Abstract
In this mini thesis, we study the application of Lyapunov functions in epidemiological
modeling. The aim is to give an extensive discussion of Lyapunov functions, and use
some specific classes of epidemiological models to demonstrate the construction of
Lyapunov functions. The study begins with a review of Lyapunov functions in general,
and their usage in global stability analysis. Lyapunov’s “direct method” is used
to analyse the stability of the disease-free equilibrium. Moreover, a matrix-theoretic
method is critically examined for its capability and overall functionality in the construction
and development of an appropriate Lyapunov function for the stability analysis of the
nonlinear dynamical systems. This method additionally demonstrates the construction
of the basic reproduction number for the SEIR model, and it is shown that the disease-free
equilibrium is locally asymptotically stable ifR0 1. Furthermore,
a Lyapunov function is constructed for the Vector-Host model to study the global
stability of the disease-free equilibrium. The results indicate that the disease-free
equilibrium is globally asymptotically stable whenR0 1 (i.e. every solution trajectory
of the Vector-Host model converges to the largest compact invariant setM=f(Sho; Ih;Svo; Iv)g)
and unstable when R0 > 1.
LAZARUS, E (2021). Lyapunov Functions In Epidemiological Modeling. Afribary. Retrieved from https://tracking.afribary.com/works/lyapunov-functions-in-epidemiological-modeling
LAZARUS, ELISE "Lyapunov Functions In Epidemiological Modeling" Afribary. Afribary, 27 Apr. 2021, https://tracking.afribary.com/works/lyapunov-functions-in-epidemiological-modeling. Accessed 22 Dec. 2024.
LAZARUS, ELISE . "Lyapunov Functions In Epidemiological Modeling". Afribary, Afribary, 27 Apr. 2021. Web. 22 Dec. 2024. < https://tracking.afribary.com/works/lyapunov-functions-in-epidemiological-modeling >.
LAZARUS, ELISE . "Lyapunov Functions In Epidemiological Modeling" Afribary (2021). Accessed December 22, 2024. https://tracking.afribary.com/works/lyapunov-functions-in-epidemiological-modeling