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Background: The COVID-19 pandemic stressed public health systems worldwide due to emergence of several highly transmissible variants of concern. Diverse and complex intervention policies deployed over the last years have shown varied effectiveness in controlling the pandemic. However, a systematic analysis and modelling of the combined effects of different viral lineages and complex intervention policies remains a challenge due to the lack of suitable measures of pandemic inequality and nonlinear effects. Methods: Using large-scale agent-based modelling and a high-resolution computational simulation matching census-based demographics of Australia, we carried out a systematic comparative analysis of several COVID-19 pandemic scenarios. The scenarios covered two most recent Australian census years (2016 and 2021), three variants of concern (ancestral, Delta and Omicron), and five representative intervention policies. We introduced pandemic Lorenz curves measuring an unequal distribution of the pandemic severity across local areas. We also quantified pandemic biomodality, distinguishing between urban and regional waves, and measured bifurcations in the effectiveness of interventions. Results: We quantified nonlinear effects of population heterogeneity on the pandemic severity, highlighting that (i) the population growth amplifies pandemic peaks, (ii) the changes in population size amplify the peak incidence more than the changes in density, and (iii) the pandemic severity is distributed unequally across local areas. We also examined and delineated the effects of urbanisation on the incidence bimodality, distinguishing between urban and regional pandemic waves. Finally, we quantified and examined the impact of school closures, complemented by partial interventions, and identified the conditions when inclusion of school closures may decisively control the transmission. Conclusions: Public health response to long-lasting pandemics must be frequently reviewed and adapted to demographic changes. To control recurrent waves, mass-vaccination rollouts need to be complemented by partial NPIs. Healthcare and vaccination resources need to be prioritised towards the localities and regions with high population growth and/or high density. [ABSTRACT FROM AUTHOR]