Numerical investigations of stochastic HIV/AIDS infection model

In this paper, a stochastic HIV/AIDS epidemic model has been studied numerically. A discussion among the solutions related to deterministic HIV/AIDS model and stochastic HIV/ AIDS epidemic model has shown that the stochastic solution is more realistic than the deterministic solution. To control the diseases, the threshold parameter R₀ plays a key role in the stochastic HIV/AIDS epidemic model. If R₀<1 then disease is under control while the disease is out of control if R₀>1. The explicit approaches such as the Milstein scheme, stochastic Euler scheme, and stochastic Runge-Kutta 4 are dependent on temporal step size, whereas non-standard finite difference approaches are independent of step size. The results for numerical approaches like the Milstein scheme, stochastic Euler scheme, and stochastic Runge-Kutta 4 scheme fail for outsized step size. The stochastic non-standard finite difference scheme conserves dynamic features like confinedness, consistency and positivity.