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| The COVID-19 epidemic is still spreading all over the world. With the mutation of the virus, now the mainstream strains in the world are Delta and Omicron. Considering the actual situation of large-scale vaccination, under the assumption that the vaccine mainly protects against Delta strain infection and the antibody concentration induced by the vaccine has an attenuation effect, this paper constructs a new dynamic model to simulate the spread of the disease. The model uses two general incidence rates to describe the spread of these two strains. Include non-monotonous, non-concave forms of morbidity, which can infer media education or psychological effects. Theoretically, we find that there are at most four equilibriums in the model, and the global asymptotic stability condition of the model is obtained by using Lyapunov function analysis. Furthermore, the numerical simulation results confirm that the equilibria of this system are global asymptotic stability under the conditions of each universality condition. |
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| Keywords:Applied Mathematics, Asymptotically stability, General nonlinear incidence rate |
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