Stability of delayed pathogen dynamics models with latency and two routes of infection

We consider a pathogen dynamics model with antibodies and both pathogen-to-susceptible and infected-to-susceptible transmissions. We consider two types of infected cells, latently infected cells, and actively infected cells. The model considers three types of discrete or distributed delays to characterize the time between the pathogen or the infected cell contacts a susceptible cell and the creation of mature pathogens. We deduct the basic reproduction number and antibody response activation number which determine the existence and stability of the steady states. The global stability analysis of the steady states is established using Lyapunov method. The theoretical results are confirmed by numerical simulations.