On a Mathematical Model with a Free Boundary of the Dynamics of Diffuse Infection with an Immune Response

A model of viral infection with self-proliferation of cytotoxic \(T-\) lymphocytes (CTLs) with a nonlinear infection rate and free boundaries is proposed, and its global dynamics are studied. The existence, uniqueness and uniform estimates of the global solution are proved, as well as the behavior of the components of the solution and the unknown boundary over large time intervals. With the help of the basic reproductive number \(R_{0}\) , sufficient conditions are created for the spread or disappearance of the virus.