Threshold dynamics of HCV model with cell-to-cell transmission and a non-cytolytic cure in the presence of humoral immunity

Abstract

A mathematical model for HCV infection, which incorporates both the routes of infection spread, namely, virus-to-cell and cell-to-cell transmission along with a cure rate of infected cells through the non-cytolytic process, is presented. In addition, the model also includes the effect of humoral immune response using a nonlinear activation rate. To the best of our knowledge, this is the first model for HCV dynamics which incorporates both the cell-free and cell-to-cell transmission as well as cure rate within the same model, in addition to antibody being a part of the model setup. The non-negativity and boundedness of solutions of the model system are established and the basic as well as viral reproduction number is determined. The local and global stability analysis of the three equilibria, namely, disease-free, immune response free and infected equilibrium with humoral immune response are investigated theoretically as well as numerically in terms of conditions on the basic reproduction number and viral reproduction number. Comparison of four different HCV models is carried out numerically. The numerical results indicate that the consideration of cell-to-cell infection increases the concentration of infected cells, while the humoral immune response neutralizes the virus density effectively and it has a less significant effect in reducing the infection. The inclusion of the non-cytolytic cure increases the level of uninfected cells. The effects of both the modes of infection spread and cure in infected cells, on the basic reproduction number and the subsequent impact on the dynamical behavior of the system are illustrated.