Title: Lyapunov function of SIR and SEIR model for transmission of dengue fever disease

Authors: S. Syafruddin; Mohd Salmi Md. Noorani

Addresses: Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Makassar, Parang Tambung, 90244 Sulawesi Selatan, Indonesia ' School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Abstract: In this paper, we construct a new Lyapunov function for a variety of SIR and SEIR model in epidemiology. Lyapunov functions are used to show that when the basic reproduction ratio is less than or equal to one, the disease-free equilibrium is globally asymptotically stable and the basic reproduction ratio is greater than one, and the endemic equilibrium is also globally asymptotically stable for both models.

Keywords: dengue fever; Lyapunov function; stability; SEIR model; SIR model; disease transmission; epidemiology; modelling.

DOI: 10.1504/IJSPM.2013.057544

International Journal of Simulation and Process Modelling, 2013 Vol.8 No.2/3, pp.177 - 184

Received: 08 Mar 2012
Accepted: 17 Oct 2012

Published online: 08 Nov 2013 *

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