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.
In this paper, we will study mathematically and numerically the dynamics of the hepatitis C virus disease with the consideration of two fundamental modes of transmission of the infection, namely virus-to-cell and cell-to-cell. In our model, we will take into account the role of cure rate of the infected cells and the effect of the adaptive immunity. The model consists of five nonlinear differential equations, describing the interaction between the uninfected cells, the infected cells, the hepatitis C virions and the adaptive immunity. This immunity will be represented by the humoral and cellular immune responses. This work begins with proving the non-negativity and the boundedness of solutions and determining the basic reproduction number. Secondly, five equilibria are established, the local stability analysis for all the equilibria is demonstrated theoretically and numerically. Finally, we have concluded that the numerical results are coherent with our theoretical postulations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.