Mathematical model for the dynamics of visceral leishmaniasis–malaria co-infection

Ibrahim M. ELmojtaba

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3 Citations (Scopus)


A mathematical model to understand the dynamics of malaria–visceral leishmaniasis co-infection is proposed and analyzed. Results show that both diseases can be eliminated if R0, the basic reproduction number of the co-infection, is less than unity, and the system undergoes a backward bifurcation where an endemic equilibrium co-exists with the disease-free equilibrium when one of Rm or Rl, the basic reproduction numbers of malaria-only and visceral leishmaniasis-only, is precisely less than unity. Results also show that in the case of maximum protection against visceral leishmaniasis (VL), the disease-free equilibrium is globally asymptotically stable if malaria patients are protected from VL infection; similarly, in the case of maximum protection against malaria, the disease-free equilibrium is globally asymptotically stable if VL and post-kala-azar dermal leishmaniasis patients and the recovered humans after VL are protected from malaria infection. Numerical results show that if Rm and Rl are greater than unity, then we have co-existence of both disease at an endemic equilibrium, and malaria incidence is higher than visceral leishmaniasis incidence at steady state.

Original languageEnglish
Pages (from-to)4334-4353
Number of pages20
JournalMathematical Methods in the Applied Sciences
Issue number15
Publication statusPublished - Oct 1 2016
Externally publishedYes


  • backward bifurcation
  • basic reproduction number
  • co-infection
  • malaria
  • PKDL
  • visceral leishmaniasis

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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