A novel family of produced distributions, odd inverse power generalized Weibull generated distributions, is introduced. Various mathematics structural properties for the odd inverse power generalized Weibull generated family are computed. Numerical analysis for mean, variance, skewness, and kurtosis is performed. The new family contains many new models, and the densities of the new models can be right skewed and symmetric with “unimodal” and “bimodal” shapes. Also, its hazard rate function can be “constant,” “decreasing,” “increasing,” “increasing-constant,” “upside-down-constant,” and “decreasing-constant.” Different types of entropies are calculated. Some numerical values of various entropies for some selected values of parameters for the odd inverse power generalized Weibull exponential model are computed. The maximum likelihood estimation, least square estimation, and weighted least square estimation approaches are used to estimate the OIPGW-G parameters. Many bivariate and multivariate type models have been also derived. Two real-world data sets are used to demonstrate the new family’s use and versatility.

Infectious disease transmission between individuals in a heterogeneous population is often best modelled through a contact network. However, such contact network data are often unobserved. Such missing data can be accounted for in a Bayesian data augmented framework using Markov chain Monte Carlo (MCMC). Unfortunately, fitting models in such a framework can be highly computationally intensive. We investigate the fitting of network-based infectious disease models with completely unknown contact networks using approximate Bayesian computation population Monte Carlo (ABC-PMC) methods. This is done in the context of both simulated data, and data from the UK 2001 foot-and-mouth disease epidemic. We show that ABC-PMC is able to obtain reasonable approximations of the underlying infectious disease model with huge savings in computation time when compared to a full Bayesian MCMC analysis.

In this article, we use Lehmann alternative-II to extend the odd generalized exponential family. The uniqueness of this family lies in the fact that this transformation has resulted in a multitude of inverted distribution families with important applications in actuarial field. We can characterize the density of the new family as a linear combination of generalised exponential distributions, which is useful for studying some of the family’s properties. Among the structural characteristics of this family that are being identified are explicit expressions for numerous types of moments, the quantile function, stress-strength reliability, generating function, Rényi entropy, stochastic ordering, and order statistics. The maximum likelihood methodology is often used to compute the new family’s parameters. To confirm that our results are converging with reduced mean square error and biases, we perform a simulation analysis of one of the special model, namely OGE2-Fréchet. Furthermore, its application using two actuarial data sets is achieved, favoring its superiority over other competitive models, especially in risk theory.

In this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Carathéodory approximation approach and stochastic calculus to present the existence and uniqueness theorem of the stochastic system under Carathéodory-type conditions with Lipschitz and non-Lipschitz conditions as special cases. Some existing results are generalized and enhanced. Finally, an application is offered to illustrate the obtained theoretical results.

In this study, we will look at a new flexible model known as the new double‐weighted Weibull distribution. The new Weibull double‐weighted distribution model is highly versatile because numerous submodels are included. The proposed model is very flexible because its density function has many shapes; it can be right skewness, decreasing, and unimodal. Also, the hazard rate function can be increasing, decreasing, up‐side‐down, and J‐shaped. Diverse features of the novel are computed. These qualities include moments, incomplete moments, and Lorenz and Bonferroni curves and quantiles, as well as entropy and order statistics. The maximum likelihood approach is used to estimate the model's parameters. In order to evaluate the accuracy and performance of maximum likelihood estimators, simulation data are presented. The utility and adaptability of the proposed model are demonstrated by utilizing three significant datasets: daily fatalities confirmed cases of COVID‐19 in Egypt and Georgia and relief times of twenty patients using an analgesic.

Since the early days of the coronavirus (COVID-19) outbreak in Wuhan, China, Saudi Arabia started to implement several preventative measures starting with the imposition of travel restrictions to and from China. Due to the rapid spread of COVID-19, and with the first confirmed case in Saudi Arabia in March 2019, more strict measures, such as international travel restriction, and suspension or cancellation of major events, social gatherings, prayers at mosques, and sports competitions, were employed. These non-pharmaceutical interventions aim to reduce the extent of the epidemic due to the implications of international travel and mass gatherings on the increase in the number of new cases locally and globally. Since this ongoing outbreak is the first of its kind in the modern world, the impact of suspending mass gatherings on the outbreak is unknown and difficult to measure. We use a stratified SEIR epidemic model to evaluate the impact of Umrah, a global Muslim pilgrimage to Mecca, on the spread of the COVID-19 pandemic during the month of Ramadan, the peak of the Umrah season. The analyses shown in the paper provide insights into the effects of global mass gatherings such as Hajj and Umrah on the progression of the COVID-19 pandemic locally and globally.