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Mathematical Biosciences and Engineering (MBE)
 

Modeling and analyzing the transmission dynamics of visceral leishmaniasis

Pages: 1585 - 1604, Volume 14, Issue 5/6, October/December 2017      doi:10.3934/mbe.2017082

 
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Lan Zou - Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China (email)
Jing Chen - Department of Mathematics, University of Miami, Coral Gables, FL 33146, United States (email)
Shigui Ruan - Department of Mathematics, University of Miami, Coral Gables, FL 33146, United States (email)

Abstract: In this paper, we develop a mathematical model to study the transmission dynamics of visceral leishmaniasis. Three populations: dogs, sandflies and humans, are considered in the model. Based on recent studies, we include vertical transmission of dogs in the spread of the disease. We also investigate the impact of asymptomatic humans and dogs as secondary reservoirs of the parasites. The basic reproduction number and sensitivity analysis show that the control of dog-sandfly transmission is more important for the elimination of the disease. Vaccination of susceptible dogs, treatment of infective dogs, as well as control of vertical transmission in dogs are effective prevention and control measures for visceral leishmaniasis.

Keywords:  Visceral leishmaniasis, mathematical modeling, reservoir, vertical transmission, basic reproduction number.
Mathematics Subject Classification:  Primary: 92D25, 92D30; Secondary: 37N25.

Received: August 2016;      Accepted: September 2016;      Available Online: May 2017.

 References