Stability analysis and optimal control of a vector-borne disease with nonlinear incidence
type: Item
instance of: scholarly article
title: Stability analysis and optimal control of a vector-borne disease with nonlinear incidence
zbMATH Open document ID: 1253.93090
DOI: 10.1155/2012/595487
author: Muhammad Ozair
author: Abid Ali Lashari
author: Il Hyo Jung
author: Kazeem Oare Okosun
published in: Discrete Dynamics in Nature and Society
publication date: 2012-12-18T00:00:00Z
review text: Summary: We consider a model for the transmission dynamics of a vector-borne disease with nonlinear incidence rate. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. In order to assess the effectiveness of disease control measures, the sensitivity analysis of the basic reproductive number \(R_0\) and the endemic proportions with respect to epidemiological and demographic parameters are provided. From the results of the sensitivity analysis, the model is modified to assess the impact of three control measures; the preventive control to minimize vector human contacts, the treatment control to the infected human, and the insecticide control to the vector. Analytically the existence of the optimal control is established by the use of an optimal control technique and numerically it is solved by an iterative method. Numerical simulations and optimal analysis of the model show that restricted and proper use of control measures might considerably decrease the number of infected humans in a viable way.
Mathematics Subject Classification ID: 93C95
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 37N25
zbMATH DE Number: 6116511
zbMATH Keywords: transmission dynamics
zbMATH Keywords: vector-borne disease
zbMATH Keywords: nonlinear incidence rate
zbMATH Keywords: global dynamics
zbMATH Keywords: basic reproduction number
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/595487
OpenAlex ID: W2103601267
Wikidata QID: Q57620385
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description: scientific article; zbMATH DE number 6116511