletes

Abstract

The compartmental model is a mathematical model (usually described by a set of differential equations) that describes how individuals from different compartments (or groups) that represent a population, interacts. The model is suitable especially for epidemic model, modeling spread of disease but also in simulation of interaction among social groups. The compartmental model has few assumptions to be feasible: “the infection/contamination rate” can be a function of many parameters (seasonality, epidemic waves, dependence of social distancing, policy of awareness, policy, and so one). The main assumption is that the population is homogeneous but, in reality, the heterogeneity of population (spatial localization, seasonal, demography) plays an important role in accuracy of models. Our approach was based on another method that has been used in the last years, the inclusion of a temporal function including heterogeneity in the influence that conduct to doping similar to rate of infection from epidemic models. In this paper, a new model is proposed for quantitative analysis of doping in a particular selected sport. Almost all the models in doping use the biological markers and effect of doping in declared by athletes involved in use of banned substances in a quantitative analysis over a group of high-performance athletes. The proposed compartmental model SEDRS (Susceptible-Exposed-Doped-Recovered-Susceptible) includes the heterogeneity shaped by awareness, due to social interaction that transmit the anti-doping policy. These measures are patterned by social interaction, especially during competitions and training, and this approach is included in system of integrodifferential equations. A heterogeneous (SEDRS) model is numerically solved and the solutions show how the social factor can contribute to decay of doping phenomenon of male athletes and the quantifiable influence in a healthier atmosphere in sport. The scope of the paper is the prediction of doping cases based on SEDRS model.

Keywords

• anti-doping policy
• compartmental models
• probability distribution
• heterogenous models