Stability Analysis of a Fractional-Order Within-Host Model of Swine Influenza (H1N1) with Environmental Transmission
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.
K. M. Koko
Department of Mathematics and Statistics, Air Force Institute of Technology, Kaduna, Nigeria.
H. Mansur
Department of Mathematics, Sule Lamido University Kafin Hausa, Jigawa, Nigeria.
G. O. Nwafor
Centre of Excellence in Sustainable Procurement, Environmental & Social Standards, Federal University of Technology, Owerri, Nigeria.
V. O. Obi
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
T. W. Owolabi
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
B. N. Okechukwu
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
C. Nwutara
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
J. O. Obioma
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
I. C. Obinwanne
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Swine influenza (H1N1) continues to be a major public health problem of interest because of the high potential for transmission and the ability to have rapid mutagenesis and to cause persistence in infected hosts. Here, we introduce and discuss a novel within-host fractional-order mathematical model including environmental viral transmission and nonlinear dynamics of the infection through saturated incidence functions. The model includes healthy epithelial cells, infected cells, free virus particles, and environmental viral load, and the Caputo fractional derivative, accounting for memories of delayed biological responses and viral replication. First, we demonstrate the well-posedness of the model by establishing existence, uniqueness, positivity, and boundedness of solutions. We come up with an invariant region to guarantee that all state variables are biologically significant for time. The basic reproduction number R0 is obtained based on the next-generation matrix methodology and is shown to have two additively related contributions related to the route of either the direct viral transmission and/or the environmental feedback pathways. Analyses of equilibria stability are performed with linearization, Routh–Hurwitz criteria, and the fractional order stability theory. We found that viral dynamics outside the host significantly increase the effective reproduction number and can prolong infection by reinfection mechanisms. Collectively, these results illustrate that environmental transmission effects, nonlinear infection, and memory exert significant contributions to an infection process on infection outcomes. The model provides an integrated perspective of swine flu physiology, and could serve as a framework for effective control programmes.
Keywords: Fractional-order, dynamical systems, within-host, swine influenza, H1N1, environmental transmission, autophagy, saturated incidence