Research Articles (Mathematics)
http://hdl.handle.net/10566/159
2023-12-01T16:10:33ZModeling the impact of combined use of Covid Alert SA app and vaccination to curb Covid-19 infections in South Africa
http://hdl.handle.net/10566/9084
Modeling the impact of combined use of Covid Alert SA app and vaccination to curb Covid-19 infections in South Africa
Kinyili, Musyoka; Munyakazi, Justin B.; Mukhtar, Abdulaziz Y. A.
The unanticipated continued deep-rooted trend of the Severe Acute Respiratory Syndrome
Corona-virus-2 the originator pathogen of the COVID-19 persists posing concurrent anxiety
globally. More effort is affixed in the scientific arena via continuous investigations in a prolific
effort to understand the transmission dynamics and control measures in eradication of the
epidemic. Both pharmaceutical and non-pharmaceutical containment measure protocols
have been assimilated in this effort. In this study, we develop a modified SEIR deterministic
model that factors in alternative-amalgamation of use of COVID Alert SA app and vaccination
against the COVID-19 to the Republic of South Africa’s general public in an endeavor to
discontinue the chain of spread for the pandemic. We analyze the key properties of the
model not limited to positivity, boundedness, and stability.
2023-01-01T00:00:00ZA NSFD method for the singularly perturbed Burgers-Huxley equation
http://hdl.handle.net/10566/9071
A NSFD method for the singularly perturbed Burgers-Huxley equation
Derzie, Eshetu B.; Munyakazi, Justin B.; Dinka, Tekle G.
This article focuses on a numerical solution of the singularly perturbed
Burgers-Huxley equation. The simultaneous presence of a singular perturbation
parameter and the nonlinearity raise the challenge of finding a reliable and e cient
numerical solution for this equation via the classical numericalmethods. To overcome
this challenge, a nonstandard finite dierence (NSFD) scheme is developed in the
following manner. The time variable is discretized using the backward Euler method.
This gives rise to a system of nonlinear ordinary dierential equations which are then
dealt with using the concept of nonlocal approximation. Through a rigorous error
analysis, the proposed scheme has been shown to be parameter-uniformconvergent.
Simulations conducted on two numerical examples confirm the theoretical result. A
comparison with other methods in terms of accuracy and computational cost reveals
the superiority of the proposed scheme.
2023-01-01T00:00:00ZBinary codes from m-ary n-cubes Q(n) (m)
http://hdl.handle.net/10566/8974
Binary codes from m-ary n-cubes Q(n) (m)
Key, Jennifer D.; Rodrigues, Bernardo G.
We examine the binary codes from adjacency matrices of the graph with vertices the nodes
of the m-ary n-cube Qmn
and with adjacency de ned by the Lee metric. For n = 2 and m odd,
we obtain the parameters of the code and its dual, and show the codes to be LCD. We also
nd s-PD-sets of size s + 1 for s < m1
2 for the dual codes, i.e. [m2; 2m 1;m]2 codes, when
n = 2 and m 5 is odd.
2021-01-01T00:00:00ZOn the exact constants in one-sided maximal inequalitiesfor Bessel processes
http://hdl.handle.net/10566/8620
On the exact constants in one-sided maximal inequalitiesfor Bessel processes
Makasu, Cloud
In this paper, we establish a one-sided maximal moment inequalitywith exact constants for Bessel processes. As a consequence, weobtain an exact constant in the Burkholder-Gundy inequality. Theproof of our main result is based on a pure optimal stopping prob-lem of the running maximum process for a Bessel process. The pre-sent results extend and complement a number of related resultspreviously known in the literature.
2023-01-01T00:00:00Z