by Abeysinghe A Sunethra and Marina R Sooriyarachchi
Original Research
This research is motivated by the correlated outcomes of survival times and counts particularly in medical data. Analysis on individual patient data consisting of recurrent events of disease progression and survival times/death times give better results when a bivariate model/joint model of ‘survival’ and ‘count’ is used rather than fitting separate univariate models. For this purpose, a joint model for a proportional hazard survival response and a Poisson count responses is presented. The methodological aspects of the proposed model is outlined including parameter estimation. The proposed model was examined on a large scale simulation study and superior performance was demonstrated over the separate univariate models. The model was further showcased on an actual clinical trial data and found out to be capable of capturing the correlation between the survival and count variables found in the data.
American Journal of Applied Mathematics and Statistics. 2018, 6(2), 72-79. DOI: 10.12691/ajams-6-2-6
Pub. Date: May 04, 2018
8301 Views2110 Downloads
by Michael Gr. Voskoglou
Original Research
Mathematical modelling appears today as a dynamic tool for teaching/learning mathematics, because it connects mathematics with real world applications and therefore increases the student interest on the subject. Fuzzy relation equations, which are obtained by the composition of binary fuzzy relations, are used in this work as a tool for evaluating student mathematical modelling skills. A classroom application and other suitable examples are also presented illustrating our results.
American Journal of Applied Mathematics and Statistics. 2018, 6(2), 67-71. DOI: 10.12691/ajams-6-2-5
Pub. Date: May 02, 2018
9809 Views2607 Downloads
by Ayoola F.J. and Balogun K.O
Original Research
Education has been acknowledged as a central component that determines the character and social economic development of any nation especially in this era of globalization and technological revolution failure in addressing adequate education in any country could lead to retrograde in both social and economic development. The study aimed at estimating the factors that are capable of influencing students; academic performance at some selected public Senior Secondary Schools Certificate Examination in Akinyele Local Government of Oyo State, Nigeria. This study employed the binary logistic regression to estimate the academic performance based on gender and general academic performance. The students’ academic performance were categorized into two: passed if the student has at least five credits including English and Mathematics and failed if otherwise. The result shows that students’ performance in senior school certificate examination of public secondary schools in Akinyele Local Government Area of Oyo State will be better if the number of students per teacher follows international best practice (IBP) and library and laboratory are well equipped.
American Journal of Applied Mathematics and Statistics. 2018, 6(2), 61-66. DOI: 10.12691/ajams-6-2-4
Pub. Date: April 27, 2018
7760 Views1434 Downloads
by Ikeme John Dike and Chinyere Ogochukwu Dike
Original Research
Ebola Virus Disease (EVD) is a complicated and unparalleled epidemic disease. In recent times, the disease has been ravaging human lives and economy in West African nations. The most affected countries are Guinea, Liberia and Sierra Leone. Contagious disease like Ebola transmits through networks, made by bodily interactions among persons. As a result of the transmission mode and deadly nature of the disease, this paper proposes an EVD transmission and control model which incorporates queueing network that considers all the transmission phases in order to understand the real nature of the disease and predict its behaviour. The result for network indicates that the population was vulnerable to large scale epidemics before intervention in the three countries. In network model, critical transmissibility or epidemic threshold is the least transmissibility necessary for an outbreak to turn into a large scale epidemic. The for the three countries was 0.0644. Before intervention, the transmissibility for Guinea was 0.1365, Liberia, 0.2093 and Sierra Leone, 0.1325. After intervention, the transmissibility for Guinea became 0.0595, Liberia, 0.0440 and Sierra Leone, 0.0571. The before and after transmissibility results in comparison with the indicate that intervention was effective in containing the EVD epidemic. The vulnerability decreased drastically after intervention.
American Journal of Applied Mathematics and Statistics. 2018, 6(2), 54-60. DOI: 10.12691/ajams-6-2-3
Pub. Date: April 26, 2018
12752 Views2978 Downloads
by Shyam Sundar, Agraj Tripathi and Ram Naresh
Original Research
Today unemployment has become a global phenomenon which may be instrumental in forcing unemployed persons to earn their livelihood in an illegal manner resulting in a crime. It is possible that unemployed individuals may become more prone to develop a tendency of committing a crime when they come in contact with persons involved in criminal activities but are still unexposed. Further, when unemployed individuals are exposed to have committed a crime, they are captivated and finally awarded imprisonment if the offence charged on them is proved under the existing criminal laws. In this paper, a nonlinear mathematical model is developed to study the role of unemployment in inducing crime by taking into account four dependent variables representing the unemployment class, the employment class, the criminal class and the jail class. The model analysis, using stability theory of ordinary differential equations, provides some local and nonlinear stability conditions regarding stability of equilibrium of the model system. It is inferred that the endemic equilibrium is locally asymptotically stable as well as nonlinearly stable. Numerical simulations of the model system have also been carried to support the analytical findings and showing the effect of certain key parameters on different variables. It is observed that the increase in unemployment rate induces crime in the community leading to increase the burden on jail class.
American Journal of Applied Mathematics and Statistics. 2018, 6(2), 44-53. DOI: 10.12691/ajams-6-2-2
Pub. Date: April 24, 2018
12554 Views1929 Downloads
by Banerjee S., Awad R. and Agrawal B.
Original Research
This paper deals with general construction methods of nearly µ - resolvable balanced incomplete block designs with illustration using nearly one resolvable balanced incomplete block (BIB) designs and some known group divisible (GD) designs.
American Journal of Applied Mathematics and Statistics. 2018, 6(2), 36-43. DOI: 10.12691/ajams-6-2-1
Pub. Date: April 18, 2018
7305 Views1194 Downloads