Optimization of renewal input (a, c, b) policy working vacation queue with change over time and bernoulli schedule vacation interruption

This paper presents a renewal input single working vacation queue with change over time and Bernoulli schedule vacation interruption under (a, c, b) policy. The service and vacation times are exponentially distributed. The server begins service if there are at least c units in the queue and the service takes place in batches with a minimum of size a and a maximum of size b (a ≤ c ≤ b). The change over period follows if there are (a − 1) customers at service completion instants. The steady state queue length distributions at arbitrary and pre-arrival epochs are obtained. An optimal cost policy is presented along with few numerical experiences. The genetic algorithm and quadratic fit search method are employed to search for optimal values of some important parameters of the system.Publisher's Versio

Transmission dynamics model of Tuberculosis with optimal control strategies in Haramaya district, Ethiopia

Abstract In this study, we use a compartmental nonlinear deterministic mathematical model to investigate the effect of different optimal control strategies in controlling Tuberculosis (TB) disease transmission in the community. We employ stability theory of differential equations to investigate the qualitative behavior of the model by obtaining the basic reproduction number and determining the local stability conditions for the disease-free and endemic equilibria. We consider three control strategies representing distancing, case finding, and treatment efforts and numerically compare the levels of exposed and infectious populations with and without control strategies. The results suggest that combination of all controls is the best strategy to eradicate TB disease from the community at an optimal level with minimum cost of interventions

Cooperative Learning as a Window of Opportunity to Transact Mathematics Instruction in Alamata and Korem Secondary Schools of Tigray, Ethiopia

Mathematics instruction would be more effective if students were able to help each other and exchange information actively. This can effectively be done when students are engaged in cooperative learning. The study was intended to analyse the extent to which mathematics education is supplemented with cooperative learning in Grade 9 of Secondary Schools in Alamata and Korem, Tigray. In order to address the research objectives, mixed methods design was employed. Questionnaires, interview and classroom observation were used to collect quantitative and qualitative data from a sample of 15 teachers and 322 students. The data was analysed using descriptive statistics. The results of the study revealed that the extent of practicing cooperative learning methods was not up to the expected level. The attitude of teachers toward using cooperative learning methods was favourable and yet, teachers’ action in dealing with the basic components of cooperative learning was not promising. The findings showed that the major factors that inhibit the implementation of cooperative learning were lack of adequate training, lack of classroom facilities, lack of administrative support, lack of time, dependency of slow learners on more able learners, and traditional teaching methods. It is suggested that teachers should take basic training about the use and deliberation of cooperative learning as one of innovative teaching methods of mathematics education and as a means to realize their commitment

Stochastic model of measles transmission dynamics with double dose vaccination

In this paper we developed a stochastic model of measles transmission dynamics with double dose vaccination. The total population in this model was sub-divided in to five compartments, namely SusceptibleS(t), Infected I(t), Vaccinated first dose V1(t),Vaccinated second dose V2(t) and Recovered R(t). First the model was developed by deterministic approach and then transformed into stochastic one, which is known to play a significant role by providing additional degree of realism compared to the deterministic approach. The analysis of the model was done in both approaches. The qualitative behavior of the model, like conditions for positivity of solutions, invariant region of the solution, the existence of equilibrium points of the model and their stability, and also sensitivity analysis of the model were analyzed. We showed that in both deterministic and stochastic cases if the basic reproduction number is less than 1 or greater than 1 the disease free equilibrium point is stable or unstable respectively, so that the disease dies out or persists within the population. Numerical simulations were carried out using MATLAB to support our analytical solutions. These simulations show that how double dose vaccination affect the dynamics of human population