Abstract
This paper studies the global stability of a discrete-time pathogen dynamic model with both cell-mediated and antibody immune responses. Both latently and actively infected cells are incorporated into the model. We discretize the continuous-time model by using the nonstandard finite difference (NSFD) method. We establish that NSFD preserves the nonnegativity and boundedness of the solutions of the model. We derive four threshold parameters which govern the existence and stability of the steady states. We establish by using the Lyapunov method, the global stability of the five steady states of the model. We illustrate our theoretical results by using numerical simulations.
Highlights
Studying and analysing the inward host dynamics of pathogens that infect the human body such as the human immunodeficiency virus (HIV), hepatitis C virus (HCV), hepatitis B virus (HBV), and human T-cell leukemia virus (HTLV) have received great attention from scientists and researchers. e dynamical behavior of pathogens can be understood by using mathematical modeling. e adaptive immune system plays an important role in controlling pathogenic infections
In the case of nonstandard finite difference (NSFD), we can see that the increasing of h does not affect the stability of the steady states
We studied a discrete-time pathogen dynamic model with adaptive immunity. e model incorporated two classes of infected cells, latently infected cells and actively infected cells
Summary
Studying and analysing the inward host dynamics of pathogens that infect the human body such as the human immunodeficiency virus (HIV), hepatitis C virus (HCV), hepatitis B virus (HBV), and human T-cell leukemia virus (HTLV) have received great attention from scientists and researchers (see, e.g., [1,2,3,4,5,6,7,8,9,10,11,12]). e dynamical behavior of pathogens can be understood by using mathematical modeling. e adaptive immune system plays an important role in controlling pathogenic infections. The impact of antibody immune response on pathogenic infections has been studied in several mathematical models (see, e.g., [13,14,15,16,17,18,19,20]). The effect of cell-mediated immune response on pathogen dynamics has been modeled in several works (see, e.g., [21,22,23,24,25,26,27]). E effect of the cell-mediated immune response has been considered of discrete-time pathogen dynamic models in [41, 42]. E present paper aims to study the impact of both antibody and cell-mediated immune responses on the pathogen dynamic model. We construct Lyapunov functions to prove the global stability of the steady states
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