Stability analysis of spatiotemporal reaction–diffusion mathematical model incorporating the varicella virus transmission

We introduce an epidemic disease reaction–diffusion model to study the transmission of the varicella-zoster virus in both space and time. More precisely, we present a system of partial differential equations with the Neumann boundary conditions (NBC) concerned to model the evolution of the virus. Firstly, the wellposedness results of the model are studied using the semigroup theory. Then, the boundedness of the solutions is also derived. Further, the basic reproduction number (BRN) for the proposed model is determined using the eigenvalue problem. Moreover, asymptotic profiles of the equilibrium points of the susceptible and infected compartments of the model are investigated. Finally, the advantage of the spatiotemporal model and the above theoretical results are validated with numerical experiments.