Bulletin of Mathematical Biology

, Volume 75, Issue 7, pp 1104–1137

Dynamics Analysis of a Multi-strain Cholera Model with an Imperfect Vaccine

  • Mohammad A. Safi
  • Dessalegn Y. Melesse
  • Abba B. Gumel
Original Article

DOI: 10.1007/s11538-013-9845-2

Cite this article as:
Safi, M.A., Melesse, D.Y. & Gumel, A.B. Bull Math Biol (2013) 75: 1104. doi:10.1007/s11538-013-9845-2

Abstract

A new two-strain model, for assessing the impact of basic control measures, treatment and dose-structured mass vaccination on cholera transmission dynamics in a population, is designed. The model has a globally-asymptotically stable disease-free equilibrium whenever its associated reproduction number is less than unity. The model has a unique, and locally-asymptotically stable, endemic equilibrium when the threshold quantity exceeds unity and another condition holds. Numerical simulations of the model show that, with the expected 50 % minimum efficacy of the first vaccine dose, vaccinating 55 % of the susceptible population with the first vaccine dose will be sufficient to effectively control the spread of cholera in the community. Such effective control can also be achieved if 50 % of the first vaccine dose recipients take the second dose. It is shown that a control strategy that emphasizes the use of antibiotic treatment is more effective than one that emphasizes the use of basic (non-pharmaceutical) anti-cholera control measures only. Numerical simulations show that, while the universal strategy (involving all three control measures) gives the best outcome in minimizing cholera burden in the community, the combined basic anti-cholera control measures and treatment strategy also has very effective community-wide impact.

Keywords

CholeraEquilibriaStabilityVaccineBasic control measures

Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  • Mohammad A. Safi
    • 1
  • Dessalegn Y. Melesse
    • 2
  • Abba B. Gumel
    • 3
  1. 1.Department of MathematicsThe Hashemite UniversityZarqaJordan
  2. 2.The Centre for Global Public Health, Department of Community Health SciencesUniversity of ManitobaWinnipegCanada
  3. 3.Department of MathematicsUniversity of ManitobaWinnipegCanada