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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Bibliographic Details
Published in:Symmetry (Basel) 2022-11, Vol.14 (11), p.2288
Main Authors: Safan, Muntaser, Barley, Kamal, Elhaddad, Mohamed M., Darwish, Mohamed A., Saker, Samir H.
Format: Article
Language:English
Subjects:
Adaptive immunity
Antibodies
Equilibrium
equilibriums
Immunity
Infections
Infectious diseases
mathematical model
natural boosting
Partial differential equations
pertussis infection
stability
Stability analysis
Vaccines
waning immunity
Whooping cough
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14112288