Mathematical analysis of the role of repeated exposure on malaria transmission dynamics

Ashrafi M. Niger, Abba B. Gumel

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


This paper presents a deterministic model for assessing the role of repeated exposure on the transmission dynamics of malaria in a human population. Rigorous qualitative analysis of the model, which incorporates three immunity stages, reveals the presence of the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction threshold is less than unity. This phenomenon persists regardless of whether the standard or mass action incidence is used to model the transmission dynamics. It is further shown that the region for backward bifurcation increases with decreasing average life span of mosquitoes. Numerical simulations suggest that this region increases with increasing rate of re-infection of first-time infected individuals. In the absence of repeated exposure (re-infection) and loss of infection-acquired immunity, it is shown, using a non-linear Lyapunov function, that the resulting model with mass action incidence has a globally-asymptotically stable endemic equilibrium when the reproduction threshold exceeds unity.

Original languageEnglish (US)
Pages (from-to)251-287
Number of pages37
JournalDifferential Equations and Dynamical Systems
Issue number3
StatePublished - Jul 2008
Externally publishedYes


  • Backward bifurcation
  • Endemic equilibrium
  • Global asymptotic stability
  • Malaria transmission dynamics
  • Repeated exposure
  • Simulations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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