Visualizing the fatality of coronavirus is a very tricky point through the world. In this paper, a new construction via the proportional hazard rate model with Rayleigh marginal is introduced and applied on COVID-19 data set. The statistical and reliability characteristics of bivariate Rayleigh proportional hazard (BRPH) distribution are derived. The copula dependence structure and its properties are studied. The point estimation of the marginal and dependence parameters is introduced via maximum likelihood, method of moments, and inference function for margins (IFM) method. A simulation study is carried out to examine the effectiveness and the performance of the parameter estimates. Finally, an application on COVID-19 data is used in a comparison study between BRPH model and other constructed bivariate models. This application concerned with modeling the fatality on COVID-19. Throughout the results of goodness-of-fit criteria, BRPH provides a better fit than different competitors constructed bivariate models which reflects its flexibility and applicability on modeling the fatality of COVID-19.

Some international pharmaceutical companies have succeeded in producing vaccines against COVID-19. Countries all over the world have aimed to obtain these vaccines with minimum cost. We consider a set of -independent Markovian waiting lists. Each list contains a set of countries, where each one of them has an exponential service time and a Poisson arrival process. These companies differ in some characteristics such as the vaccine production cost and the speed of the required quantity delivery. We present a new detection model that helps in providing an appropriate decision to choose a suitable company. Moreover, the concept of balking and the retention of reneged countries is taken into consideration under the quality control process of each waiting list. Under steady state, we face an interesting and difficult discrete stochastic optimization problem. Its solution gives an optimal distribution of the searching effort, which is bounded by a known probability distribution. A simulation study has been derived to get the minimum value of the paid cost random values. The highest service rate, the total expected profit of each queuing system, and the optimum performance measures, which depend on this cost, have been obtained to show the effectiveness of this model.