Mathematical Analysis of an SIVRWS Model for Pertussis with Waning and Naturally Boosted Immunity
This work aims mainly to study the controllability of pertussis infection in the presence of waning and natural booster of pertussis immunity and to study their impact on the overall dynamics and disease outcomes. Therefore, an SIVRWS (Susceptible-Infected-Vaccinated-Recovered-Waned-Susceptible) mod...
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| Format: | Article |
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MDPI AG
2022-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/11/2288 |
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| author | Muntaser Safan Kamal Barley Mohamed M. Elhaddad Mohamed A. Darwish Samir H. Saker |
| author_facet | Muntaser Safan Kamal Barley Mohamed M. Elhaddad Mohamed A. Darwish Samir H. Saker |
| author_sort | Muntaser Safan |
| collection | DOAJ |
| description | This work aims mainly to study the controllability of pertussis infection in the presence of waning and natural booster of pertussis immunity and to study their impact on the overall dynamics and disease outcomes. Therefore, an SIVRWS (Susceptible-Infected-Vaccinated-Recovered-Waned-Susceptible) model for pertussis infection spread in a demographically stationary, homogeneous, and fully symmetric mixing population is introduced. The model has been mathematically analyzed, where both equilibrium and stability analyses have been established, and uniform persistence of the model has been shown. The conditions on model parameters that ensure effective control of the infection have been derived. The effects of the interplay between waning and boosting pertussis immunity by re-exposure to Bordetella pertussis and vaccination on the dynamics have been investigated. The analytical results have been numerically confirmed and explained. The analysis reveals that ignoring the natural booster of immunity overestimates the endemic prevalence of the infection. Moreover, ignoring the differential susceptibility between secondary and primary susceptible individuals overestimates the critical vaccination coverage required to eliminate the infection. Moreover, the shorter the period of immunity acquired by either vaccination or experiencing natural infection, the higher the reproduction number and the endemic prevalence of infection, and therefore, the higher the effort needed to eliminate the infection. |
| first_indexed | 2024-03-09T18:36:44Z |
| format | Article |
| id | doaj.art-f870a47484ea4727bba0da5c12cf51c5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T18:36:44Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f870a47484ea4727bba0da5c12cf51c52023-11-24T07:07:56ZengMDPI AGSymmetry2073-89942022-11-011411228810.3390/sym14112288Mathematical Analysis of an SIVRWS Model for Pertussis with Waning and Naturally Boosted ImmunityMuntaser Safan0Kamal Barley1Mohamed M. Elhaddad2Mohamed A. Darwish3Samir H. Saker4Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics and Natural Science, Allen University, 1530 Harden Street, Columbia, SC 29204, USADepartment of Mathematics, Faculty of Sciences, Damanhour University, Damanhour 22511, EgyptDepartment of Mathematics, Faculty of Sciences, Damanhour University, Damanhour 22511, EgyptMathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, EgyptThis work aims mainly to study the controllability of pertussis infection in the presence of waning and natural booster of pertussis immunity and to study their impact on the overall dynamics and disease outcomes. Therefore, an SIVRWS (Susceptible-Infected-Vaccinated-Recovered-Waned-Susceptible) model for pertussis infection spread in a demographically stationary, homogeneous, and fully symmetric mixing population is introduced. The model has been mathematically analyzed, where both equilibrium and stability analyses have been established, and uniform persistence of the model has been shown. The conditions on model parameters that ensure effective control of the infection have been derived. The effects of the interplay between waning and boosting pertussis immunity by re-exposure to Bordetella pertussis and vaccination on the dynamics have been investigated. The analytical results have been numerically confirmed and explained. The analysis reveals that ignoring the natural booster of immunity overestimates the endemic prevalence of the infection. Moreover, ignoring the differential susceptibility between secondary and primary susceptible individuals overestimates the critical vaccination coverage required to eliminate the infection. Moreover, the shorter the period of immunity acquired by either vaccination or experiencing natural infection, the higher the reproduction number and the endemic prevalence of infection, and therefore, the higher the effort needed to eliminate the infection.https://www.mdpi.com/2073-8994/14/11/2288mathematical modelwaning immunitynatural boostingpertussis infectionequilibriumsstability |
| spellingShingle | Muntaser Safan Kamal Barley Mohamed M. Elhaddad Mohamed A. Darwish Samir H. Saker Mathematical Analysis of an SIVRWS Model for Pertussis with Waning and Naturally Boosted Immunity Symmetry mathematical model waning immunity natural boosting pertussis infection equilibriums stability |
| title | Mathematical Analysis of an SIVRWS Model for Pertussis with Waning and Naturally Boosted Immunity |
| title_full | Mathematical Analysis of an SIVRWS Model for Pertussis with Waning and Naturally Boosted Immunity |
| title_fullStr | Mathematical Analysis of an SIVRWS Model for Pertussis with Waning and Naturally Boosted Immunity |
| title_full_unstemmed | Mathematical Analysis of an SIVRWS Model for Pertussis with Waning and Naturally Boosted Immunity |
| title_short | Mathematical Analysis of an SIVRWS Model for Pertussis with Waning and Naturally Boosted Immunity |
| title_sort | mathematical analysis of an sivrws model for pertussis with waning and naturally boosted immunity |
| topic | mathematical model waning immunity natural boosting pertussis infection equilibriums stability |
| url | https://www.mdpi.com/2073-8994/14/11/2288 |
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