A Fractional-Order Within-Host Model of Swine Flu Infection with Autophagy Effects: Qualitative and Stability Analysis
I. C. Nwokike *
Department of Mathematics, Federal University of Technology, Owerri, Nigeria and Centre of Excellence in Sustainable Procurement, Environmental & Social Standards, Federal University of Technology, Owerri, Nigeria.
M. O. Ezekoye
Centre of Excellence in Sustainable Procurement, Environmental & Social Standards, Federal University of Technology, Owerri, Nigeria and Department of Chemistry, Federal University of Technology, Owerri, Nigeria.
K. M. Koko
Department of Mathematics and Statistics, Air Force Institute of Technology, Kaduna, Nigeria.
T. W. Owolabi
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
G. O. Onukwube
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
G. O. Nwafor
Centre of Excellence in Sustainable Procurement, Environmental & Social Standards, Federal University of Technology, Owerri, Nigeria and Department of Statistics, Federal University of Technology, Owerri, Nigeria.
C. Nwutara
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
H. Mansur
Department of Mathematics, Sule Lamido University Kafin Hausa, Jigawa, Nigeria.
N. C. Umelo-Ibemere
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Swine influenza (H1N1) is a rapidly replicating respiratory virus characterized by complex within-host interactions between epithelial target cells, infected cells, and immune-mediated intracellular processes. In this study, we develop and analyze a fractional-order mathematical model describing the within-host dynamics of H1N1 infection, explicitly incorporating autophagy as a key intracellular antiviral mechanism. The model is formulated using Caputo fractional derivatives to account for memory effects associated with delayed viral replication, immune activation, and persistence of infection observed in influenza pathogenesis. We establish fundamental qualitative properties of the model, including positivity, boundedness, and the existence of a biologically feasible invariant region. The disease-free equilibrium and was derived, and the basic reproduction number R0 is obtained using the next-generation matrix. This represents the threshold for viral establishment within the host. The stability analysis conducted showed that the infection was cleared when R0 < 1. Sustained viral replication occurs when R0 > 1, consistent with known influenza infection behavior. The results of the study demonstrates that autophagy does not influence the initial infection threshold. It although reduces viral load significantly and impede infected cell burden during the progression phase of H1N1 infection. The fractional-order model analysis further reveals that memory effects slow down infection dynamics. This reflects clinically observed delays in viral peak and immune response activation. The findings of this study provides a more realistic mathematical representation of swine flu infection kinetics. It also highlights the potential of targeting autophagy pathways as a therapeutic strategy for controlling influenza severity.
Keywords: Swine flu, H1N1, influenza infections, influenza virus, mathematical modeling, autophagy, stability analysis