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

Mohammad A. Safi, Dessalegn Y. Melesse, Abba Gumel

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1104-1137
Number of pages34
JournalBulletin of Mathematical Biology
Volume75
Issue number7
DOIs
StatePublished - Jul 2013
Externally publishedYes

Fingerprint

cholera
Vaccines
Cholera
Vaccine
vaccine
dynamic analysis
Dynamic Analysis
Imperfect
Dynamic analysis
Dose
vaccines
control methods
dosage
Mass Vaccination
Model
vaccination
Reproduction number
at-risk population
Numerical Simulation
Endemic Equilibrium

Keywords

  • Basic control measures
  • Cholera
  • Equilibria
  • Stability
  • Vaccine

ASJC Scopus subject areas

  • Neuroscience(all)
  • Computational Theory and Mathematics
  • Mathematics(all)
  • Pharmacology
  • Immunology
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Environmental Science(all)

Cite this

Dynamics Analysis of a Multi-strain Cholera Model with an Imperfect Vaccine. / Safi, Mohammad A.; Melesse, Dessalegn Y.; Gumel, Abba.

In: Bulletin of Mathematical Biology, Vol. 75, No. 7, 07.2013, p. 1104-1137.

Research output: Contribution to journalArticle

Safi, Mohammad A. ; Melesse, Dessalegn Y. ; Gumel, Abba. / Dynamics Analysis of a Multi-strain Cholera Model with an Imperfect Vaccine. In: Bulletin of Mathematical Biology. 2013 ; Vol. 75, No. 7. pp. 1104-1137.
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