@Article{cmc.2020.011289,
AUTHOR = {Ali Raza, Muhammad Rafiq, Nauman Ahmed, Ilyas Khan, Kottakkaran Sooppy Nisar, Zafar Iqbal},
TITLE = {A Structure Preserving Numerical Method for Solution of  Stochastic Epidemic Model of Smoking Dynamics},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {65},
YEAR = {2020},
NUMBER = {1},
PAGES = {263--278},
URL = {http://www.techscience.com/cmc/v65n1/39565},
ISSN = {1546-2226},
ABSTRACT = {In this manuscript, we consider a stochastic smoking epidemic model from 
behavioural sciences. Also, we develop a structure preserving numerical method to 
describe the dynamics of stochastic smoking epidemic model in a human population. The 
structural properties of a physical system include positivity, boundedness and dynamical 
consistency. These properties play a vital role in non-linear dynamics. The solution for 
nonlinear stochastic models necessitates the conservation of these properties.
Unfortunately, the aforementioned properties of the model have not been restored in the 
existing stochastic methods. Therefore, it is essential to construct a structure preserving 
numerical method for a reliable analysis of stochastic smoking model. The usual explicit 
stochastic numerical methods are time-dependent and violate most of the structural
properties. In this work, we have developed the implicitly driven explicit method for the 
solution of stochastic smoking model. It is also proved that the newly developed method 
sustains all the aforementioned properties of the system. Finally, the convergence 
analysis of the newly developed method and graphical illustrations are presented.},
DOI = {10.32604/cmc.2020.011289}
}