ABSTRACT
We propose a theoretical study to investigate the spread of the SARS-CoV-2 virus, reported in Wuhan, China. We develop a mathematical model based on the characteristic of the disease and then use fractional calculus to fractionalize it. We use the Caputo-Fabrizio operator for this purpose. We prove that the considered model has positive and bounded solutions. We calculate the threshold quantity of the proposed model and discuss its sensitivity analysis to find the role of every epidemic parameter and the relative impact on disease transmission. The threshold quantity (reproductive number) is used to discuss the steady states of the proposed model and to find that the proposed epidemic model is stable asymptotically under some constraints. Both the global and local properties of the proposed model will be performed with the help of the mean value theorem, Barbalat’s lemma, and linearization. To support our analytical findings, we draw some numerical simulations to verify with graphical representations.
ABSTRACT
The purpose of this paper is to identify an effective statistical distribution for examining COVID-19 mortality rates in Canada and Netherlands in order to model the distribution of COVID-19. The modified Kies Frechet (MKIF) model is an advanced three parameter lifetime distribution that was developed by incorporating the Frechet and modified Kies families. In particular with respect to current distributions, the latest one has very versatile probability functions: increasing, decreasing, and inverted U shapes are observed for the hazard rate functions, indicating that the capability of adaptability of the model. A straight forward linear representation of PDF, moment generating functions, Probability weighted moments and hazard rate functions are among the enticing features of this novel distribution. We used three different estimation methodologies to estimate the pertinent parameters of MKIF model like least squares estimators (LSEs), maximum likelihood estimators (MLEs) and weighted least squares estimators (WLSEs). The efficiency of these estimators is assessed using a thorough Monte Carlo simulation analysis. We evaluated the newest model for a variety of data sets to examine how effectively it handled data modeling. The real implementation demonstrates that the proposed model outperforms competing models and can be selected as a superior model for developing a statistical model for COVID-19 data and other similar data sets.
ABSTRACT
Microorganisms lives with us in our environment, touching infectious material on the surfaces by hand-mouth which causes infectious diseases and some of these diseases are rapidly spreading from person to person. These days the world facing COVID-19 pandemic disease. This article concerned with existence of results and stability analysis for a nabla discrete ABC-fractional order COVID-19. The nabla discrete ABC-fractional operator as more general and applicable in modeling of dynamical problems due to its non-singular kernel. For the existence and uniqueness theorems and Hyers-Ulam stability, we need to suppose some conditions which will play important role in the proof of our main results. At the end, an expressive example is given to provide an application for the nabla discrete ABC-fractional order COVID-19 model.
ABSTRACT
In this article, we develop a generator to suggest a generalization of the Gumbel type-II model known as generalized log-exponential transformation of Gumbel Type-II (GLET-GTII), which extends a more flexible model for modeling life data. Owing to basic transformation containing an extra parameter, every existing lifetime model can be made more flexible with suggested development. Some specific statistical attributes of the GLET-GTII are investigated, such as quantiles, uncertainty measures, survival function, moments, reliability, and hazard function etc. We describe two methods of parametric estimations of GLET-GTII discussed by using maximum likelihood estimators and Bayesian paradigm. The Monte Carlo simulation analysis shows that estimators are consistent. Two real life implementations are performed to scrutinize the suitability of our current strategy. These real life data is related to Infectious diseases (COVID-19). These applications identify that by using the current approach, our proposed model outperforms than other well known existing models available in the literature.
ABSTRACT
The aim of this study is to analyze the number of deaths due to COVID-19 for Europe and China. For this purpose, we proposed a novel three parametric model named as Exponentiatedtransformation of Gumbel Type-II (ETGT-II) for modeling the two data sets of death cases due to COVID-19. Specific statistical attributes are derived and analyzed along with moments and associated measures, moments generating functions, uncertainty measures, complete/incomplete moments, survival function, quantile function and hazard function etc. Additionaly, model parameters are estimated by utilizing maximum likelihood method and Bayesian paradigm. To examine efficiency of the ETGT-II model a simulation analysis is performed. Finally, using the data sets of death cases of COVID-19 of Europe and China to show adaptability of suggested model. The results reveal that it may fit better than other well-known models.
ABSTRACT
In this article, the mathematical model with different compartments for the transmission dynamics of coronavirus-19 disease (COVID-19) is presented under the fractional-order derivative. Some results regarding the existence of at least one solution through fixed point results are derived. Then for the concerned approximate solution, the modified Euler method for fractional-order differential equations (FODEs) is utilized. Initially, we simulate the results by using some available data for different fractional-order to show the appropriateness of the proposed method. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.