The complex dynamical study of a UAI epidemic model in non-spatial and spatial environments

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.