Dynamical and nonstandard computational analysis of heroin epidemic model

Abstract

Numerical modelling of real-world problems has a significant role in different disciplines like biology, physics, chemistry, economics, and many more. The numerical results are the authentication of the results of the dynamical analysis. We studied the heroin epidemic model's dynamics based on the law of mass action. The essential features of the model like positivity, boundedness, equilibria, and reproduction number are presented. Some standard and nonstandard computational methods like Euler, Runge-Kutta, and Nonstandard finite difference (NSFD) are given for the said model. The nonstandard finite difference method was developed to restore the fundamental properties of biological problems. Also, the proposed numerical model is consistent with the behaviour of the continuous model. To that end, simulations for the comparison of computational methods are presented.

Keywords

• Deterministic model
• Nonlinear differential equations
• Computational methods
• Stability analysis
• Simulations