  The semi-implicit schemes for the nonlinear predator-prey reaction-diffusion
model with the space-time fractional derivatives are discussed, where the space
fractional derivative is discretized by the fractional centered difference and
WSGD scheme. The stability and convergence of the semi-implicit schemes are
analyzed in the $L_\infty$ norm. We theoretically prove that the numerical
schemes are stable and convergent without the restriction on the ratio of space
and time stepsizes and numerically further confirm that the schemes have first
order convergence in time and second order convergence in space. Then we
discuss the positivity and boundedness properties of the analytical solutions
of the discussed model, and show that the numerical solutions preserve the
positivity and boundedness. The numerical example is also presented.
