Fractional-Order Epidemic Model for Measles Infection

Abstract

In this study, a nonlinear dynamic SEVIQR measles epidemic model is constructed and analyzed using the novel Caputo fractional-order derivative operator. The model’s existence and uniqueness are established. In addition, the model equilibria are determined, and the novel Jacobian determinant method recently constructed in the literature of epidemiological modeling of infectious diseases is applied to determine the threshold quantity, R0. Furthermore, we construct appropriate Lyapunov functions to establish the global asymptotic stability of the disease-free and endemic equilibrium points. Finally, the numerical solution of the model is executed employing the efficient and widely known Adams-type predictor-corrector iterative scheme, and simulation is conducted to investigate the impact of memory index and diverse preventive measures on the occurrence of the disease. Numerical simulation of the model indicates that quarantine, vaccination, and treatment can reduce the numbers of infectious and exposed populations, thereby controlling the disease. Therefore, it is recommended that the government provide financial assistance for vaccine distribution.