Global Dynamics and Continuum of Equilibria in a Two-Strain SAIR Epidemic Model with Asymptomatic Transmission

In this paper, we develop a two-strain SAIR epidemic model with asymptomatic transmission to investigate the mechanisms governing strain competition and coexistence. The basic reproduction numbers are derived, and threshold conditions for disease extinction and persistence are established. When the reproduction numbers differ, the strain with the larger value dominates, leading to competitive exclusion. In contrast, when the two strains have identical transmission potential, the model admits a continuum of endemic equilibria, representing a regime of neutral competition. The global dynamics of the system are rigorously characterized using Lyapunov functions and center manifold theory, including the stability of the disease-free equilibrium, boundary equilibria, and the coexistence equilibrium set. Numerical simulations are performed to support the analytical results and to illustrate the effects of key parameters on the system dynamics. These findings reveal how asymptomatic transmission and parameter balance shape multi-strain interactions, providing new insights into the persistence and coexistence of competing pathogens.