Theoretical assessment of public health impact of imperfect prophylactic HIV-1 vaccines with therapeutic benefits

Elamin H. Elbasha, Abba B. Gumel

Research output: Contribution to journalArticlepeer-review

98 Scopus citations


This paper presents a number of deterministic models for theoretically assessing the potential impact of an imperfect prophylactic HIV-1 vaccine that has five biological modes of action, namely "take," "degree," "duration," "infectiousness," and "progression," and can lead to increased risky behavior. The models, which are of the form of systems of nonlinear differential equations, are constructed via a progressive refinement of a basic model to incorporate more realistic features of HIV pathogenesis and epidemiology such as staged progression, differential infectivity, and HIV transmission by AIDS patients. The models are analyzed to gain insights into the qualitative features of the associated equilibria. This allows the determination of important epidemiological thresholds such as the basic reproduction numbers and a measure for vaccine impact or efficacy. The key findings of the study include the following (i) if the vaccinated reproduction number is greater than unity, each of the models considered has a locally unstable disease-free equilibrium and a unique endemic equilibrium; (ii) owing to the vaccine-induced backward bifurcation in these models, the classical epidemiological requirement of vaccinated reproduction number being less than unity does not guarantee disease elimination in these models; (iii) an imperfect vaccine will reduce HIV prevalence and mortality if the reproduction number for a wholly vaccinated population is less than the corresponding reproduction number in the absence of vaccination; (iv) the expressions for the vaccine characteristics of the refined models take the same general structure as those of the basic model.

Original languageEnglish (US)
Pages (from-to)577-614
Number of pages38
JournalBulletin of mathematical biology
Issue number3
StatePublished - Apr 2006
Externally publishedYes


  • AIDS
  • Backward bifurcation
  • Differential infectivity
  • Equilibrium
  • HIV
  • Mathematical model
  • Stability
  • Staged progression
  • Vaccine

ASJC Scopus subject areas

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


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