Dynamics and optimal control of an extended SIQR model with protected human class and public awarenessFahad Al Basir, Kottakkaran Sooppy Nisar, Ibraheem M. Alsulami and Amar Nath ChatterjeeEur. Phys. J. Plus, 140 2 (2025) 152DOI: https://doi.org/10.1140/epjp/s13360-025-06108-3