Abstract
In this paper, we study the dynamics of a viral infection model formulated by five fractional differential equations (FDEs) to describe the interactions between host cells, virus, and humoral immunity presented by antibodies. The infection transmission process is modeled by Hattaf-Yousfi functional response which covers several forms of incidence rate existing in the literature. We first show that the model is mathematically and biologically well-posed. By constructing suitable Lyapunov functionals, the global stability of equilibria is established and characterized by two threshold parameters. Finally, some numerical simulations are presented to illustrate our theoretical analysis.
Highlights
We study the dynamics of a viral infection model formulated by five fractional differential equations (FDEs) to describe the interactions between host cells, virus, and humoral immunity presented by antibodies
The immune response plays an important role to control the dynamics of viral infections such as human immunodeficiency virus (HIV), hepatitis B virus (HBV), hepatitis C virus (HCV), and human T-cell leukemia virus (HTLV)
We improve the above ordinary differential equations (ODEs) and FDE models by proposing a new fractional order model that describes the interactions between susceptible host cells, viral particles, and the humoral immune response mediated by the antibodies; that is, Dαx (t) = λ − dx − f (x, V) V + ρl, Dαl (t) = f (x, V) V − (m + ρ + γ) l, International Journal of Differential Equations
Summary
The immune response plays an important role to control the dynamics of viral infections such as human immunodeficiency virus (HIV), hepatitis B virus (HBV), hepatitis C virus (HCV), and human T-cell leukemia virus (HTLV). The humoral immune response is more effective than cellular immune response [32] For this reason, we improve the above ODE and FDE models by proposing a new fractional order model that describes the interactions between susceptible host cells, viral particles, and the humoral immune response mediated by the antibodies; that is, Dαx (t) = λ − dx − f (x, V) V + ρl, Dαl (t) = f (x, V) V − (m + ρ + γ) l, International Journal of Differential Equations.
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