The complex dynamical study of a UAI epidemic model in non-spatial and spatial environments
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Date
2024
Authors
Journal Title
European Physical Journal Plus
Journal ISSN
Volume Title
Publisher
Springer Science and Business Media Deutschland GmbH
Abstract
In the realm of disease transmission dynamics, assigning blame to every susceptible individual for propagating an illness proves untenable. This limitation plagues prevailing compartmental models, including SI, SIS, SIR, SEIR, and others, impeding accurate disease-spread prognostication. This study innovatively partitions the susceptible population into two distinct classes: the unaware and the aware. This conceptual leap facilitates the evolution of the SIR model into a more realistic UAIR epidemic model, characterized by a bilinear incidence rate in the unaware class and a saturated incidence rate in the aware class. The study rigorously establishes key insights, encompassing the stability of the endemic equilibrium state, transcritical and Hopf bifurcations, and stability of bifurcated periodic solutions in the reduced UAI epidemic model. Notably, the analysis uncovers potential disease-induced chaos, the turbulence that heightened community awareness can potentially harness. Delving deeper, the research explores a self-diffusive spatio-temporal UAI epidemic model with zero-flux boundary conditions, unveiling instability insights that preclude the emergence of Turing patterns and associated Turing bifurcation. Rigorous numerical simulations validate the analytical framework, unveiling captivating non-Turing patterns within a 2-dimensional domain. This study proffers a predictive exploration, poised to unearth diverse medically significant observations, further enriching our understanding of disease dynamics. � The Author(s), under exclusive licence to Societ� Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.