## 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 solutions to ordinary differential equations 65C20 Probabilistic models, generic numerical methods in probability and statistics

### Keywords:

Lyapunov function
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### References:

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