Rich dynamics and data analysis of immune decline against SARS-CoV-2

The global pandemic of SARS-CoV-2 has constituted a serious threat to public health. Although natural infection or vaccination can induce immune protection in individuals, such immunity typically wanes nonlinearly over time. Therefore, to characterize the dynamic process of immunity, we construct a model that includes a two-stage immune waning mechanism. Theoretical analysis reveals under certain conditions there are forward and backward bifurcations in the system, and the coexistence of multiple endemic equilibria can also occur. Numerical simulations further show that under specific parameter conditions, the endemic equilibrium undergoes a saddle-node bifurcation along the extended branch of the forward bifurcation and exhibits bistability, allowing the epidemic to persist even when the basic reproduction number \(\mathcal{R}_{0}