A rigorous theoretical and numerical analysis of a nonlinear reaction-diffusion epidemic model pertaining dynamics of COVID-19.

The spatial movement of the human population from one region to another and the existence of super-spreaders are the main factors that enhanced the disease incidence. Super-spreaders refer to the individuals having transmitting ability to multiple pathogens. In this article, an epidemic model with spatial and temporal effects is formulated to analyze the impact of some preventing measures of COVID-19. The model is developed using six nonlinear partial differential equations. The infectious individuals are sub-divided into symptomatic, asymptomatic and super-spreader classes. In this study, we focused on the rigorous qualitative analysis of the reaction-diffusion model. The fundamental mathematical properties of the proposed COVID-19 epidemic model such as boundedness, positivity, and invariant region of the problem solution are derived, which ensure the validity of the proposed model. The model equilibria and its stability analysis for both local and global cases have been presented. The normalized sensitivity analysis of the model is carried out in order to observe the crucial factors in the transmission of infection. Furthermore, an efficient numerical scheme is applied to solve the proposed model and detailed simulation are performed. Based on the graphical observation, diffusion in the context of confined public gatherings is observed to significantly inhibit the spread of infection when compared to the absence of diffusion. This is especially important in scenarios where super-spreaders may play a major role in transmission. The impact of some non-pharmaceutical interventions are illustrated graphically with and without diffusion. We believe that the present investigation will be beneficial in understanding the complex dynamics and control of COVID-19 under various non-pharmaceutical interventions.

Advancing COVID-19 stochastic modeling: a comprehensive examination integrating vaccination classes through higher-order spectral scheme analysis.

This research article presents a comprehensive analysis aimed at enhancing the stochastic modeling of COVID-19 dynamics by incorporating vaccination classes through a higher-order spectral scheme. The ongoing COVID-19 pandemic has underscored the critical need for accurate and adaptable modeling techniques to inform public health interventions. In this study, we introduce a novel approach that integrates various vaccination classes into a stochastic model to provide a more nuanced understanding of disease transmission dynamics. We employ a higher-order spectral scheme to capture complex interactions between different population groups, vaccination statuses, and disease parameters. Our analysis not only enhances the predictive accuracy of COVID-19 modeling but also facilitates the exploration of various vaccination strategies and their impact on disease control. The findings of this study hold significant implications for optimizing vaccination campaigns and guiding policy decisions in the ongoing battle against the COVID-19 pandemic.