https://doi.org/10.1140/epjp/s13360-023-04777-6
Regular Article
Stability analysis of spatiotemporal reaction–diffusion mathematical model incorporating the varicella virus transmission
1
Department of Applied Sciences, National Institute of Technology Goa, 403 401, Goa, India
2
Department of Mathematics, Guelma University, 24000, Guelma, Algeria
3
Department of Mathematics, Peter the Great Saint Petersburg Polytechnic University, 195251, Saint Petersburg, Russia
Received:
11
November
2023
Accepted:
5
December
2023
Published online:
17
December
2023
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.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
