Stability of a Fractional Multi-Strain Epidemic Model

Abstract

We investigate a fractional-order epidemic model with three competing strains, incorporating memory effects through the Caputo derivative of order alpha between zero and one. Strain one follows a saturated Holling type-II incidence, while strains two and three spread through bilinear mass-action contact. We establish well-posedness by proving existence, uniqueness, positivity, and boundedness of solutions within a compact invariant region. The strain-specific basic reproduction numbers are computed via the next-generation matrix method. Applying Matignon's criterion, we prove local asymptotic stability of the disease-free and monomorphic endemic equilibria. Suitable Lyapunov functions then establish their global asymptotic stability.