Hepatitis C virus fractional-order model: mathematical analysis

Abstract

Mathematical analysis of epidemics is crucial for the prediction of diseases over time and helps to guide decision makers in terms of public health policy. It is in this context that the purpose of this paper is to study a fractional-order differential mathematical model of HCV infection dynamics, incorporating two fundamental modes of transmission of the infection; virus-to-cell and cell-to-cell along with a cure rate of infected cells. The model includes four compartments, namely, the susceptible hepatocytes, the infected ones, the viral load and the humoral immune response, which is activated in the host to attack the virus. Each compartment involves a long memory effect that is modeled by a Caputo fractional derivative. Our paper starts with the investigation of some basic analytical results. First, we introduce some preliminaries about the needed fractional calculus tools. Next, we establish the well-posedness of our mathematical model in terms of proving the existence, positivity and boundedness of solutions. We present the different problem steady states depending on some reproduction numbers. After that, the paper moves to the stage of proving the global stability of the three steady states. To evaluate the theoretical study of the global stability, we apply a numerical method based on the fundamental theorem of fractional calculus as well as a three-step Lagrange polynomial interpolation method. The numerical simulations show that the free-endemic equilibrium is stable if the basic reproduction number is less than unity. In addition, the numerical tests demonstrate the stability of the other endemic equilibria under some optimal conditions. It is observed that the numerical simulations and the founding theoretical results are coherents.

An incommensurate fractional order model for complex dynamics of viral infection with immunity

“…Many integer and non-integer order models for viral infection exist in the literature. This current study can be compared with an integer order model by Hattaf [11] and a noninteger order model by Marya et al [28]. Use of fractional order derivative in this model gives advantage of memory effect as compared to the integer order model by Hattaf.…”

Spatially modulated ablation driven by chaotic attractors in human lung epithelial cancer cells

“…The mathematical description of energy transfer in cells samples is attractive not only for explaining optical damage [44], but energy distributions associated with biological functions involved in diseases, like viral infections or cancer [45]. Furthemore, fractional differential systems also can describe electrical activity in human skin [46] and cellular reproduction [47].…”

Incorporating Intracellular Processes in Virus Dynamics Models

“…The so-called "standard model", derived from these early efforts and based on predator-prey dynamics, saw success in the mid-1990s when its validation against HIV viral load data from patients undergoing antiretroviral therapy allowed for the quantification of in-host dynamical quantities, such as the infected cell death rate [5]. Since that time, the standard model and its extensions have been used to further describe HIV [6][7][8][9][10][11][12][13][14][15][16][17] and a series of other viral infections, with pathogens such as hepatitis C (HCV) [18][19][20][21], hepatitis B (HBV) [22][23][24][25][26][27][28], influenza [29,30], ebola [31], and SARS-CoV-2 [32][33][34][35][36][37][38].…”