Mathematical analysis of an influenza epidemic model, formulation of different controlling strategies using optimal control and estimation of basic reproduction number

Adnan Khan, Muhammad Waleed and Mudassar Imran

Mathematical and Computer Modelling of Dynamical Systems, 2015, vol. 21, issue 5, 432-459

Abstract: In this article, a deterministic model is formulated to perform a thorough investigation of the transmission dynamics of influenza. In particular, our model takes into account the effects of medication as well as hospitalization. An in-depth stability analysis of the model is performed, and it is subsequently shown that the model is locally, as well as globally asymptotically stable, when R0 > 1. It is also shown that there exists a unique endemic equilibrium whenever R0 > 1. After estimating the effective contact rate, we estimate the basic reproduction number, using both an ordinary least squares and generalized least squares methodology. We also estimated confidence intervals for the effective contact rate using parametric bootstrapping. Furthermore, we perform uncertainty and sensitivity analysis to recognize the impact of crucial model parameters on R0. In addition, using ideas from the optimal control theory, optimal medication and hospitalization strategies are proposed to eliminate the disease.

Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/13873954.2015.1016975 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:nmcmxx:v:21:y:2015:i:5:p:432-459

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/NMCM20

DOI: 10.1080/13873954.2015.1016975

Access Statistics for this article

Mathematical and Computer Modelling of Dynamical Systems is currently edited by I. Troch

More articles in Mathematical and Computer Modelling of Dynamical Systems from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().