Global analysis and optimal control of a periodic visceral leishmaniasis model

Ibrahim Elmojtaba, Santanu Biswas, Joydev Chattopadhyay

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper, we propose and analyze a mathematical model for the dynamics of visceral leishmaniasis with seasonality. Our results show that the disease-free equilibrium is globally asymptotically stable under certain conditions when R0, the basic reproduction number, is less than unity. When R0 > 1 and under some conditions, then our system has a unique positive ω-periodic solution that is globally asymptotically stable. Applying two controls, vaccination and treatment, to our model forces the system to be non-periodic, and all fractions of infected populations settle on a very low level.

Original languageEnglish
Article number80
Issue number4
Publication statusPublished - Dec 14 2017


  • Global stability analysis
  • Non-autonomous system
  • Optimal control
  • Periodic solutions
  • Visceral leishmaniasis

ASJC Scopus subject areas

  • General Mathematics


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