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Mathematical analysis of a time delay visceral leishmaniasis model

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Abstract

In this paper, we discuss some of the dynamical characteristics of a visceral leishmaniasis (VL) model with time delay. We have derived sufficient conditions to ensure the stability of the considered delayed VL model at the steady states. Taking the time delay as a bifurcation parameter, we have established a criteria for the existence of Hopf bifurcation of the considered model. Moreover, conditions for global stability of the steady states are also presented. Finally, some numerical simulations are given to show the effectiveness of our theoretical results.

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Acknowledgements

The authors would like to acknowledge financial support from Sultan Qaboos University, Oman and United Arab Emirates University, UAE through the joint research Grant No. CL/SQU-UAEU/17/01. The authors acknowledge, with thanks, the comments of an anonymous reviewer, which enhanced the clarity and readability of the paper.

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Correspondence to Ibrahim M. Elmojtaba.

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Gandhi, V., Al-Salti, N.S. & Elmojtaba, I.M. Mathematical analysis of a time delay visceral leishmaniasis model. J. Appl. Math. Comput. (2020). https://doi.org/10.1007/s12190-019-01315-5

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Keywords

  • Visceral leishmaniasis model
  • Stability
  • Time-delay
  • Hopf bifurcation
  • Numerical simulation

Mathematics Subject Classification

  • 92B05
  • 34K18