  In this paper, we design a semi-implicit scheme for the scalar time
fractional reaction-diffusion equation. We theoretically prove that the
numerical scheme is stable without the restriction on the ratio of the time and
space stepsizes, and numerically show that the convergent orders are 1
%$2-\alpha$ in time and 2 in space. As a concrete model, the subdiffusive
predator-prey system is discussed in detail. First, we prove that the
analytical solution of the system is positive and bounded. Then we use the
provided numerical scheme to solve the subdiffusive predator-prey system, and
theoretically prove and numerically verify that the numerical scheme preserves
the positivity and boundedness.
