TY - JOUR
T1 - Mathematical analysis of the dynamics of visceral leishmaniasis in the Sudan
AU - Elmojtaba, Ibrahim M.
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 -