Mathematical analysis of the dynamics of visceral leishmaniasis in the Sudan

Ibrahim Elmojtaba; J. Y.T. Mugisha; Mohsin H.A. Hashim

doi:10.1016/j.amc.2010.07.069

Mathematical analysis of the dynamics of visceral leishmaniasis in the Sudan

Ibrahim Elmojtaba, J. Y.T. Mugisha, Mohsin H.A. Hashim

Mathematics

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

37 Citations (Scopus)

Abstract

In this paper we develop a mathematical model to study the dynamics of visceral leishmaniasis in the Sudan. To develop this model we consider the dynamics of the disease between three different populations, human, reservoir and vector populations. The model is analyzed at equilibrium and the stability of the equilibria is analyzed. The basic reproduction number is derived, and the threshold conditions for disease elimination established. Results show that the disease can be eliminated under certain conditions. Simulations of the model show that human treatment helps in disease control, and its synergy with vector control will more likely result in the elimination of the disease.

Original language	English
Pages (from-to)	2567-2578
Number of pages	12
Journal	Applied Mathematics and Computation
Volume	217
Issue number	6
DOIs	https://doi.org/10.1016/j.amc.2010.07.069
Publication status	Published - Nov 15 2010

Keywords

Animal reservoir
Basic reproduction number
PKDL
Sandfly
Visceral leishmaniasis

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1016/j.amc.2010.07.069

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title = "Mathematical analysis of the dynamics of visceral leishmaniasis in the Sudan",

abstract = "In this paper we develop a mathematical model to study the dynamics of visceral leishmaniasis in the Sudan. To develop this model we consider the dynamics of the disease between three different populations, human, reservoir and vector populations. The model is analyzed at equilibrium and the stability of the equilibria is analyzed. The basic reproduction number is derived, and the threshold conditions for disease elimination established. Results show that the disease can be eliminated under certain conditions. Simulations of the model show that human treatment helps in disease control, and its synergy with vector control will more likely result in the elimination of the disease.",

keywords = "Animal reservoir, Basic reproduction number, PKDL, Sandfly, Visceral leishmaniasis",

author = "Ibrahim Elmojtaba and Mugisha, {J. Y.T.} and Hashim, {Mohsin H.A.}",

note = "Funding Information: The research of Ibrahim M. ELmojtaba is supported by a Grant from Faculty of Mathematical Sciences-University of Khartoum . The authors would like to thank Professor A.B. Gumel, of University of Manitoba for his helpful comments. One of the authors (Ibrahim M. ELmojtaba) would like to thank the Department of Mathematics at Makerere University for their hospitality, and special thanks to Ms. B. Nannyonga for her help. The authors would like to thank the anonymous reviewers for their helpful comments.",

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AU - Elmojtaba, Ibrahim

AU - Mugisha, J. Y.T.

AU - Hashim, Mohsin H.A.

N1 - Funding Information: The research of Ibrahim M. ELmojtaba is supported by a Grant from Faculty of Mathematical Sciences-University of Khartoum . The authors would like to thank Professor A.B. Gumel, of University of Manitoba for his helpful comments. One of the authors (Ibrahim M. ELmojtaba) would like to thank the Department of Mathematics at Makerere University for their hospitality, and special thanks to Ms. B. Nannyonga for her help. The authors would like to thank the anonymous reviewers for their helpful comments.

PY - 2010/11/15

Y1 - 2010/11/15

N2 - In this paper we develop a mathematical model to study the dynamics of visceral leishmaniasis in the Sudan. To develop this model we consider the dynamics of the disease between three different populations, human, reservoir and vector populations. The model is analyzed at equilibrium and the stability of the equilibria is analyzed. The basic reproduction number is derived, and the threshold conditions for disease elimination established. Results show that the disease can be eliminated under certain conditions. Simulations of the model show that human treatment helps in disease control, and its synergy with vector control will more likely result in the elimination of the disease.

AB - In this paper we develop a mathematical model to study the dynamics of visceral leishmaniasis in the Sudan. To develop this model we consider the dynamics of the disease between three different populations, human, reservoir and vector populations. The model is analyzed at equilibrium and the stability of the equilibria is analyzed. The basic reproduction number is derived, and the threshold conditions for disease elimination established. Results show that the disease can be eliminated under certain conditions. Simulations of the model show that human treatment helps in disease control, and its synergy with vector control will more likely result in the elimination of the disease.

KW - Animal reservoir

KW - Basic reproduction number

KW - PKDL

KW - Sandfly

KW - Visceral leishmaniasis

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Mathematical analysis of the dynamics of visceral leishmaniasis in the Sudan

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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