The article presents an SEIRS-type reaction-diffusion disease transmission model with nonlinear disease incidence. The qualitative study reflects that local and global stability properties of equilibria are fully determined by the threshold value of the basic reproductive number \((\mathcal {R}_0)\) . The existence of a traveling wave solution that connects epidemic-free steady state to endemic steady state has been examined by upper and lower solution techniques with the verification of Schauder’s fixed point theorem. The existence criterion is further examined through a weak upper-lower solution pair that may lack continuous differentiability at countably many points. The system does not possess a traveling wave solution for \(\mathcal {R}_0<1,~\mathcal {R}_0=1\) , and the case when \(\mathcal {R}_0>1\) but speed of wave (c) is less than the critical or minimal wave speed \((c^*)\) . The analytically obtained results are verified by numerical simulations.
