Kinetics of a Reaction-Diffusion Mtb/SARS-CoV-2 Coinfection Model with Immunity

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and Mycobacterium tuberculosis (Mtb) coinfection has been observed in a number of nations and it is connected with severe illness and death. The paper studies a reaction–diffusion within-host Mtb/SARS-CoV-2 coinfection model with immunity. This model explores the connections between uninfected epithelial cells, latently Mtb-infected epithelial cells, productively Mtb-infected epithelial cells, SARS-CoV-2-infected epithelial cells, free Mtb particles, free SARS-CoV-2 virions, and CTLs. The basic properties of the model's solutions are verified. All equilibrium points with the essential conditions for their existence are calculated. The global stability of these equilibria is established by adopting compatible Lyapunov functionals. The theoretical outcomes are enhanced by implementing numerical simulations. It is found that the equilibrium points mirror the single infection and coinfection states of SARS-CoV-2 with Mtb. The threshold conditions that determine the movement from the monoinfection to the coinfection state need to be tested when developing new treatments for coinfected patients. The impact of the diffusion coefficients should be monitored at the beginning of coinfection as it affects the initial distribution of particles in space. © 2023 by the authors.

Bayesian Inference and Data Analysis of the Unit–Power Burr X Distribution

The unit–power Burr X distribution (UPBXD), a bounded version of the power Burr X distribution, is presented. The UPBXD is produced through the inverse exponential transformation of the power Burr X distribution, which is also beneficial for modelling data on the unit interval. Comprehensive analysis of its key characteristics is performed, including shape analysis of the primary functions, analytical expression for moments, quantile function, incomplete moments, stochastic ordering, and stress–strength reliability. Rényi, Havrda and Charvat, and d-generalized entropies, which are measures of uncertainty, are also obtained. The model's parameters are estimated using a Bayesian estimation approach via symmetric and asymmetric loss functions. The Bayesian credible intervals are constructed based on the marginal posterior distribution. Monte Carlo simulation research is intended to test the accuracy of various estimators based on certain measures, in accordance with the complex forms of Bayesian estimators. Finally, we show that the new distribution is more appropriate than certain other competing models, according to their application for COVID-19 in Saudi Arabia and the United Kingdom. © 2023 by the authors.

Best selected forecasting models for COVID-19 pandemic

This study sought to identify the most accurate forecasting models for COVID-19-confirmed cases, deaths, and recovered patients in Pakistan. For COVID-19, time series data are available from 16 April to 15 August 2021 from the Ministry of National Health Services Regulation and Coordination's health advice portal. Descriptive as well as time series models, autoregressive integrated moving average, exponential smoothing models (Brown, Holt, and Winters), neural networks, and Error, Trend, Seasonal (ETS) models were applied. The analysis was carried out using the R coding language. The descriptive analysis shows that the average number of confirmed cases, COVID-19-related deaths, and recovered patients reported each day were 2,916, 69.43, and 2,772, respectively. The highest number of COVID-19 confirmed cases and fatalities per day, however, were recorded on April 17, 2021 and April 27, 2021, respectively. ETS (M, N, M), neural network, nonlinear autoregressive (NNAR) (3, 1, 2), and NNAR (8, 1, 4) forecasting models were found to be the best among all other competing models for the reported confirmed cases, deaths, and recovered patients, respectively. COVID-19-confirmed outbreaks, deaths, and recovered patients were predicted to rise on average by around 0.75, 5.08, and 19.11% daily. These statistical results will serve as a guide for disease management and control.