Authors:Senyefia Bosson-Amedenu, Joseph Acquah, Christiana Cynthia Nyarko, Noureddine Ouerfelli Abstract: The typical Cox proportional hazard (PH) model will provide erroneous estimates if the PH assumption is broken, which is quite prevalent in medical research. We have developed an expanded version of the basic Cox Model that includes a time-lag function and a frailty parameter to account for time-variant covariates, heterogeneity and unobserved components in this study. Secondary data from 558 Breast cancer (BC) patients diagnosed at Korle Bu teaching hospital were analyzed. The dataset was divided into two parts: training (which had 70% of the data) and validation (30 percent). Tests for the functional form of continuous covariates and outliers were included in the model diagnostics. The Shoenfeld residual test and the graphical test served as the foundation for the PH assumption test. In a noncompeting risk environment, the PH assumption was violated by progesteron receptor status, molecular subtype, and tumor grade at diagnosis. Frailty component was revealed to be a significant contributor to the developed model, accounting for around 15% of all fatalities attributable to heterogeneity and unobserved variables. Our model outperformed current models such as the Exponential AFT model, stratified Cox (interaction) model, the standard Cox PH Model and Park and Qiu (2017) model in terms of AIC, BIC, likelihood ratio test and area under the ROC curve. Breast cancer survival in Ghana is influenced by stage at diagnosis, metastatic status, lymph node involvement, and HER2 overexpression, according to our model. Among other findings, BC patients who develop metastasis are 41.264 times more likely to die from the disease than individuals who do not develop metastasis. Individuals with higher stages of BC (III and IV) are 6.89 times more likely to die from the disease than patients with lower stages (I and II). To improve BC care and prognosis, it was suggested that medical officers and diagnosticians take into account the identified significant determinants regulating survival as well as the estimated risk and survival probability. Keywords: Breast Cancer, Frailty, Heterogeneity, Cox Proportional Hazard Model, Stratified Cox (interaction), Extended Cox. Issue No:Vol. 12

Authors:Soni Roopani, Asif Ali Shaik, Feroz Shah Abstract: The thesis accomplishes the theoretical study of the effect of inertia on Newtonian fluid in squeezed. This research undertaking to get in ingenious knowledge for the procedure of the axisymmetric viscous fluid flow in between parallel plates steadily approaching to each other, as well the inertia effect is under consideration. Thereby, the crucial part of this thesis is to theoretically investigate rather than experimentally. Be sure that as it may, the expectation from this study is that it could be experimentally performed, so will get practical benefits, in the form of the improvement in the process of flow of oil in bearing and governs with capacity of load – bearing and improving the results of oil in bearing. The primary focused object of this work is to develop a mathematical model, thereby, to calculate the velocity profile likewise radial and axial velocity and pressure. In this research work, the squeezed film of Newtonian fluid between two disks is taken to obtain an analytical solution (PDE – Partial Differential Equations) subject to the favorable boundary conditions, as well as the inertia effect is under consideration. In this thesis the recursive approach is utilized to get an analytical solution and the obtained solution is examined with perturbation method. The examined solution has been found as the main objective of this study. It is analyzed that the recursive approach is easy to use and appears more effective. Keywords: Newtonian fluid, Non-Newtonian fluids. Ideal fluids Squeezed fluid, Inertia effect, Velocity Profile, Pressure. DOI : 10.7176/MTM/12-1-04 Publication date: February 28th 2022 Issue No:Vol. 12

Authors:Angham A. Jabar, A. S. J. Al- Saif Abstract: In this paper, the delay differential equations of Gene expression models with mechanisms of signal-dependent transcription regulation are solved and studied in two cases: When there is (i) competition and (ii) without competition(non-competition) for Deoxy ribo Nucleic Acid (DNA) regulatory binding sites in a cell. Also, we studied the effect of both increasing the inhibitor or decreasing the abundance of the activator (inhibition mechanism), and decreasing the inhibitor or increasing the abundance of the activator (activator mechanism) on the steady-state of the solutions. A new analytical approximation approach derived from Taylor series expansion is used for solving the delay differential equations of gene expression models. From the analytical approximate solutions of gene expression models that are resulting from using the proposed method, we found that the behavior of the solution in the activation mechanisms whether in the competitive or non-competitive model is more stable than the abundance of the activator increases, while the inhibition mechanisms are less stable. We also noticed that the convergence of these solutions is achieved with a few iterations. Keywords: Taylors’ technique, activator, inhibitor, Gen, mRNA, protein, convergence analysis. DOI : 10.7176/MTM/12-1-01 Publication date: January 31st 2022 Issue No:Vol. 12

Authors:Iddrisu A. Mohammed Katali, Baba Seidu, Elijah B. Baloba Abstract: Cholera is an acute intestinal infection and water borne disease that has claimed and continue to claim the lives of millions of people in the developing countries. Its effects on developing countries cannot be ignored since most of the people who get infected or die from the disease are usually children and adults who are in their economically active years. This paper presents an epidemic mathematical model that is aimed at describing the dynamics of the spread of Cholera. In this paper, infection of the disease is considered to be through contact with Infectives or vibrio cholerae in the dry lands and the water bodies. The model is qualitatively analyzed to determine conditions for successful fight against cholera. It is shown that if the basic reproduction number , is less than unity, then the disease-free equilibrium is locally asymptotically stable and the disease dies out and when the basic reproduction number is greater than unity, the vibrio cholerae and the disease will persist in the population. Numerical simulations are also carried out and various combinations of intervention strategies are compared to determine the most effective strategy that should be employed in order to control the spread of the v.cholerae. It is observed that the strategy that adopts education on open defecation, environmental sanitation and water treatment are the most effective strategies in the fight against the spread of the disease Keywords and phrases: Mathematical model, local stability, basic reproduction number, optimal control. DOI : 10.7176/MTM/12-1-02 Publication date: January 31st 2022 Issue No:Vol. 12

Authors:Augustine Adu Frimpong Abstract: This essay investigates the theory behind principal-agent problems by utilizing mathematical tools and contractual policies for the offered analysis. With a reliance on Boolean Search technique, the essay’s study design follows narrative literature reviews. The overall effort has been answering several study questions, which included the following: (a) does the type of contract matter to the two parties—the principal and the agent' (b) what informs the determination of fixed wage' and (c) how does the risk types among the agent and principal influence the type of contract' Also, as a part of the study findings: it has been concluded that the type of prevailing contract or offer matters to both the agent and the principal. A crucial factor of the study is the revealed that fixed wage determination should be tied to the agent’s reservation utility and the type of effort embarked on. With regard to the effect of the type of prevailing risk on the offer, it is concluded in the essay that once effort is observable and the agent is risk averse, then such agent has to be insured. The rationale behind the foregoing scenario is the fact that risk sharing becomes possible if the principal is risk neutral. Meanwhile, efficiency demands that it is advisable for the principal to insure the agents, who is risk averse, by offering a wage that does not depend on the variability of profit. The research for the study has revealed further that, in instances whereby both the principal and the agent are risk neutral, then there are several kinds of options made available to the agent, which include (a) fixed wage, and (b) tying wages to efforts when efforts are observable. Also, for the situation whereby a pursued effort is not observable while the agent is risk averse, then the principal has to provide a variety of incentive schemes or structure in the context of the agents for him/her to improve upon his/her utility, thereby either choosing or putting in the right effort. Finally, in a case whereby the requisite effort is not observable and agent is risk neutral, it is advisable that the principal should, in principle, sell the project to the agent for a fixed income (F). Thus, if the agent is risk neutral, then one should allow the agent to face the risk and subsequently for one to choose the optimal effort to maximize the ultimate or expected utility. Keywords: Principal, Utility, Firm, Risk, Business, Agent, Moral-Hazard, Maximize, Asymmetric-Information, Hires, Incentives, Insurance. DOI : 10.7176/MTM/12-1-03 Publication date: January 31st 2022 Issue No:Vol. 12