Zoonotic Visceral Leishmania: Modeling and ControlZamir Muhammad1* and Rahmat Ali2
- *Corresponding Author:
- Zamir M
Department of Mathematics, University of Science and Technology Bannu
Khyber Pakhtunkhwa, Pakistan
E-mail: [email protected]
Received May 17, 2015; Accepted July 17, 2015; Published July 24, 2015
Citation: Muhammad Z, Ali R (2015) Zoonotic Visceral Leishmania: Modeling and Control. J Appl Computat Math 4: 238. doi:10.4172/2168-9679.1000238
Copyright: © 2015 Muhammad Z, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
In this work we focus on the transmission dynamics of Visceral strains of leishmania, using mathematical model with two latent compartments in human. From the governing differential equations of the model, we find the reproductive number R0; the number of secondary infection and its biological interpretation. Using Routh- Hurwitz criteria on upper bound matrix, the threshold condition, for stability of the Disease Free State, is calculated. Finally we show that the disease free equilibrium is globally asymptotically stable if R0<<ξ 11.