International Journal of Mathematical Sciences and Optimization: Theory and Applications

Common Fixed Point Theorems of Some Certain Generalized Contractive Conditions in Convex Metric Space Settings

O. J. Omidire — 2024-05-15

This paper investigates convergence results for fixed point iterations to the unique common fixed point of sequences of Akram-Jungck and MJ type contractive operators, using Jungck-Schaefer-like iterative technique. We also demonstrate the applicability of these results to solving optimization problems.

Application of Diffusion Magnetic Resonance Imaging Equation to Compressible and Incompressible Fluid Particles in a Spherical Region

Ahmed Saba — 2024-05-25

In the previous work, the response of viscous and non-viscous fluids to magnetic resonance was examined. In this research work, Diffusion magnetic resonance imaging, MRI, is used to study, analyse and compare the response of particles of compressible and incompressible fluids in a spherical region. The fluids considered are hydrogen gas and paraffin oil. The general flow equation was evolved from the fundamental Bloch equations. The general flow equation was
solved using the method of separation of variables and applied to spherical region leading to Legendre equation of the first and second kinds. From the results obtained, it can be concluded that the value of Magnetization for hydrogen gas ranges from 9.28819444503×1013 to 9.35×1014. However, appreciable change can be noticed when magnetization is 9.2881944500003 × 1013. For paraffin oil, the value of Magnetization ranges from 2.749305556000075×1014 to 2.75×1014
with appreciable change noticed at magnetization value of 2.7493055560000094 × 1014. The analytical solution of Diffusion MRI equation adopted in this research work has shown the difference in compressible (hydrogen gas) and incompressible (paraffin oil) fluids in a spherical region through the magnetization values that were generated. This is laying credence to the effectiveness and non-invasive properties of MRI.

Mathematical modeling of mosquito borne diseases with vertical transmissions as applied to Dengue

U. A. Danbaba — 2024-06-10

Aedes aegypti mosquitoes transmit important mosquito borne diseases that include dengue, yellow fever, zika, chikungunya, rift valley, and west nile among others. The dynamics of these diseases are influenced by various factors such as population dynamics of humans and mosquitoes, mosquito behaviour, and transmission modes. This study focuses on multiple transmissions, where both vertical and horizontal modes are considered with application to dengue virus. We therefore present a model that incorporates vertical transmission within the mosquito population. Threshold quantities for the model are computed, with the mosquito extinction equilibrium being globally asymptotically stable when the basic offspring number (N0) is less than one, also, the disease free equilibrium is shown to be locally asymptotically stable when the basic reproduction number (R0) is less than one. The model is shown to undergo backward bifurcation, and conditions under which the disease free equilibrium would be globally asymptotically stable is presented. Type reproduction numbers are also computed. Some results of numerical simulations, and sensitivity (

Some Geometric Characterization Of Star-like 3D Conjugacy C3ω∗n On Partial One-One Transformation Semigroups

I. R. Peter — 2024-06-10

Let Xn = {1, 2, 3, ...} be a set of distinct non negative integer then C3ω∗n be star-like conjugacy transformation semigroup for all D(α∗) (domain of α∗) and I(α∗) (Image of α∗) such that an operator | αωi − ωi+1 |≤| αωi − ωi | was generated. A star-like transformation semigroup is said to satisfy collapse function if C+(α∗) =| ∪tα− : t ∈ Tαω∗n | while the finding shows that the collapse of 3D star-like conjugacy classes are zero. The geometry model of 3D starlike conjugacy was obtained by using folding principle on a standard A4 paper which shows the star-like 3D conjugacy relation α(ij) = αi+αi+1 αi−αi+1 = αi+1+αi αi+1−αi .Some tables were formed to analyse the structure of star-like derank of C3ω∗n be | n − Imα∗ |= d, star-like collapse C+(α∗) =| ∪tα−1 : t ∈ Tαω∗n |, Star-like relapse C−(α∗) =| n−C+(α∗), Star-like pivot of C3ω∗n be |n.r+(α∗)c−(α∗) + c+(α∗|= p and Star-like joint of C3ω∗n be | r+(α∗)−m∗(α∗)−C+(α∗)+n |= j . The study conclude that C3ω∗n has n order conjugacy classes and we show that ϕ ∈ C3ω∗n.

Development and Analysis of a Nested Multiscale Model of Hepatitis B Viral Infection

O. T. Ogunfowote — 2024-06-20

Hepatitis B remains a global health concern owing to its deadly nature. A Nested Multiscale
Model was developed by applying the Replication-Transmission Theory at the cell level of
biological organisation. A new set of measures to assess infectiousness at the individual and
community levels was presented at the biological organisation’s cell level, where we grounded
our analysis. These models make it possible to investigate the dynamics of the virus within
infected cells, as well as the dynamics of future cell infections and the discharge of the virus
from infected cells. To study quantitatively how the dynamics of within-cell replication affect
the dynamics of between-cell transmission, mathematical analysis and numerical simulations
were carried out. These simulations can be used to evaluate the effectiveness of treatment and
preventive interventions.

Markov Switching Autoregressive Model: A Volatility Model With Application to All Share Index Returns

E. M. Ikegwu — 2024-07-10

This study explored the Autoregressive models incorporating Regime switching or Markov
switching non-linear predictive models. This stemmed from the complexities observed in economic
phenomena the understanding of which will help in recommending better model fits.
The study collected data on all share index returns (Jan, 1985 - December 2019) from the
Nigeria Stock Exchange, fit an appropriate MS-AR model and estimate its parameters. The
parameters of the model were obtained while their properties like the expected duration, autocorrelation
measure and the goodness of fit were equally computed in testing the applicability
of the model. The result shows that the MS (3)-AR (3) as a predictive model was appropriate,
efficient and robust enough for forecasting the returns of the all-share index of the Nigerian
stock exchange over the sampled period. The study is therefore relevant for modelling all share
index returns by investors, policy makers, researchers and the general public.

Bifurcation Analysis of an Age Structured Malaria Model

N. Isah — 2024-07-10

Malaria is one of the diseases that account for the highest mortality in sub-Saharan Africa
particularly among children below the age of five. On 17 April 2023, Nigeria became the
second country in the world to approve R21 malaria vaccine to prevent malaria infections
in children from five months to thirty-six months of age. In an attempt to investigate the
implications of vaccine development for malaria and the subsequent approval of its use in some
endemic regions, an age-structured malaria model was designed and some important factors
that could shape malaria dynamics were incorporated (e.g. vaccination, nonlinear incidence,
asymptomatic carriers, relapse and migration). The validity of the model is established using
some mathematics theorems and the reproduction number is computed following the next
generation matrix method. Bifurcation analysis is conducted by employing the center manifold
theorem. The results of the study indicated that the development of malaria vaccines and
the subsequent approval of its use in some malaria endemic regions (e.g. Ghana, Nigeria,
etc.) are a welcome development. However, while the vaccines may guarantee the necessary
protection, its application and coverage to the fullest may not instigate malaria eradication.
The policy implication of the results is that the prevalence of vectors in the endemic regions
necessitated adequate vector control in addition to the application of vaccines to minimize
malaria transmission.

Green functions of Fractional Partial Differential Equation With a Modified Elliptic Potential By a Weighted Bessel Function

U.S. Idiong — 2024-07-30

In this paper, the Green function of a fractional partial differential equation [(−Δ)1+α + V (x)]Ψ = δ(x − a), α ∈ (0, 1) is obtained where the Laplacian Δ, the potential V (x) and the Dirac delta function δ(x) are defined over a closed ball B(0, r) of radius r > 0 in an Euclidean space Rn and V (x) is a modified vector-valued Weierstrass sigma elliptic potential weighted by a Bessel function. A combination of Fourier and Hankel transform techniques are employed in obtaining the main result.

A Stochastic Model for the Variation of Fourier Series Expansions with Time Delay Arising in Financial Market Price Changes

I. U. Amadi — 2024-07-30

In this paper, we derive a closed-form solution for the Stochastic Delay Differential Equation
(SDDE). We formulated and proved theorems using Fourier series coefficients, which provided
exact conditions for asset proce returns in three scenarios : linear, quadratic, and cubic functions.
These price functions were utilized as the drift, representing the return rate in the SDDE
solution, resulting in three distinct solutions. We empirically evaluated these solutions to analyze the periodic impact of delay on each asset price
function, revealing that an increase in the delay parameter reduces the value of time-varying
asset investments. Finally, our comparison of the asset values indicated that return rates following a linear trend
offer the highest precision.

Maximum Likelihood Estimation Of Hidden Markov Model: Application To Markers of Infectious Disease Progression

R. U. Okafor — 2024-08-30

Hidden Markov models describe the probabilistic dependence between the latent state and the
observed variable of a system. It is a stochastic model with a sequence of observable events
where the underlying process that generates these events is unobserved. Hidden Markov models
could be used to analyze the history of various diseases, including infectious disease progression.
These models in life experiments describe the disease evolution, estimate the transition rates,
and evaluate the therapy effects on progression. In many cases, the states characterize the
markers of the diseases. Parameter estimation is indispensable when using the hidden Markov
model to model any dataset. In this work, the hidden Markov model is used to analyze the
dataset of HIV-infected patients undergoing antiretroviral treatments at a university teaching
hospital in Nigeria with different compliance levels. The model’s parameters were estimated
using the maximum likelihood estimation (MLE) method. The variables are the CD4 counts
and viral load results, often clinically characterized as markers of infectious diseases. The
transition probabilities provide insights into the stability and dynamics of the hidden states,
which is crucial for understanding the underlying processes modeled by the HMM. The results
indicate that stage 1 has a high probability of staying on that stage with ART treatment,
whereas stage 2 has a higher chance of sliding to stage 3. The results also indicate a high
chance of remaining in stage 3 once a patient is diagnosed with AIDS. The results show that
keeping the CD4 count up with antiretroviral treatments holds off symptoms and complications
of the Human Immunodeficiency Virus (HIV) and helps patients live longer. These highlight
the importance of maintaining an undetectable viral load with ART to ensure a healthy life
for HIV-infected individuals. Consequently, patient compliance in completing the treatment
regimes is optimal.