Dynamics of an SEIQHR-based mathematical model for infectious disease with awareness-driven optimal control

In this article, we extended the basic Susceptible-Exposed-Infectious-Quarantined-Hospitalized-Recovered (SEIQHR) compartmental model to the Susceptible-Exposed-Infectious-Quarantined-Hospitalized-Recovered-Awareness (SEIQHRA) framework by incorporating the level of awareness, $A$, as an additional model population to gain deeper insights into the dynamic process of infectious disease outbreaks, with particular emphasis on awareness-based interventions. Hospitalization, treatment, and quarantining procedures informed by awareness were integrated into this refined model. We investigated the key mathematical properties including boundedness of solutions, the basic reproduction number, and the existence of equilibriums. The model admitted two equilibria: The disease-free and the endemic equilibrium. The disease-free equilibrium was shown to be globally asymptotically stable when $R_0<1$ and unstable when $R_0>1$. Forward bifurcation occurred at $R_0=1$. The endemic equilibrium underwent a Hopf bifurcation, resulting in a stability switch. To design effective awareness-based interventions, the Pontryagin maximum principle was employed to derive optimal control parameters. Numerical simulations were conducted to validate the analytical findings, highlighting the role of awareness-driven control measures in controlling an infectious disease and enhancing public health outcomes.