This paper focuses on infectious disease transmission between multiple regions, in which partial cross-immunity, reinfection, and the interaction of all regions are considered. We construct a time-delayed SEIRC epidemic model which considers an exposed compartment for incubation effect, a cross-immune class for transient immunity, and a discrete delay to consider the survival during the latent period. The basic reproductive number $R_0$ is computed, and its significance in determining the threshold behavior of the model is demonstrated. Disease-free equilibrium is analyzed for local and global stability and is found to be stable for the case when $R_0 <1$. It is also shown that there exists a unique endemic equilibrium, which is asymptotically stable when $R_0 >1$. Global stability properties are examined by the Lyapunov approach. For the influence of the delay parameter, it is shown that a small delay cannot affect disease-free equilibrium's stability if $R_0 <1$, and a larger delay will destabilize the endemic equilibrium and cause periodic solutions to appear. Conditions for delay-induced Hopf bifurcation are also provided. Our analytical results are also supported by numerical simulations. One and two-parameter bifurcation analysis concerning the transmission rate and the probability of reinfection are carried out to indicate the possible transition between the disease-free equilibrium and endemic equilibrium. Sensitivity analysis of the basic reproduction number and the long-term endemic infection burden reveals that the transmission rate and reinfection probability are the most influential parameters governing epidemic persistence, whereas an increase in the latent delay consistently suppresses disease prevalence.