Global analysis of a mathematical model for hepatitis C considering the host immune system

Dynamics of a stochastic hepatitis C virus system with host immunity

“…In this paper, we study the effect of environmental noise on the dynamics of a hepatitis C virus model with host immune. The results extend the paper of Blé [5] in understanding the dynamics of a deterministic hepatitis C virus. Various types of Lyapunov functions are designed to study the stationary distribution and ergodicity as well as the extinction of the stochastic system.…”

“…In recent decades, many successful mathematical models investigating fundamental Hepatitis C viruses dynamics have been developed, among which we may mention the papers by Banerjee et al [2], Dixit et al [12], Neumann et al [27] and Rong et al [29] to cite only a few. In 2018, Blé et al [5] investigated the dynamics of a hepatitis C virus system with the host immune. The system contains four variables, namely the target cells, the infected liver cells, the viral load and the T killer cells.…”

“…For the deterministic system (1), Blé et al [5] stated that the global stability is determined in terms of the basic reproduction number R 0 = kβsp µiµsµv . When R 0 ≤ 1, the system (1) admits a unique infection-free equilibrium E 0 = ( βs µs , 0, 0, 0), which is globally asymptotically stable.…”

“…where B i (t) are standard Brownian motions with intensities σ 2 i , i = 1, · · · , 4. This paper is aimed at extending the work of Blé [5] in understanding the dynamics of a deterministic hepatitis C virus model with host immunity, and further studying how environmental noise affect the dynamics of hepatitis C viruses. The rest of the paper is organized as follows: In Section 2, we introduce some preliminary lemmas for further studies.…”

A Fractional Order Hepatitis C Mathematical Model with Mittag-Leffler Kernel

“…As better theories are discovered, a lack of concordance between mathematical models that are theoretical and experimental findings frequently leads to significant advancements. Many mathematical models were formulated for the Hepatitis C diseases to understand the dynamics of the diseases and control the spreading of diseases; we refer to [11][12][13][14].…”