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

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

Publication date: Apr 04, 2024

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.

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Concepts Keywords
Efficient Finite-difference operator-splitting approach
Epidemic Personal protection
Mathematical Simulation
Pharmaceutical Spatial heterogeneity
Super-spreader events
Threshold dynamics

Semantics

Type Source Name
disease MESH COVID-19
disease VO population
disease MESH infection
disease VO efficient
drug DRUGBANK Coenzyme M
disease VO organization
drug DRUGBANK Aspartame
disease IDO pathogen
disease MESH infectious diseases
disease IDO history
disease MESH tuberculosis
pathway KEGG Tuberculosis
disease MESH measles
pathway KEGG Measles
disease MESH hepatitis
disease MESH AIDS
pathway REACTOME Infectious disease
disease IDO infectious disease
disease VO time
disease IDO intervention
disease MESH death
disease IDO susceptible population
disease IDO infected population
disease VO A2
disease VO effective
disease VO effectiveness
disease IDO infection incidence
drug DRUGBANK Carboxyamidotriazole
disease VO USA
disease VO vaccinated
disease MESH influenza
disease VO vaccination
disease VO vaccine
drug DRUGBANK Diamorphine

Original Article

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