Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

You searched for +publisher:"University of Pretoria" +contributor:("Mureithi, Eunice W."). One record found.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters


University of Pretoria

1. Terefe, Yibeltal Adane. Bifurcation analysis and nonstandard finite difference schemes for Kermack and McKendrick type epidemiological models.

Degree: Mathematics and Applied Mathematics, 2013, University of Pretoria

The classical SIR and SIS epidemiological models are extended by considering the number of adequate contacts per infective in unit time as a function of the total population in such a way that this number grows less rapidly as the total population increases. A diffusion term is added to the SIS model and this leads to a reaction–diffusion equation, which governs the spatial spread of the disease. With the parameter R0 representing the basic reproduction number, it is shown that R0 = 1 is a forward bifurcation for the SIR and SIS models, with the disease–free equilibrium being globally asymptotic stable when R0 is less than 1. In the case when R0 is greater than 1, for both models, the endemic equilibrium is locally asymptotically stable and traveling wave solutions are found for the SIS diffusion model. Nonstandard finite difference (NSFD) schemes that replicate the dynamics of the continuous SIR and SIS models are presented. In particular, for the SIS model, a nonstandard version of the Runge-Kutta method having high order of convergence is investigated. Numerical experiments that support the theory are provided. On the other hand the SIS model is extended to a Volterra integral equation, for which the existence of multiple endemic equilibria is proved. This fact is confirmed by numerical simulations. Advisors/Committee Members: Lubuma, Jean M.-S. (advisor), Mureithi, Eunice W. (advisor).

Subjects/Keywords: Sis and sir epidemiological models; Nonstandard finite difference scheme; Nsfd; UCTD

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Terefe, Y. A. (2013). Bifurcation analysis and nonstandard finite difference schemes for Kermack and McKendrick type epidemiological models. (Masters Thesis). University of Pretoria. Retrieved from http://hdl.handle.net/2263/24917

Chicago Manual of Style (16th Edition):

Terefe, Yibeltal Adane. “Bifurcation analysis and nonstandard finite difference schemes for Kermack and McKendrick type epidemiological models.” 2013. Masters Thesis, University of Pretoria. Accessed November 19, 2019. http://hdl.handle.net/2263/24917.

MLA Handbook (7th Edition):

Terefe, Yibeltal Adane. “Bifurcation analysis and nonstandard finite difference schemes for Kermack and McKendrick type epidemiological models.” 2013. Web. 19 Nov 2019.

Vancouver:

Terefe YA. Bifurcation analysis and nonstandard finite difference schemes for Kermack and McKendrick type epidemiological models. [Internet] [Masters thesis]. University of Pretoria; 2013. [cited 2019 Nov 19]. Available from: http://hdl.handle.net/2263/24917.

Council of Science Editors:

Terefe YA. Bifurcation analysis and nonstandard finite difference schemes for Kermack and McKendrick type epidemiological models. [Masters Thesis]. University of Pretoria; 2013. Available from: http://hdl.handle.net/2263/24917

.