Effect of cross-immunity on the transmission dynamics of two strains of dengue

S. M. Garba, Abba Gumel

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

A deterministic model for the transmission dynamics of two strains of dengue disease is presented. The model, consisting of mutually exclusive epidemiological compartments representing the human and vector dynamics, has a locally asymptotically stable, disease-free equilibrium whenever the maximum of the associated reproduction numbers of the two strains is less than unity. The model can have infinitely many co-existence equilibria if infection with one strain confers complete cross-immunity against the other strain and the associated reproduction number of each strain exceeds unity. On the other hand, if infection with one strain confers partial immunity against the other strain, disease elimination, competitive exclusion or co-existence of the two strains can occur. The effect of seasonality on dengue transmission dynamics is explored using numerical simulations, where it is shown that the oscillation pattern differs between the strains, depending on the degree of the cross-immunity between the strains.

Original languageEnglish (US)
Pages (from-to)2361-2384
Number of pages24
JournalInternational Journal of Computer Mathematics
Volume87
Issue number10
DOIs
StatePublished - Aug 2010
Externally publishedYes

Fingerprint

Immunity
Reproduction number
Coexistence
Infection
Competitive Exclusion
Mutually exclusive
Seasonality
Computer simulation
Deterministic Model
Asymptotically Stable
Elimination
Exceed
Oscillation
Partial
Numerical Simulation

Keywords

  • co-existence equilibria
  • dengue disease
  • mosquitoes
  • reproduction number
  • stability

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications
  • Computational Theory and Mathematics

Cite this

Effect of cross-immunity on the transmission dynamics of two strains of dengue. / Garba, S. M.; Gumel, Abba.

In: International Journal of Computer Mathematics, Vol. 87, No. 10, 08.2010, p. 2361-2384.

Research output: Contribution to journalArticle

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