Numerical simulation and analysis of the stochastic HIV/AIDS model in fractional order

Abstract

The current work analyzes the HIV/AIDS model under stochastic fractional differential equations in the Caputo sense. The articulation of the model both in integer and arbitrary order with stochastic differential equation are presented. We provide the solution’s positivity and boundedness for the proposed system. The existence and uniqueness of the fractional stochastic order differential equations are given. We give a novel numerical approach based on Newton’s polynomial to numerically solve the fractional stochastic model. Also, we provide a numerical technique for the solution in the power law model. The results for the Caputo fractional case and stochastic fractional Caputo case are shown and discussed in detail. Sensitivity analysis are done and provide their respective results graphically. The numerical solution of the model based on their sensitive parameters is shown graphically in order to minimize the infection.

Keywords

• Numerical simulations
• HIV/AIDS model
• Existence and uniqueness
• Stochastic differential equations
• Theoretical results