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