The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910

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3: Paper Source PDF document

Paper's Title:

A Note on Divergent Fourier Series and λ-Permutations

Author(s):

A. Castillo, J. Chavez and H. Kim

Tufts University,
Department of Mathematics,
Medford, MA 02155,
USA
E-mail: angel.castillo@tufts.edu

Texas Tech University,
Department of Mathematics and Statistics,
Lubbock, TX 79409,
USA
E-mail: josechavez5@my.unt.edu

University of Michigan-Dearborn,
Department of Mathematics and Statistics,
Dearborn, MI 48128,
USA.
E-mail: khyejin@umich.edu

Abstract:

We present a continuous function on [-π,π] whose Fourier series diverges and it cannot be rearranged to converge by a λ-permutation.

3: Paper Source PDF document

Paper's Title:

The Dynamics of an Ebola Epidemic Model with Quarantine of Infectives

Author(s):

Eliab Horub Kweyunga

Department of Mathematics,
Kabale University,
P.O.Box 317, Kabale,
Uganda.

E-mail: hkweyunga@kab.ac.ug

Abstract:

The recurrent outbreaks of ebola in Africa present global health challenges. Ebola is a severe, very fatal disease with case fatality rates of up to 90%. In this paper, a theoretical deterministic model for ebola epidemic with quarantine of infectives is proposed and analyzed. The model exhibits two equilibria; the disease free and endemic equilibrium points. The basic reproduction number, R0, which is the main threshold, is obtained and the stability of the equilibrium points established. Using parameter values drawn from the 2014 West Africa ebola outbreak, a numerical simulation of the model is carried out. It is found that the dynamics of the model are completely determined by R0 and that a quarantine success rate of at least 70% is sufficient to contain the disease outbreak.

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