A model of viral infection of monocytes population by the dengue virus is formulated as a system of four ordinary differential equations. The model takes into account the immune response and nonlinear incidence rate of susceptible and free virus particles.
Global stability of the uninfected steady state is investigated. Such a steady state always exists. If it is the only steady state, then it is globally asymptotically stable. If any infected steady state exists, then the uninfected steady state is unstable and one of the infected steady states is locally asymptotically stable. These different cases depend on the values of the basic reproduction ratio and other parameters.