Most of SDE models in epidemics, ecology, biology, finance etc. are highly nonlinear and do not have explicit solutions. Monte Carlo simulations have played a more and more important role. This talk will point out several well-known numerical schemes may fail to preserve the positivity or moment of the solutions to SDE models. Reliable numerical schemes are therefore required to be designed so that the corresponding Monte Carlo simulations can be trusted. The talk will then concentrate on new numerical schemes for the well-known stochastic Lotka--Volterra model for interacting multi-species. This model has some typical features: highly nonlinear, positive solution and multi-dimensional. The known numerical methods including the tamed/truncated Euler-Maruyama (EM) applied to it do not preserve its positivity. The aim of this talk is to modify the truncated EM to establish a new positive preserving truncated EM (PPTEM).