Positivity and boundedness preserving numerical scheme for the stochastic epidemic model with square-root diffusion term
The authors study the following stochastic differential equation \[ dx(t) = [\beta x(t) (N-x(t)) - (\mu +\gamma)x(t)]dt +\sigma_1 x(t) (N-x(t)) dB_1(t) - \sigma_2 x(t) \sqrt{N-x(t)}dB_2(t). \] They modify the classical Euler-Maruyama scheme to create the positivity and boundedness preserving Euler-Maruyama scheme and they show that the PBPEM convergences strongly to the true solution over finite time intervals.
positivity and boundedness preserving numerical method
scientific article; zbMATH DE number 7603711