Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures. (English) Zbl 1312.34086
Summary: We formulate an SIR epidemic model with hybrid of multigroup and patch structures, which can be regarded as a model for the geographical spread of infectious diseases or a multi-group model with perturbation. We show that if a threshold value, which corresponds to the well-known basic reproduction number \(R_0\), is less than or equal to unity, then the disease-free equilibrium of the model is globally asymptotically stable. We also show that if the threshold value is greater than unity, then the model is uniformly persistent and has an endemic equilibrium. Moreover, using a Lyapunov functional technique, we obtain a sufficient condition under which the endemic equilibrium is globally asymptotically stable. The sufficient condition is satisfied if the transmission coefficients in the same groups are large or the per capita recovery rates are small.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 34D23 | Global stability of solutions to ordinary differential equations |
| 92D30 | Epidemiology |
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