Abstract
In this paper, we propose a mathematical framework that governs the evolution of epidemic dynamics, encompassing both intra-population dynamics and inter-population mobility within a meta-population network. By linearizing this dynamical system, we can identify the spatial starting point(s), namely the source(s) and the initiation time of the epidemic, which we refer to as the "Big Bang" of the epidemic. Furthermore, we introduce a novel concept of effective distance to track disease spread within the network. Our analysis reveals that the contagion geometry can be represented as a line with a universal slope, for any disease type (R0) or mobility network configuration. The mathematical derivations presented in this framework are corroborated by empirical data, including observations from the COVID-19 pandemic in Iran and the US and the H1N1 outbreak worldwide. Within this framework, to detect the Big Bang of an epidemic we require two types of data: (1) A snapshot of the active infected cases in each subpopulation during the linear phase. (2) A coarse-grained representation of inter-population mobility. Also even with access to only the first type of data, we can still demonstrate the universal contagion geometric pattern. Additionally, we can estimate errors and assess the precision of the estimations. This comprehensive approach enhances our understanding of when and where epidemics began and how they spread. It equips us with valuable insights for developing effective public health policies and mitigating the impact of infectious diseases on populations worldwide.