Numerical Analysis of Fractional Order Drinking Mathematical Model

Abstract

This manuscript is concerned to fractional order SMR-type alcohol drinking model that shows the interaction between alcohol drinkers and non consumers of alcohols. In the model, the whole population is classified into three different classes regarding to their alcohol utilization, namely, Susceptible class S, i.e non consumers, Moderate consumers M, and Risk consumers R. Since, alcohol consumption is a risk factor for various chronic diseases like Psychiatric conditions, cardiovascular diseases, digestive issues, and certain types of cancers. That’s why the qualitative and quantitative behavior of the alcohol drinking model is analyzed in this research article. The authors used the results of fixed point theory and the results of Ulam stability to analyze the model qualitatively. For the quantitative analysis, we have constructed a general scheme for solution of proposed model by using the two steps Adam’s Bashforth method involving Caputo’s fractional derivative. The structure of the method converges to the traditional Adams-Bashforth technique when the fractional order derivatives approach the conventional derivative. The constructed scheme is also authenticated through numerical example. Finally, the results obtained are simulated graphically using Matlab.