Competitive exclusion principal definition
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To explore the mechanisms of these diseases, scientists have proposed plenty of mathematical models describing the transmission of disease such as the infectious disease model (SI, SIR, SEI, and SIS) and the within-host virus model (HBV, HCV, HIV, Ebola, and Zika). Nowadays, more and more people in the world are dying of various diseases such as AIDS, avian influenza, cholera, Ebola, and Zika virus. Furthermore, numerical simulations are also carried out to illustrate the theoretical results, which is seldom seen in the relevant known literatures. Meanwhile, we can prove that the single-strain and multistrain viral infection models are well posed. Thus, competitive exclusion happens and all other strains die out except strain. If the reproduction number for strain is maximal and larger than one, the steady state corresponding to the strain is globally stable. For the multistrain viral infection model, we have discussed the competitive exclusion problem. For the single-strain viral infection model, by using the linearization method and constructing appropriate Lyapunov functionals, we obtain that the global threshold dynamics of the model is determined by the reproductive numbers for viral infection. In this paper, we investigate single-strain and multistrain viral infection models with general incidence function and density-dependent diffusion subject to the homogeneous Neumann boundary conditions.