Necessary and sufficient condition for extinction and persistence of SIRS system with random perturbation. (English) Zbl 1334.92412
Summary: This paper characterizes the qualitative dynamics of a stochastic SIRS epidemic model. The study shows that the dynamics of the model are determined by a certain threshold quantity \(\mathcal{R}_{\mathcal{S}}\) expressed in terms of the model parameters and the intensity of the noise. If \(\mathcal{R}_{\mathcal{S}} < 1\), the disease will be eliminated from the community; whereas an epidemic occurs if \(\mathcal{R}_{\mathcal{S}} > 1\). Our results recover the known results in the earlier literature as special cases. The presented results are illustrated by numerical simulations.
MSC:
| 92D30 | Epidemiology |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
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