Magdalena Djordjevic1*, Bojana Ilic1, Stefan Stojku1, Igor Salom1, and Marko Đorđević2
1Institute of Physics Belgrade, National Institute of the Republic of Serbia, Serbia
2Faculty of Biology, University of Belgrade, Serbia
magda [at] ipb.ac.rs
Abstract
Understanding the impact of social distancing measures on epidemic outbreaks is crucial, yet computational studies have predominantly focused on interventions like vaccination and quarantine. We present a realistic, analytically solvable framework that explicitly incorporates the influence of social distancing measures on COVID-19 dynamics [1]. Our extended SEIR model (SPEIRD) derives closed-form expressions for epidemiological observables, such as detected cases and fatalities, revealing simple quantitative relationships with model variables. These analytical solutions offer valuable insights into the cause-effect connections underlying outbreak dynamics, often obscured in numerical approaches. Our findings hold general applicability beyond COVID-19, providing particular relevance to emerging pandemics where effective pharmaceutical treatments are limited. We report distinct growth signatures in confirmed case counts, spanning exponential, superlinear, and sublinear regimes [2]. Through the synergy of analytical and numerical analyses, our framework leverages these signatures, akin to approaches in physics, to identify common dynamical features. This enables effective analytical derivations, insights into qualitative disease progression changes, and inference of key infection parameters. By combining empirical COVID-19 growth patterns with analytical and numerical analyses, our framework enhances the fundamental understanding of infection progression under stringent control measures applicable to various infectious diseases. This bridging of theory and observation promises to advance knowledge and inform effective strategies for managing future outbreaks.
Keywords: SEIR model, Analytical solutions, Infection progression, Population Dynamics, Epidemics peak, Infection tipping points
Acknowledgement: This work is supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia.
