In this paper, we consider an SI epidemic reaction-diffusion model with logistic source and saturation infection mechanism. We first establish the uniform boundedness and the extinction and persistence of the infectious disease in terms of the basic reproductive number. We also discuss the global stability of the unique endemic equilibrium when the spatial environment is homogeneous. Then we investigate the asymptotic behavior of the endemic equilibria in the heterogeneous environment when the movement rate of the susceptible and infected populations is small. Our results, together with the other two related epidemic models , not only show that the logistic growth, the infection mechanism, and the population movement can play an important role in the transmission dynamics of disease, but also suggest that increasing the inhibitory effect of the susceptible individuals instead of reducing the mobility of the populations can control the epidemic disease modeled by the SI system under consideration.

Matrix-type operators with the off-diagonal decay of polynomial or sub-exponential types are revisited with weaker assumptions concerning row or column estimates, still giving the continuity results for the frame type operators. Such results are extended from Banach to Fréchet spaces. Moreover, the localization of Fréchet frames is used for the frame expansions of tempered distributions and a class of Beurling ultradistributions.

The COVID-19 (SARS-CoV-2 virus) pandemic has led to a substantial loss of human life worldwide by providing an unparalleled challenge to the public health system. The economic, psychological, and social disarray generated by the COVID-19 pandemic is devastating. Public health experts and epidemiologists worldwide are struggling to formulate policies on how to control this pandemic as there is no effective vaccine or treatment available which provide long-term immunity against different variants of COVID-19 and to eradicate this virus completely. As the new cases and fatalities are recorded daily or weekly, the responses are likely to be repeated or longitudinally correlated. Thus, studying the impact of available covariates and new cases on deaths from COVID-19 repeatedly would provide significant insights into this pandemic's dynamics. For a better understanding of the dynamics of spread, in this paper, we study the impact of various risk factors on the new cases and deaths over time. To do that, we propose a marginal-conditional based joint modelling approach to predict trajectories, which is crucial to the health policy planners for taking necessary measures. The conditional model is a natural choice to study the underlying property of dependence in consecutive new cases and deaths. Using this model, one can examine the relationship between outcomes and predictors, and it is possible to calculate risks of the sequence of events repeatedly. The advantage of repeated measures is that one can see how individual responses change over time. The predictive accuracy of the proposed model is also compared with various machine learning techniques. The machine learning algorithms used in this paper are extended to accommodate repeated responses. The performance of the proposed model is illustrated using COVID-19 data collected from the Texas Health and Human Services.

The economic production quantity (EPQ) model for delayed deteriorating items considering two-phase production periods, exponential demand rate and linearly increasing function of time holding cost is proposed to solve a production problem similar to the one caused by the Covid-19 pandemic. Without shortages, the necessary and sufficient conditions for optimality of this model are characterized through a theorem and lemmas while a solution methodology based on differential calculus is adopted. This paper determines the best replenishment cycle length corresponding to the optimal total variable cost and production quantity of imperfect production industry. To illustrate this model, a numerical experiment is conducted. The results demonstrate that a higher carrying charge decreases the production quantity and a longer demanding period decreases the total variable cost of an industry with a distracted production period. Finally, managerial insights are discussed using sensitivity analysis and future research directions are exposed.

This paper presents a transfer function time series forecast model for COVID-19 deaths using reported COVID-19 case positivity counts as the input series. We have used deaths and case counts data reported by the Center for Disease Control for the USA from July 24 to December 31, 2021. To demonstrate the effectiveness of the proposed transfer function methodology, we have compared some summary results of forecast errors of the fitted transfer function model to those of an adequate autoregressive integrated moving average model and observed that the transfer function model achieved better forecast results than the autoregressive integrated moving average model. Additionally, separate autoregressive integrated moving average models for COVID-19 cases and deaths are also reported.

The evaluation of the information entropy content in the data analysis is an effective role in the assessment of fatigue damage. Due to the connection between the generalized half-normal distribution and fatigue extension, the objective inference for the differential entropy of the generalized half-normal distribution is considered in this paper. The Bayesian estimates and associated credible intervals are discussed based on different non-informative priors including Jeffery, reference, probability matching, and maximal data information priors for the differential entropy measure. The Metropolis-Hastings samplers data sets are used to estimate the posterior densities and then compute the Bayesian estimates. For comparison purposes, the maximum likelihood estimators and asymptotic confidence intervals of the differential entropy are derived. An intensive simulation study is conducted to evaluate the performance of the proposed statistical inference methods. Two real data sets are analyzed by the proposed methodology for illustrative purposes as well. Finally, non-informative priors for the original parameters of generalized half-normal distribution based on the direct and transformation of the entropy measure are also proposed and compared.

The statistical inference of multi-component reliability stress-strength system with nonidentical-component strengths is considered for the modified Weibull extension distribution in the presence of progressive censoring samples. For this aim, we study the estimation of multi-component reliability parameter in classical and Bayesian inference. So we derive some point and interval estimates such as maximum likelihood estimation, asymptotic confidence intervals, uniformly minimum variance unbiased estimation, approximate and exact Bayes estimation and highest posterior density intervals. Comparing of different estimates is provided by employing the Monte Carlo simulation, the mean squared error and coverage probabilities. Finally, one real data is utilized to illustrate the applicability of this new model.