Exploring Symmetry in an Epidemiological Model: Numerical Analysis of Backward Bifurcation and Sensitivity Indices

In the face of the COVID-19 pandemic, understanding the dynamics of disease transmission is crucial for effective public health interventions. This study explores the concept of symmetry within compartmental models, employing compartmental analysis and numerical simulations to investigate the intricate interactions between compartments and their implications for disease spread. Our findings reveal the conditions under which the disease-free equilibrium is globally asymptotically stable while the endemic equilibrium exhibits local stability. Additionally, we investigate the phenomenon of backward bifurcation, shedding light on the critical role of quarantine measures in controlling outbreaks. By integrating the concept of symmetry into our model, we enhance our understanding of transmission dynamics and provide a robust framework for evaluating intervention strategies. The insights gained from this research are vital for policymakers and health authorities aiming to mitigate the impact of infectious diseases in the future.