Global stability analysis and control of leptospirosis
Date
2016
Journal Title
Journal ISSN
Volume Title
Publisher
De Gruyter Open
Abstract
The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control
measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For
this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination,
treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’
case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria.
The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be
achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of
multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters
measures the sensitivity index of the basic reproductive number to the model’s parameters are calculated. In the
time-dependent constant control case, Pontryagin’s Maximum Principle is used to derive necessary conditions for the
optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on
the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of
the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis
is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control
measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from
policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the
disease epidemic.
Description
CITATION: Okosun, K. O., Mukamuri, M. & Makinde, D. O. 2016. Global stability analysis and control
of leptospirosis. Open Mathematics, 14(1): 567–585, doi:10.1515/math-2016-0053.
The original publication is available at https://www.degruyter.com
The original publication is available at https://www.degruyter.com
Keywords
Leptospirosis -- Control -- Cost-effectiveness, Leptospirosis -- Control -- Mathematical models, Leptospirosis -- Transmission
Citation
Okosun, K. O., Mukamuri, M. & Makinde, D. O. 2016. Global stability analysis and control
of leptospirosis. Open Mathematics, 14(1): 567–585, doi:10.1515/math-2016-0053