Control strategies and sensitivity analysis of anthroponotic visceral leishmaniasis model. (1st January 2017)

• Record Type: Journal Article
• Authors: Zamir, Muhammad; Zaman, Gul; Alshomrani, Ali Saleh
• Is Part Of: Journal of biological dynamics. Volume 11(2017)supplement 1
• Page Start: 323
• Page End: 338
• Publication Date: 2017-01-01
• Subjects: Leishmaniasis -- basic reproductive number -- stability of matrices -- mathematical modelling -- local and global stability -- sensitivity analysis; 93D20 -- 49J15 -- 92D25; Biology -- Mathematical models -- Periodicals; 570.15118
• DOI: 10.1080/17513758.2017.1339835
• Languages: English
• ISSNs: 1751-3758

Abstract

ABSTRACT: This study proposes a mathematical model of Anthroponotic visceral leishmaniasis epidemic with saturated infection rate and recommends different control strategies to manage the spread of this disease in the community. To do this, first, a model formulation is presented to support these strategies, with quantifications of transmission and intervention parameters. To understand the nature of the initial transmission of the disease, the reproduction numberR 0 is obtained by using the next-generation method. On the basis of sensitivity analysis of the reproduction numberR 0, four different control strategies are proposed for managing disease transmission. For quantification of the prevalence period of the disease, a numerical simulation for each strategy is performed and a detailed summary is presented. Disease-free state is obtained with the help of control strategies. The threshold condition for globally asymptotic stability of the disease-free state is found, and it is ascertained that the state is globally stable. On the basis of sensitivity analysis of the reproduction number, it is shown that the disease can be eradicated by using the proposed strategies.