Through joint analytical and numerical analysis we developed a novel framework, which in distinction to the compartmental models in epidemiology, accounts for the social distancing measures analytically. Guided by the solution of transformed form of Bessel differential equation, we were able to generate/obtain the nonlinear dynamics of infection progression data (i.e., confirmed case counts, active cases and fatalities), reproducing globally observed COVID'?'�'?'19 growth signatures of confirmed cases, i.e., its three nonlinear dynamical regimes (exponential, superlinear and sublinear).
An approach familiar to theoretical physics is applied, where the characteristics of the regimes and related scaling laws are utilized as a powerful tool to determine regions where analytical derivations are most effective for i) setting rigorous constraints on parameter quantifying the effect of social distancing; ii) reproducing the nearly constant value of the scaling exponent in the superlinear regime of confirmed counts; iii) explaining the changes in the effective reproduction number from outburst to extinguishing of the infection in this regime; iv) obtaining the dependence of time duration of the same regime on the strength of social distancing. Moreover, this tool is successfully applied for inferring key infection parameters (such as case fatality rate, infected fatality rate and attack rate), necessary to estimate the epidemic risks.
Our approach demonstrates the shift of paradigm in quantitative epidemiology from state-of-the-art numerical simulations toward simpler, but analytically tractable models, which are able to explain qualitatively and quantitatively common nonlinear dynamical features of a system, provide an understanding of infection progression under strong control measures, and tightly constrain the parameter inference.
Keywords:
nonlinearity, COVID-19, systems biology, epidemiology, compartmental model, social distancing measures, disease progression parameters