A generalized viral immunological model in presence of adaptive immunity with lytic and non-lytic effects

Abstract

This article develops a new mathematical model that describes the dynamics of viral infections in presence of adaptive immunity. The developed model accounts for the presence of a non-cytolytic cure and considers both cell-to-cell and virus-to-cell transmission modes, along with the lytic and non-lytic effects of both cellular and humoral immune responses. Moreover, the well-posedness of the model is demonstrated through the non-negativity and boundedness of its solutions. Also, five equilibriums are established and five threshold parameters are derived to ensure the global stability of these equilibria. Finally, the dynamics of the model have been shown through numerical illustrations using specific parameters related to human immunodeficiency virus (HIV) infection.