Research Articles (Mathematics)
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Codenseness and openness with respect to an interior operator
(Springer Nature, 2021)Working in an arbitrary category endowed with a fixed (E, M) factorization system such that M is a fixed class of monomorphisms, we first define and study a concept of codense morphisms with respect to a given categorical ... 
Quasiuniform structures determined by closure operators
(Elsevier, 2021)We demonstrate a onetoone correspondence between idempotent closure operators and the socalled saturated quasiuniform structures on a category C. Not only this result allows to obtain a categorical counterpart P of the ... 
An unconditionally stable nonstandard finite difference method to solve a mathematical model describing Visceral Leishmaniasis
(Elsevier, 2021)In this paper, a mathematical model of Visceral Leishmaniasis is considered. The model incorporates three populations, the human, the reservoir and the vector host populations. A detailed analysis of the model is presented. ... 
A robust numerical solution to a timefractional Black–Scholes equation
(Springer Nature, 2021)Dividend paying European stock options are modeled using a timefractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work are appropriate for ... 
Mathematical analysis of TB model with vaccination and saturated incidence rate
(Hindawi, 2020)The model system of ordinary differential equations considers two classes of latently infected individuals, with different risk of becoming infectious. The system has positive solutions. By constructing a Lyapunov function, ... 
Stochastic modeling of a mosquitoborne disease
(Springer Nature, 2020)We present and analyze a stochastic differential equation (SDE) model for the population dynamics of a mosquitoborne infectious disease. We prove the solutions to be almost surely positive and global. We introduce a ... 
Numerical solution for a problem arising in angiogenic signalling
(American Institute of Mathematical Sciences, 2019)Since the process of angiogenesis is controlled by chemical signals, which stimulate both repair of damaged blood vessels and formation of new blood vessels, then other chemical signals known as angiogenesis inhibitors ... 
A fitted operator method for a model arising in vascular tumor dynamics
(Tianjin Polytechnic University, 2020)In this paper, we consider a model for the population kinetics of human tumor cells in vitro, differentiated by phases of the cell division cycle and length of time within each phase. Since it is not easy to isolate ... 
A fitted operator method for tumor cells dynamics in their microenvironment
(Tianjin Polytechnic University, 2019)In this paper, we consider a quasi nonlinear reactiondiffusion model designed to mimic tumor cells’ proliferation and migration under the influence of their microenvironment in vitro. Since the model can be used to ... 
A fitted numerical method for a model arising in HIVrelated cancerimmune system dynamics
(Tianjin Polytechnic University, 2019)The effect of diseases such as cancer and HIV among our societies is evident. Thus, from the mathematical point of view many models has been developed with the aim to contribute towards understanding the dynamics of ... 
Efficient numerical method for a model arising in biological stoichiometry of tumor dynamics
(American Institute of Mathematical Sciences, 2019)In this paper, we extend a system of coupled first order nonlinear system of delay differential equations (DDEs) arising in modeling of stoichiometry of tumour dynamics, to a system of diffusionreaction system of partial ... 
Mathematical analysis and numerical simulation of a tumorhost model with chemotherapy application
(Tianjin Polytechnic University, 2018)In this paper, a system of nonlinear quasiparabolic partial differential system, modeling the chemotherapy application of spatial tumorhost interaction is considered. At some certain parameters, we derive the steady state ... 
Closure, interior and neighbourhood in a category
(Hacettepe University, 2018)The natural correspondences in topology between closure, interior and neighbourhood no longer hold in an abstract categorical setting where subobject lattices are not necessarily Boolean algebras. We analyse three ... 
New parameteruniform discretisations of singularly perturbed Volterra integrodifferential equations
(Natural Sciences Publishing, 2018)We design and analyse two numerical methods namely a fitted mesh and a fitted operator finite difference methods for solving singularly perturbed Volterra integrodifferential equations. The fitted mesh method we propose ... 
Mathematical analysis and numerical simulation of a tumorhost model with chemotherapy application
(Communications in Mathematical Biology and Neuroscience, 2018)In this paper, a system of nonlinear quasiparabolic partial differential system, modeling the chemotherapy application of spatial tumorhost interaction is considered. At some certain parameters, we derive the steady ... 
A stochastic TB model for a crowded environment
(Hindawi, 2018)We propose a stochastic compartmental model for the population dynamics of tuberculosis. The model is applicable to crowded environments such as for people in high density camps or in prisons. We start off with a known ... 
Modelling the effect of bednet coverage on malaria transmission in South Sudan
(Public Library of Science, 2018)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 ... 
A model of HIV/AIDS population dynamics including ARV treatment and preexposure prophylaxis
(SpringerOpen, 2018)Antiretroviral treatment (ART) and oral preexposure prophylaxis (PrEP) have recently been used efficiently in management of HIV infection. Preexposure prophylaxis consists in the use of an antiretroviral medication to ... 
Implicitexplicit predictorcorrector methods combined with improved spectral methods for pricing European style vanilla and exotic options
(Kent State University, 2013)In this paper we present a robust numerical method to solve several types of European style option pricing problems. The governing equations are described by variants of BlackScholes partial differential equations (BSPDEs) ... 
Contour integral method for European options with jumps
(Elsevier, 2013)We develop an efficient method for pricing European options with jump on a single asset. Our approach is based on the combination of two powerful numerical methods, the spectral domain decomposition method and the Laplace ...