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Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates. (English) Zbl 1223.92057
Summary: We introduce a basic reproduction number for a multigroup SEIR model with nonlinear incidence of infection and nonlinear removal functions between compartments. Then, we establish that the global dynamics are completely determined by the basic reproduction number ${R}_{0}$. This shows that the basic reproduction number ${R}_{0}$ is a global threshold parameter in the sense that if it is less than or equal to one, the disease free equilibrium is globally stable and the disease dies out; whereas if it is larger than one, there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population. Finally, two numerical examples are also included to illustrate the effectiveness of the proposed result.
##### MSC:
 92D30 Epidemiology 34D23 Global stability of ODE 65C20 Models (numerical methods)
##### Keywords:
Lyapunov function