The goal of this paper is to demonstrate the well-posedness of a nonlinear parabolic reaction-diffusion system modeling the
spread of infectious diseases. The considered mathematical model is of the SEIRDS type. We prove the global existence
of a weak solution by using an approximation system with a delay operator λτ (which we define in the subsection 3.1) ,
along with a priori estimates and compactness arguments. Additionally, we establish the uniqueness of the solution and
its continuous dependence on the contagion rates using Gronwall’s lemma. These results not only show the existence of
a solution but also ensure that it is unique and responds stably to variations in the model parameters.

reaction-diffusion, nonlinear parabolic system, infectious diseases, SEIRD model, weak solution, well- posedness