Abstract
Smoking is the world's biggest public health concern. In epidemiology, the mechanisms of smoking addiction play a crucial role in mathematical models. In this paper Evolutionary Padé Approximation (EPA) scheme has been implemented for the treatment of the non-linear epidemiological smoking model. The evolutionary Padé Approximation scheme transforms the nonlinear epidemiology smoking model into an optimization problem by using Padé-approximation. Sufficient parameter settings for EPA have been implemented through MATLAB. Simulations represent numerical solutions of the epidemiology smoking model by solving the established optimization problem. First, the convergence solution of EPA scheme on population; potential smokers occasional smokers, heavy smokers, temporary quitters, and smokers who quit permanently have been studied and found to be significant. Evolutionary Padé Approximation has provided a convergence solution regarding the relationship among the different population compartments for diseases free equilibrium, it has been observed that the results EPA scheme are more reliable and significant when a comparison is drawn with Non-Standard Finite Difference (NSFD) numerical scheme. Finally, the EPA scheme reduces the contaminated levels for disease-free equilibrium very rapidly and restricts the spread of smoking within the population.
