Modeling Crimean-Congo Hemorrhagic fever with behavioral awareness: Mathematical analysis via Chebyshev spectral collocation solutions

In this paper, we develop a deterministic awareness-driven compartmental model for the transmission dynamics of Crimean-Congo Hemorrhagic Fever (CCHF), incorporating vector-mediated infection, zoonotic spillover, limited human-to-human transmission, and awareness-induced behavioral responses. The well-posedness of the model is established by proving positivity and boundedness of solutions. The basic reproduction number ℛ₀ is derived via the next-generation matrix approach, and the local stability of the disease-free equilibrium is analysed and shown to be governed by this threshold. A sensitivity analysis has been performed to validate the most significant parameters. To solve the resulting nonlinear system accurately over extended time horizons, a high-order numerical framework is constructed by coupling the quasilinearization method with Chebyshev spectral collocation and a domain decomposition strategy. Convergence and spectral accuracy of the proposed scheme are established rigorously. Numerical simulations validate the theoretical findings and demonstrate the effectiveness of awareness-based interventions in reducing disease burden.