Abstract
In this paper, we propose a fractional-order viral infection model, which includes latent infection, a Holling type II response function, and a time-delay representing viral production. Based on the characteristic equations for the model, certain sufficient conditions guarantee local asymptotic stability of infection-free and interior steady states. Whenever the time-delay crosses its critical value (threshold parameter), a Hopf bifurcation occurs. Furthermore, we use LaSalle’s invariance principle and Lyapunov functions to examine global stability for infection-free and interior steady states. Our results are illustrated by numerical simulations.
Highlights
Various mathematical models have been developed to describe, within-host, the dynamics of various viral infections, with a focus on virus-to-cell transmission, such as human immunodeficiency virus (HIV) [1], COVID-19 [2,3], hepatitis C virus (HCV) [4], hepatitis B virus (HBV) [5], and human T-cell lymphotropic virus 1 (HTLV-1) [6]
The classical integer-order differential models can be useful for the study of disease dynamics, the fractional-order models are more useful for exploring disease dynamics
This paper examines the global dynamics of a fractional-order viral infection model with latent infection
Summary
Various mathematical models have been developed to describe, within-host, the dynamics of various viral infections, with a focus on virus-to-cell transmission, such as human immunodeficiency virus (HIV) [1], COVID-19 [2,3], hepatitis C virus (HCV) [4], hepatitis B virus (HBV) [5], and human T-cell lymphotropic virus 1 (HTLV-1) [6]. Wang et al [12] discussed the global stability results of HIV viral infection model with latently infected cells, B-cell immune response, Beddington–DeAngelis functional response, and various timedelays. The authors in [13] reported the stability and bifurcation results of generalized viral infection system with humoral immunity and distributed delays in virus production and cell infection, and time lags described the time needed to activate the immune response. The authors in [18] analyzed the local stability results of fractional-order Ebola viral infection model with time-delayed immune response (cytotoxic T-lymphocyte term) in heterogeneous complex networks. The authors reported in [21] derived the sufficient conditions of stability and optimal control results for the fractional-order HIV model with transmission dynamics.
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