Unilag Journal of Mathematics and Applications

APPLICATION OF GEE IN THE FIT OF ORDINAL MARGINAL REGRESSION MODEL FOR TREATMENT RESPONSE OF HYPERTENSION

Chijioke Nweke — 2024-11-30

This study adopts the ordinal logistic marginal model to fi t the response to treatment of hypertensive patients with a view to ascertain any importance in incorporating panels when studying such clinical data. The Generalized Estimating Equation (GEE) provides an appropriate approach for estimating the model parameters. Two versions of ordinal regression models in conjunction with two forms of covariance estimators under three working correlation structures are considered. Results obtained revealed the importance of panels when studying the risk factors and response to treatment of hypertensive patients. With the Quasi-likelihood Information Criterion obtained for ordinal regression and other fitness criteria, the exchangeable working correlation is recommended as most adequate for the given data set.

MHD CASSON NANOFLUID FLOW WITH VISCOUS DISSIPATION, CHEMICAL REACTION AND THERMAL RADIATION SUBJECTED TO CONVECTIVE BOUNDARY CONDITIONS

Soluade Joseph Aroloye — 2024-11-30

Casson nanofluid flow in the presence of nanoparticles, viscous dissipation, chemical reactions and thermal radiations under the influence of convective boundary conditions is numerically investigated. Convective conditions of temperature and nanoparticle concentration are employed in the formulation of the problem. The highly governing partial di erential equations models the problem are reduced to ordinary di erential equations via similarity variables. Numerical solutions via shooting method with six order Runge Kutta scheme used to solve the velocity, temperature and nanoparticle concentration models. The numerical simulation is carried out with the aid of Maple software. The results and influence of embedded flow parameters are presented through graphs and tables. The obtained results are compared with similar existing results in literature and there is excellent agreement. We found that temperature and nanoparticle concentration fi elds decrease when the values of Casson parameter increases. It is found that the temperature and concentrations fields enhanced as Biots numbers increase due to thermal and concentration convective conditions. The results further revealed that both the thermal and nanoparticle concentration boundary layer thicknesses are higher for the larger values of thermophoresis parameter. It is also observed that temperature and concentrations profi les reduces for large value of Brownian motion parameters. The results further reveal that both the fluid temperature and concentration increases as chemical reaction increases.

NUMERICAL APPROXIMATION OF SINGULAR MULTI-ORDER FRACTIONAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS BY LEAST SQUARES AND AKBARI-GANJI'S METHODS

O. A. Uwaheren — 2024-11-30

This article is concerned with the numerical solution of singular multi-order fractional Volterra integro-di erential equations. Two numerical methods are proposed; Least Squares and Akbari-Ganji's Methods using Legendre polynomials as basis functions. The proposed methods were demonstrated on some examples to verify their practicability and the results obtained were very close to the exact solution.

COEFFICIENT INEQUALITIES OF BAZILEVIC FUNCTIONS COLLIGATED WITH CONIC DOMAIN

OLALEKAN FAGBEMIRO — 2024-11-30

In this paper, the concept of Bazilevic function as well as Janowski function and the conic regions are combined e ectively to de ne a new domain that exemplify the conic-type regions. The sub-classes of these types of functions which map the open unit disk U onto this changed Conic domain are de ned. Also, the sub-classes of k -uniformly Janowski convex and k- uniformly Janowski starlike function involving Bazilevic functions are de ned using Salagean derivative operator. New results were obtained along with some corollaries and the consequences of our results were pointed out.

THE MODIFIED RANDOM WALK DISTRIBUTION

LATEEF ADAMU — 2024-11-30

This study presents a modification to a two-parameter distribution, yielding a discrete distribution termed the modified random walk distribution. This modification is derived from the random walk distribution and falls within the family of Lagrangian probability distributions. Comprehensive investigations are conducted on both the random walk distribution and its modified counterpart to discern and analyze their respective properties. Furthermore, a recursive formula for generating probabilities associated with this distribution is proposed. This research contributes to the understanding of the random walk distribution and provides insights into the implications of its modification.

QUASI-SYMMETRIC POLYNOMIALLY BOUNDED FReCHET ALGEBRAS

Olufemi O. Oyadare — 2024-12-10

This paper concerns the notion of a symmetric algebra and its generalization to a quasi-symmetric algebra. We study the structure of these algebras in respect to their hull-kernel regularity and existence of some ideals, especially the hull-minimal ideals. An immediate application of our results is to the Harish-Chandra Schwartz Frechet algebras, C^p(G), of a (connected) semi-simple G.

MATHEMATICAL MODELING OF CHOLERA TRANSMISSION IN EPIDEMIC AND ENDEMIC SETTINGS WITH CONTROL STRATEGIES

Sunday Nwokpoku Aloke — 2024-12-11

One of the most serious health issues in the world today is cholera, particularly in poorer nations with poor access to clean water. We have examined the distribution of cholera in both endemic and epidemic settings in this article. We develop the mathematical model of the dynamics of cholera transmission known as SEIRH with controls. The time-dependent control mechanisms (vaccine, water puri cation, and sanitation) that govern the disease's transmission and management were incorporated into the model. It was possible to acquire the potential key measure R₀, a threshold value used to forecast the prognosis of a disease. The stability of the endemic disease equilibrium point (EEP) and the cholera-free equilibrium point (DFEP) was examined. If R₀ is less than 1, then DFEP is locally asymptotically stable (LAS), and EEP is globally asymptotically stable (GAS) when R₀ is greater than 1. The impact of control measures on virus spread was investigated, and the optimal control value that minimizes the objective function was also investigated using Pontryagin's maximum principle. The model simulation shows that the methods used have a positive impact on public health by lowering morbidity and mortality. Cholera incidence can be considerably decreased by eff ective prevention and control measures, which will lower rates of morbidity and mortality.

BAYESIAN SURVIVAL ANALYSIS OF DIABETES MELLITUS IN LAGOS STATE NIGERIA

Rotimi K. OGUNDEJI — 2024-12-11

Diabetes Mellitus is an escalating public health issue in Nigeria, significantly affecting the population. This study analyzes the survival patterns of diabetes patients in Lagos State, Nigeria, using Bayesian survival analysis techniques, including the Cox Proportional Hazard model and Kaplan-Meier estimator, to identify key factors influencing survival rates and predict future outcomes. Drawing from a comprehensive, multi-year dataset that includes critical predictors and confounders, the study reveals a significant decline in survival probability over time. Posterior predictive checks confirm the models' adequacy, showing strong alignment between observed data and simulations. The Cox Proportional Hazard model identifies age, gender, and insulin use as key contributors to the hazard rate, while other factors are found to have limited impact. These findings underscore the importance of early intervention strategies targeting high-risk factors, such as age and insulin dependency, to improve outcomes and reduce the diabetes burden in Lagos State, Nigeria.