Mathematical analysis of a time delay visceral leishmaniasis model

Velmurugan Gandhi; Nasser S. Al-Salti; Ibrahim M. Elmojtaba

doi:10.1007/s12190-019-01315-5

Mathematical analysis of a time delay visceral leishmaniasis model

Velmurugan Gandhi, Nasser S. Al-Salti, Ibrahim M. Elmojtaba^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	Journal of Applied Mathematics and Computing
DOIs	https://doi.org/10.1007/s12190-019-01315-5
Publication status	Accepted/In press - Jan 1 2020
Externally published	Yes

Keywords

Hopf bifurcation
Numerical simulation
Stability
Time-delay
Visceral leishmaniasis model

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/s12190-019-01315-5

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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.",

keywords = "Hopf bifurcation, Numerical simulation, Stability, Time-delay, Visceral leishmaniasis model",

author = "Velmurugan Gandhi and Al-Salti, {Nasser S.} and Elmojtaba, {Ibrahim M.}",

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AU - Al-Salti, Nasser S.

AU - Elmojtaba, Ibrahim M.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Hopf bifurcation

KW - Numerical simulation

KW - Stability

KW - Time-delay

KW - Visceral leishmaniasis model

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