We consider a two-strain pathogen model described by a system of reaction-diffusion equations. We
define a basic reproduction number R_0 and show that when the model parameters are constant (spatially
homogeneous), if R_0 > 1 then one strain will outcompete the other strain and drive it to extinction, but if
R_0 \leq 1 then the disease-free equilibrium is globally attractive. When we assume that the diffusion rates
are equal while the transmission and recovery rates are heterogeneous, then there are two possible outcomes
under the condition R_0 > 1: 1) Competitive exclusion where one strain dies out. 2) Coexistence between the
two strains. Thus, spatial heterogeneity promotes coexistence.