Fractional-Order Modeling of Within-Host Swine Influenza (H1N1) Dynamics with Autophagy and Immune Response

Swine influenza (H1N1) is a highly transmissible respiratory infection characterised by complex within-host interactions involving viral replication, intracellular defence mechanisms, and adaptive immune response. This study establishes a fractional-order mathematical model that describes the within-host dynamics of H1N1 infection and explicitly considers autophagy and immune-mediated clearance of the virus. The model is formulated using Caputo fractional derivatives to capture memory effects of delayed viral replication, immune activation, and infection progression observed in influenza infections. Basic qualitative properties of the proposed model, such as positivity and boundedness of the solutions of the model, were established to ensure biological feasibility. The R0 provides a threshold for infection establishment within the host. We went on to conduct the local and global stability analyses. This was done using fractional stability theory, Routh–Hurwitz criteria, and Lyapunov methods. The study showed that the disease-free equilibrium is stable when R0 < 1. The study also implies that viral clearance and a unique endemic equilibrium exist. The endemic equilibrium is globally stable when R0 > 1, corresponding to persistent infection. The results show that immune response and autophagy do not affect the initial infection threshold but contribute to a marked decrease in viral load and infected cell count in the progression stage of infection. A synergistic mechanism of viral clearance is shown by the interplay between autophagy and adaptive immunity. That said, the proposed model provides a biologically consistent and more realistic framework for a within-host study of swine influenza dynamics. The role of intracellular and immune-mediated processes in regulating infection severity is a major contribution of the work.