Competitive exclusion in a multi-strain virus model with spatial diffusion and age of infection

In this paper, a multi-strain virus dynamic model with spatial diffusion, age of infection and general incidence function is formulated. The well-posedness of the initial-boundary value problem of the model in the bounded domain Ω⊂Rn is analyzed. By constructing a suitable Lyapunov functional, the global stability of the uninfected steady state is established if all reproduction numbers are smaller or equal to one. It is shown that if Ri, the reproduction number corresponding to strain i is larger than one, the steady state corresponding to strain i exists, if R1>1 is the maximal reproduction number, the steady state E1 corresponding strain one is globally stable. That is, competitive exclusion occurs and strain one eliminates all other strains.