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

نتاج البحث: المساهمة في مجلة › Article › مراجعة النظراء

37 اقتباسات (Scopus)

ملخص

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.

اللغة الأصلية	English
الصفحات (من إلى)	2567-2578
عدد الصفحات	12
دورية	Applied Mathematics and Computation
مستوى الصوت	217
رقم الإصدار	6
المعرِّفات الرقمية للأشياء	https://doi.org/10.1016/j.amc.2010.07.069
حالة النشر	Published - نوفمبر 15 2010

ASJC Scopus subject areas

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???subjectarea.asjc.2600.2604???

أهداف الأمم المتحدة للتنمية المستدامة

يساهم هذا المخرج في تحقيق أهداف الأمم المتحدة للتنمية المستدامة التالية (SDGs)

الوصول إلى المستند

10.1016/j.amc.2010.07.069

الملفات والروابط الأخرى

قم بذكر هذا

@article{502f0cb3769c4b2cb7b885f492070cac,

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.",

year = "2010",

month = nov,

day = "15",

doi = "10.1016/j.amc.2010.07.069",

language = "English",

volume = "217",

pages = "2567--2578",

journal = "Applied Mathematics and Computation",

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TY - JOUR

T1 - Mathematical analysis of the dynamics of visceral leishmaniasis in the Sudan

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

UR - http://www.scopus.com/inward/record.url?scp=77957997077&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957997077&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2010.07.069

DO - 10.1016/j.amc.2010.07.069

M3 - Article

AN - SCOPUS:77957997077

SN - 0096-3003

VL - 217

SP - 2567

EP - 2578

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 6

ER -

Mathematical analysis of the dynamics of visceral leishmaniasis in the Sudan

ملخص

ASJC Scopus subject areas

أهداف الأمم المتحدة للتنمية المستدامة

الوصول إلى المستند

الملفات والروابط الأخرى

بصمة

قم بذكر هذا