UWCScholar :: Browsing by Author "Munyakazi, Justin B."

Browsing by Author "Munyakazi, Justin B."

Now showing 1 - 13 of 13

A fitted numerical method for parabolic turning point singularly perturbed problems with an interior layer
(Wiley, 2019) Munyakazi, Justin B.; Patidar, Kailash C.; Sayi, Mbani T.
The objective of this paper is to construct and analyzea fitted operator finite difference method (FOFDM) forthe family of time-dependent singularly perturbed parabolicconvection–diffusion problems. The solution to the problemswe consider exhibits an interior layer due to the presence ofa turning point. We first establish sharp bounds on the solu-tion and its derivatives. Then, we discretize the time variableusing the classical Euler method. This results in a system ofsingularly perturbed interior layer two-point boundary valueproblems. We propose a FOFDM to solve the system above.
A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems
(Spring Verlag, 2013) Munyakazi, Justin B.; Patidar, Kailash C.
This paper treats a time-dependent singularly perturbed reaction-diffusion problem. We semidiscretize the problem in time by means of the classical backward Euler method. We develop a fitted operator finite difference method (FOFDM) to solve the resulting set of linear problems (one at each time level). We prove that the underlying fitted operator satisfies the maximum principle. This result is then used in the error analysis of the FOFDM. The method is shown to be first order convergent in time and second order convergent in space, uniformly with respect to the perturbation parameter. We test the method on several numerical examples to confirm our theoretical findings.
Mathematical study of transmission dynamics of SARS-CoV-2 with waning immunity
(AIMS Press, 2022) Egbelowo, Oluwaseun F.; Munyakazi, Justin B.; Hoang, Manh Tuan
The aim of this work is to provide a new mathematical model that studies transmission dynamics of Coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The model captures the dynamics of the disease taking into consideration some measures and is represented by a system of nonlinear ordinary differential equations including seven classes, which are susceptible class (S), exposed class (E), asymptomatic infected class (A), severely infected class (V), hospitalized class (H), hospitalized class but in ICU (C) and recovered class (R). We prove positivity and boundedness of solutions, compute the basic reproduction number, and investigate asymptotic stability properties of the proposed model.
Modeling the impact of combined use of Covid Alert SA app and vaccination to curb Covid-19 infections in South Africa
(Public Library of Science, 2023) 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. We authenticate the model by fitting it to the Republic of South Africa’s cumulative COVID-19 cases reported data utilizing the Maximum Likelihood Estimation algorithm implemented in fitR package.
Modeling the impact of combined use of Covid Alert SA app and vaccination to curb Covid-19 infections in South Africa
(Public Library of Science, 2023) 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.
Modelling the effect of bednet coverage on malaria transmission in South Sudan
(Public Library of Science, 2018) Mukhtar, Abdulaziz Y. A.; Munyakazi, Justin B.; Ouifki, Rachid; Clark, Allan E.
A campaign for malaria control, using Long Lasting Insecticide Nets (LLINs) was launched in South Sudan in 2009. The success of such a campaign often depends upon adequate available resources and reliable surveillance data which help officials understand existing infections. An optimal allocation of resources for malaria control at a sub-national scale is therefore paramount to the success of efforts to reduce malaria prevalence. In this paper, we extend an existing SIR mathematical model to capture the effect of LLINs on malaria trans- mission. Available data on malaria is utilized to determine realistic parameter values of this model using a Bayesian approach via Markov Chain Monte Carlo (MCMC) methods. Then, we explore the parasite prevalence on a continued rollout of LLINs in three different settings in order to create a sub-national projection of malaria. Further, we calculate the model’s basic reproductive number and study its sensitivity to LLINs’ coverage and its efficacy. From the numerical simulation results, we notice a basic reproduction number, R0 , confirming a substantial increase of incidence cases if no form of intervention takes place in the commu- nity. This work indicates that an effective use of LLINs may reduce R0 and hence malaria transmission. We hope that this study will provide a basis for recommending a scaling-up of the entry point of LLINs’ distribution that targets households in areas at risk of malaria.
New parameter-uniform discretisations of singularly perturbed Volterra integro-differential equations
(Natural Sciences Publishing, 2018) Iragi, Bakulikira C.; Munyakazi, Justin B.
We design and analyse two numerical methods namely a fitted mesh and a fitted operator finite difference methods for solving singularly perturbed Volterra integro-differential equations. The fitted mesh method we propose is constructed using a finite difference operator to approximate the derivative part and some suitably chosen quadrature rules for the integral part. To obtain a parameter-uniform convergence, we use a piecewise-uniform mesh of Shishkin type. On the other hand, to construct the fitted operator method, the Volterra integro-differential equation is discretised by introducing a fitting factor via the method of integral identity with the use of exponential basis function along with interpolating quadrature rules [2]. The two methods are analysed for convergence and stability. We show that the two methods are robust with respect to the perturbation parameter. Two numerical examples are solved to show the applicability of the proposed schemes.
A new parameter-uniform discretization of semilinear singularly perturbed problems
(MDPI, 2022) Munyakazi, Justin B.; Kehinde, Olawale O.
In this paper, we present a numerical approach to solving singularly perturbed semilinear convection-diffusion problems. The nonlinear part of the problem is linearized via the quasilinearization technique. We then design and implement a fitted operator finite difference method to solve the sequence of linear singularly perturbed problems that emerges from the quasilinearization process. We carry out a rigorous analysis to attest to the convergence of the proposed procedure and notice that the method is first-order uniformly convergent. Some numerical evaluations are implemented on model examples to confirm the proposed theoretical results and to show the efficiency of the method.
A NSFD discretization of two-dimensional singularly perturbed semilinear convection-diffusion problems
(Frontiers Media, 2022) Kehinde, Olawale O.; Munyakazi, Justin B.; Appadu, Appanah R.
Despite the availability of an abundant literature on singularly perturbed problems, interest toward non-linear problems has been limited. In particular, parameter-uniform methods for singularly perturbed semilinear problems are quasi-non-existent. In this article, we study a two-dimensional semilinear singularly perturbed convection-diffusion problems. Our approach requires linearization of the continuous semilinear problem using the quasilinearization technique. We then discretize the resulting linear problems in the framework of non-standard finite difference methods. A rigorous convergence analysis is conducted showing that the proposed method is first-order parameter-uniform convergent. Finally, two test examples are used to validate the theoretical findings.
A NSFD method for the singularly perturbed Burgers-Huxley equation
(Frontiers Media, 2023) 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 di􀀀erence (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 di􀀀erential 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.
A NSFD method for the singularly perturbed Burgers-Huxley equation
(Frontiers Media, 2023) 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 efficient numerical solution for this equation via the classical numerical methods. To overcome this challenge, a nonstandard finite difference (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 differential 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-uniform convergent. 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.
Performance of Richardson extrapolation on some numerical methods for a singularly perturbed turning point problem whose solution has boundary layers
(KOREAN MATHEMATICAL SOC, 2014) Munyakazi, Justin B.; Patidar, Kailash C.
Investigation of the numerical solution of singularly perturbed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. On the other hand, one could think of applying the convergence acceleration technique to improve the performance of existing numerical methods. However, that itself posed some challenges. To this end, we design and analyze a novel fitted operator finite difference method (FOFDM) to solve this type of problems. Then we develop a fitted mesh finite difference method (FMFDM). Our detailed convergence analysis shows that this FMFDM is robust with respect to the singular perturbation parameter. Then we investigate the effect of Richardson extrapolation on both of these methods. We observe that, the accuracy is improved in both cases whereas the rate of convergence depends on the particular scheme being used.
To use face masks or not after Covid-19 vaccination? An impact analysis using mathematical modeling
(Frontiers Media, 2022) Kinyili, Musyoka; Munyakazi, Justin B.; Mukhtar, Abdulaziz Y. A.
The question of whether to drop or to continue wearing face masks especially after being vaccinated among the public is controversial. This is sourced from the efficacy levels of COVID-19 vaccines developed, approved, and in use. We develop a deterministic mathematical model that factors in a combination of the COVID-19 vaccination program and the wearing of face masks as intervention strategies to curb the spread of the COVID-19 epidemic. We use the model specifically to assess the potential impact of wearing face masks, especially by the vaccinated individuals in combating further contraction of COVID-19 infections. Validation of the model is achieved by performing its goodness of fit to the Republic of South Africa’s reported COVID-19 positive cases data using the Maximum Likelihood Estimation algorithm implemented in the fitR package. We first consider a scenario where the uptake of the vaccines and wearing of the face masks, especially by the vaccinated individuals is extremely low.

Browsing by Author "Munyakazi, Justin B."

Results Per Page

Sort Options