Complex dynamics behavior in a generalized diffusive multiple delays within-host model for HBV infection with capsids and adaptive immune response in a heterogeneous viral environment.

In this paper, we investigate the dynamics of a new chronic hepatitis B model through environmental-driven infection in heterogeneous and homogenous space. The model includes spatial diffusion, five time delays, and a general incidence function. The well-posedness of solutions, including the existence of global solutions, uniqueness, non-negativity, ultimate boundedness, is established. The reproduction numbers for virus infection, CTL immune response, antibody immune response, CTL immune competition and antibody immune competition, respectively, are calculated. By employing the Lyapunov functionals and linearization methods, the threshold conditions on the global stability of the infection-free equilibrium are obtained; and the threshold conditions on the uniform persistence and the global stability of the equilibria for immune-free, antibody response, CTL response and antibody and CTL responses, respectively, are established. The occurrence of Hopf bifurcation of the spatially homogeneous equilibria is also established. An application is provided, and numerical simulations are carried out to illustrate the analytical results and verify the conjectures. Our findings reveal the rich and complex patterns of HBV infection dynamics in vivo, including regular and irregular periodic oscillations. Irregular oscillations may signify immune disorders and allergies. Also, from numerical simulations, it follows that the majority of hepatitis B infection could escape chronic infection.