A quantitative approach for mathematical model of doping in high performance sport

Abstract

Introduction. Doping or administration of substances for purpose of improving the performances in various sport has a long history, even in the modern era to most common association of doping is connected to professional cycling. The usage of doping substances has become a major public health issue. Also, some abuse of doping substance was a major cause of death in some cases. As results of effort in fighting against doping, World Anti-Doping Agency (WADA) coordinated the implementation of the athlete hematological passport, or more commonly athlete biological passport (ABP). The decision of doped or not doped based on biological markers is made using Bayesian inference. But the code of implementation and the code of software used in decisions is not available to the public, and as sequels there are also some approaches in research, as methods based on psychological questionaries. In this case, the statistical analysis using structural equation models offer a valuable tool for management of antidoping policies in order to reduce this phenomenon. Material and method. In this paper, a novel method is novel model for quantitative analysis of doping is proposed. The model doesn’t use the biological markers but the effect of this as declared doping persons in a quantitative analysis over a lot of high performance athletes. The model is based on nonlinear equations as result of compartmental model with quantitative time dependent evolution of them.  Results and discussions. The model was implemented in MATLAB and numerical solutions were obtained using ODE (Ordinary Differential Equations) tool. The stability of model was analyzed using analogies with an epidemic SIRS compartmental model. The implementation uses a GUI (Graphical User Interface) that make the application user friendly. The fitting tools model is in stage of implementation and the parameter are finding out using a data collected and optimization tools (an objective function and genetic algorithms in order to prevent the phenomenon in a trapping minima). Conclusions. The result is very encouraging, the model fit 99.7% in preliminary set of data. The future development will include the fitting module and a set of results structured on various high performance sports.