Dynamics Analyses and Parameter Estimation of an Improved Fractional-Order SEAIRQ COVID-19 Dynamic Model Based on Two Types of Fractional Derivative Operators

COVID-19, a global pandemic caused by the severe acute respiratory syndrome coronavirus 2, emerged in late 2019 and has posed significant threats to public health and economic development worldwide. To better understand and predict the spread of the disease, mathematical modeling has become essential. Based on the traditional integer-order SEAIRQ model for COVID-19, we introduce a new fractional-order extension by incorporating the transition rate ε from asymptomatic to infected individuals εA. We then analyze the existence and uniqueness of solutions for the proposed COVID-19 model, compute the equilibrium points and the basic reproduction number, and investigate the stability of the equilibria. Furthermore, two new fractional-order models are formulated using the Caputo and Caputo–Fabrizio (CF) fractional differential operators, respectively. Numerical solutions are obtained using the Gorenflo–Mainardi–Moretti–Paradisi (GMMP) scheme and the Adams–Bashforth method (ABM), correspondingly. Model parameters are estimated via the modified hybrid Nelder–Mead simplex search method, with reference to actual COVID-19 case data from Delhi. The results demonstrate that both fractional-order systems significantly outperform the integer-order model. Predictions of COVID-19 infection trends derived from the two fractional-order systems are largely consistent, underscoring their practical relevance and applicability.