A non-linear ܴܶܪܵ mathematical model was used to study the dynamics of drinking epidemic. We discussed the existence and stability of the drinking-free and endemic equilibria. The drinking-free equilibrium was locally asymptotically stable if ܴ ൏ 1 and unstable if ܴ 1. Global stability of drinking-free and endemic equilibria were also considered in the model, using Lassalle's invariance principle of Lyapunov functions. Numerical simulations were conducted to confirm our analytic results. Our findings was that, reducing the contact rate between the non-drinkers and heavy drinkers, increasing the number of drinkers that go into treatment and educating drinkers to refrain from drinking can be useful in combating the drinking epidemic.
COVID-19 remains the concern of the globe as governments struggle to defeat the pandemic. Understanding the dynamics of the epidemic is as important as detecting and treatment of infected individuals. Mathematical models play a crucial role in exploring the dynamics of the outbreak by deducing strategies paramount for curtailing the disease. The research extensively studies the SEQIAHR compartmental model of COVID-19 to provide insight into the dynamics of the disease by underlying tailored strategies designed to minimize the pandemic. We first studied the noncontrol model’s dynamic behaviour by calculating the reproduction number and examining the two nonnegative equilibria’ existence. The model utilizes the Castillo-Chavez method and Lyapunov function to investigate the global stability of the disease at the disease-free and endemic equilibrium. Sensitivity analysis was carried on to determine the impact of some parameters on R 0 . We further examined the COVID model to determine the type of bifurcation that it exhibits. To help contain the spread of the disease, we formulated a new SEQIAHR compartmental optimal control model with time-dependent controls: personal protection and vaccination of the susceptible individuals. We solved it by utilizing Pontryagin’s maximum principle after studying the dynamical behaviour of the noncontrol model. We solved the model numerically by considering different simulation controls’ pairing and examined their effectiveness.
This paper illustrates analysis of longitudinal data on students' academic performance using GEE (Generalize Estimation Equations) under various working correlation assumptions. Many factors account for students' academic performance in the fulcrum of all levels of education. Hence, any variable that triggers the academic performance of students evoke the awareness of all. The aim of this thesis is to analyze academic performance using application of Generalized Estimating Equation (GEE) Models under various working correlation assumptions. There are various statistical and mathematical models employed in the analyses of students' academic performance in different level of schools. In this paper, we formulate the Generalized Estimating Equation (GEE) model approach under various correlation assumptions to analyze the probable 3360 Isaac Owusu-Darko et al. performance in relation to variables such as gender, entry age into the school, the geographical location of students, as well as Graded level of former School attended. We used real data set of students' Semester Weighted Average (SWA), and back these with validate and reliable questionnaire about students personal information (on their Biodata response) for a complete data set. From our analyses, the test of model-based and empirical-based standard error estimates on Coefficient Estimation of the Study Parameters based on our GEE assumptions reveals that, only the geographical location of students is significant and hence affects their academic performance. Our contrast effect of linear time interactions with respect to the locations made us recommend an enhancement of mathematics teaching in locations that are lagging, especially in the Northern Belt of Ghana.
We seek to discuss how the transmission of HIV infection, and hence AIDS disease, depends on various biological and social factors, which may be different within and between the different population groups. In this paper an SIA compartment model of the transmission dynamics of HIV/AIDS is developed using Ghana Data. The resulting system of three non-linear differential equations was analyzed in respect of stability of the three equilibrium points namely the disease free which was found to be locally asymptotically stable and two endemic equilibrium points which were found to be 96 Stephen Eduafo et al. stable. Further analysis to determine the conditions for the breakout of epidemic were done using the basic reproductive number of the infection. It was found that the rate of transition from HIV infected to AIDS relative to the rate of transition from susceptible to HIV infected state would need to be increased in order to effectively control the spread of the disease.
We use SIR model to predict the prevalence and incidence of Hepatitis B in Bosomtwe District of Ghana. The study is made up of two sections. An SIR model without vaccination is used to explain the spread of the HBV in the Bosomtwe district followed by the modeling HB with vaccination in the district. 3344 Isaac Kwasi Adu et al. The model has two equilibrium states: the disease-free equilibrium and the endemic equilibrium states respectively. The stability condition of each equilibrium point is discussed. The basic reproductive number () of HB without vaccination is estimated to be 1.006 and the basic reproductive number () of HB with vaccination is estimated to be 0.9840. Our work shows that, the proportion of the population of Bosomtwe district that needs to be vaccinated in order to control HBV in the district is 871. According to the results of this study, whenever the transmission rate parameter value is increased, but when the transmission rate parameter value is reduced,. A combination of increased vaccination of newborns and immunization of susceptible adults appears to reduce HB prevalence in Bosomtwe District to the minimum.
In this paper, the concept of assignment problem was applied to solve a problem for a Legal Firm A in Kumasi which had a difficulty in assigning nine different cases to its nine junior lawyers. Based on the data collected, Management Scientist Version 5 Software which uses Hungarian Method was used to solve the problem. Optimal assignments of the cases to the junior lawyers were obtained for the Legal Firm A. It was obtained that,
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