Analysis of an initial value problem for an extracellular and intracellular model of hepatitis C virus infection

Author:

Nangue Alexis1ORCID,Rendall Alan D.2,Tcheugam Brice Kammegne3,Simo Patrick Steve Kamdem4

Affiliation:

1. Higher Teachers’ Training College of the University of Maroua, P.O. Box 55, Maroua, Cameroon

2. Institute for Mathematics, Johannes Gutenberg University, Staudingerweg 9, 55099 Mainz, Germany

3. African Institute for Mathematical Sciences, P.O. Box 608 Limbe, Cameroon

4. Sub-regional Institute of Statistics and Applied Economics, P.O. Box 294 Yaoundé, Cameroon

Abstract

In this paper, a mathematical analysis of the global dynamics of a viral infection model in vivo is carried out. We study the dynamics of a hepatitis C virus (HCV) model, under therapy, that considers both extracellular and intracellular levels of infection. At present, most mathematical modeling of viral kinetics after treatment only addresses the process of infection of a cell by the virus and the release of virions by the cell, while the processes taking place inside the cell are not included. We prove that the solutions of the new model with positive initial values are positive, exist globally in time and are bounded. The model has two virus-free steady states. They are distinguished by the fact that viral RNA is absent inside the cells in the first state and present inside the cells in the second. There are basic reproduction numbers associated to each of these steady states. If the basic reproduction number of the first steady state is less than one, then that state is asymptotically stable. If the basic reproduction number of the first steady state is greater than one and that of the second less than one, then the second steady state is asymptotically stable. If both basic reproduction numbers are greater than one, then we obtain various conclusions which depend on different restrictions on the parameters of the model. Under increasingly strong assumptions, we prove that there is at least one positive steady state (infected equilibrium), that there is a unique positive steady state and that the positive steady state is stable. We also give a condition under which every positive solution converges to a positive steady state. This is proved by methods of Li and Muldowney. Finally, we illustrate the theoretical results by numerical simulations.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation

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