Stability and Threshold of a Stochastic SIRS Epidemic Model with Vertical Transmission and Transfer from Infectious to Susceptible Individuals
The aim of this paper is to generalize the nonlinear incidence rate of a stochastic SIRS (susceptible-infected-recovered-susceptible) epidemic model. Our basic model was enriched with the hypotheses of vertical transmission and transfer from infected to susceptible individuals, to approach the reali...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/7570296 |
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| _version_ | 1832552065727987712 |
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| author | Driss Kiouach Yassine Sabbar |
| author_facet | Driss Kiouach Yassine Sabbar |
| author_sort | Driss Kiouach |
| collection | DOAJ |
| description | The aim of this paper is to generalize the nonlinear incidence rate of a stochastic SIRS (susceptible-infected-recovered-susceptible) epidemic model. Our basic model was enriched with the hypotheses of vertical transmission and transfer from infected to susceptible individuals, to approach the reality. Our analysis showed that the model is well-posed. Under some conditions imposed on the intensity of the white noise perturbation, the global stability of the system is proven. Furthermore, the threshold of our model which determines the extinction and persistence of the disease is established. Numerical examples are realized to prove the rigor of our theoretical results. |
| format | Article |
| id | doaj-art-1d205671dcfd4bfc914402efd5eeeeb0 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-1d205671dcfd4bfc914402efd5eeeeb02025-02-03T05:59:39ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/75702967570296Stability and Threshold of a Stochastic SIRS Epidemic Model with Vertical Transmission and Transfer from Infectious to Susceptible IndividualsDriss Kiouach0Yassine Sabbar1MSTI Team, High School of Technology, Ibn Zohr University, Agadir, MoroccoMSTI Team, High School of Technology, Ibn Zohr University, Agadir, MoroccoThe aim of this paper is to generalize the nonlinear incidence rate of a stochastic SIRS (susceptible-infected-recovered-susceptible) epidemic model. Our basic model was enriched with the hypotheses of vertical transmission and transfer from infected to susceptible individuals, to approach the reality. Our analysis showed that the model is well-posed. Under some conditions imposed on the intensity of the white noise perturbation, the global stability of the system is proven. Furthermore, the threshold of our model which determines the extinction and persistence of the disease is established. Numerical examples are realized to prove the rigor of our theoretical results.http://dx.doi.org/10.1155/2018/7570296 |
| spellingShingle | Driss Kiouach Yassine Sabbar Stability and Threshold of a Stochastic SIRS Epidemic Model with Vertical Transmission and Transfer from Infectious to Susceptible Individuals Discrete Dynamics in Nature and Society |
| title | Stability and Threshold of a Stochastic SIRS Epidemic Model with Vertical Transmission and Transfer from Infectious to Susceptible Individuals |
| title_full | Stability and Threshold of a Stochastic SIRS Epidemic Model with Vertical Transmission and Transfer from Infectious to Susceptible Individuals |
| title_fullStr | Stability and Threshold of a Stochastic SIRS Epidemic Model with Vertical Transmission and Transfer from Infectious to Susceptible Individuals |
| title_full_unstemmed | Stability and Threshold of a Stochastic SIRS Epidemic Model with Vertical Transmission and Transfer from Infectious to Susceptible Individuals |
| title_short | Stability and Threshold of a Stochastic SIRS Epidemic Model with Vertical Transmission and Transfer from Infectious to Susceptible Individuals |
| title_sort | stability and threshold of a stochastic sirs epidemic model with vertical transmission and transfer from infectious to susceptible individuals |
| url | http://dx.doi.org/10.1155/2018/7570296 |
| work_keys_str_mv | AT drisskiouach stabilityandthresholdofastochasticsirsepidemicmodelwithverticaltransmissionandtransferfrominfectioustosusceptibleindividuals AT yassinesabbar stabilityandthresholdofastochasticsirsepidemicmodelwithverticaltransmissionandtransferfrominfectioustosusceptibleindividuals |