A Mathematical Modelling Approach to the Long-Term Global Impacts of COVID-19

This study investigates the global post-effects of COVID-19 through mathematical modeling, focusing on the long-term impacts on health systems, economies, and societal structures. We developed an SEI 1 I 2 DR model, represented by a system of differential equations, to analyze the dynamics of COVID-19. The model includes compartments for susceptible (S), exposed (E), asymptomatic infected (I 1 ), symptomatic infected (I 2 ), deceased population (D), and recovered (R) individuals. Our analysis determined both local and global asymptotic stability conditions for the disease-free and endemic equilibria. The disease-free equilibrium is both locally and asymptotically stable when R 0 <1 and unstable when R 0 >1. Sensitivity analysis revealed that parameters such as the contact rate between susceptible and infected individuals, and the progression rate from exposed to infected classes, significantly influence the spread of COVID-19, with positive sensitivity indices indicating increased transmission. Effective control measures aimed at reducing these parameters are crucial for disease mitigation. Conversely, parameters like the recovery rate of infected individuals have a negative sensitivity index, suggesting that increasing the recovery rate through effective treatment can reduce the prevalence of the disease. Numerical simulations and sensitivity analysis, performed using MATLAB, demonstrated that the number of susceptible individuals decreases over time, while exposed individuals initially rise and then decline to zero. The number of asymptomatic and symptomatic infections also increases rapidly before dropping to zero, which correlates with a decrease in the number of deaths due to a high recovery rate. The study emphasized the need for strengthening healthcare systems, enhancing emergency preparedness, and addressing health inequities. It also highlighted the importance of economic recovery plans, supporting low-income communities, and bridging digital divides. To prevent future outbreaks, it is essential to invest in disease surveillance, continue vaccine development, and foster global cooperation. These insights provide a foundation for strategic planning and decision-making, aiming to enhance global resilience and preparedness for future crises.