Dynamics of an immune-epidemiological model with virus evolution and superinfection

To get a better understanding how virus evolution influences on the disease spread, in this paper, we develop a nested immune-epidemiological model with superinfection. The interaction between virokins of within exposed host is described by an ordinary differential equation model. For this within host model, besides the infect-free equilibrium, there are two boundary equilibria and a unique coexistence equilibrium. Virokins coexistence within exposed host leads to the superinfection occurs between hosts. To consider the superinfection between host, we proposed an age structured epidemic model with latency age, in which the transfer rate and the superinfection rate of the exposed individuals both depend on the latency age. For this between host model, the local stabilities of the two boundary steady states and the existence of coexistence steady state are totally determined by the invasion reproduction numbers, R12, R21. Especially, uniform persistence of the between host model is strictly proved by use of integral semigroup theory when R12>1 and R21>1. Some numerical simulations are carried out to verify the main theoretical results and to illustrate the two concerns ((i) the effect of virokins coexistence within exposed hosts on the superinfection between hosts, (ii) the influence of the virus evolution on the dynamics of the age structured model). Finally, a brief conclusion is given in Section 6.