Dynamics in a disease transmission model coupled virus infection in host with incubation delay and environmental effects

In this paper, a disease transmission model coupled virus infection in host with incubation delay and environmental effects is studied. For the virus infection model in host with immune, latent delay and environmental virus invading, the threshold criteria on the global stability of antibody-free and antibody response infection equilibria are established. For the disease transmission model with incubation delay and immune response in host, basic reproduction number R-0 is defined, and the local stability of equilibria are established, i.e., the disease-free equilibrium is locally asymptotically stable if R-0 < 1, and the endemic equilibrium is locally asymptotically stable if R-0 > 1. Furthermore, the uniform persistence of positive solutions is studied while there is not the direct transmission of disease by the infected individuals. Finally, the numerical examples are presented to verify the main results.