| Summary: | 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.
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