Prediction of Covid-19 spreading and optimal coordination of counter-measures: From microscopic to macroscopic models to Pareto fronts

Abstract

The Covid-19 disease has caused a world-wide pandemic with more than 60 million positive cases and more than 1.4 million deaths by the end of November 2020. As long as effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, self-isolation and quarantine as well as far-reaching shutdowns of economic activity and public life are the only available strategies to prevent the virus from spreading. These interventions must meet conflicting requirements where some objectives, like the minimization of disease-related deaths or the impact on health systems, demand for stronger counter-measures, while others, such as social and economic costs, call for weaker counter-measures. Therefore, finding the optimal compromise of counter-measures requires the solution of a multi-objective optimization problem that is based on accurate prediction of future infection spreading for all combinations of counter-measures under consideration. We present a strategy for construction and solution of such a multi-objective optimization problem with real-world applicability. The strategy is based on a micro-model allowing for accurate prediction via a realistic combination of person-centric data-driven human mobility and behavior, stochastic infection models and disease progression models including micro-level inclusion of governmental intervention strategies. For this micro-model, a surrogate macro-model is constructed and validated that is much less computationally expensive and can therefore be used in the core of a numerical solver for the multi-objective optimization problem. The resulting set of optimal compromises between counter-measures (Pareto front) is discussed and its meaning for policy decisions is outlined.

The role of super-spreaders in modeling of SARS-CoV-2

“…The paper ( Wulkow et al, 2021 ) start with a detailed AB-model focusing on mobility patterns linked to Google data, however without taking variable infectivity into account. They conclude numerically that the output of such an advanced model, when applied to the city of Berlin, is well approximated by an 11-compartment ODE model (extended SEIR).…”

Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading

“…where the first two terms on the right-hand side refer to the change caused by the exchange between subpopulations (given by the operator L), while the other two lines are describing the change through status adoptions inside the subpopulations (referring to operator G). 4 Using the definitions of the functions f (k) ij given in Theorems 2 and 3, the interaction propensities agree with the standard law of mass-action from the chemical context [20]. This is due to the fact that we assume the agents to interact independently of each other (and of the overall system state) -which we do by choosing the ABM adoption rate functions according to Equations ( 1) and (2).…”

“…For example, for a diffusive process in a potential energy landscape, the core sets are given by the vicinities around the energy's local minima (i.e., the valleys or wells of the landscape), while the transition regions around the energy's local maxima are not explicitly assigned to any core set. The advantage of considering a core set approach is a reduced approximation error in the estimated transition rates compared to 4 In the second line of (20), we need the rate to go from…”

“…Recently, epidemiological models have received lots of attention due to the COVID-19 pandemics. State of the art models for analyzing the epidemics spreading and doing forecasts include agent-based models (ABMs) [1][2][3][4], metapopulation models [5][6][7] and deterministic models based on ordinary differential equations (ODE) [8][9][10][11][12][13][14]. While ABMs have a spatial resolution on a microscale, capturing the spatial movement and interactions of each individual agent, metapopulation models distinguish between subpopulations as groups of agents which are homogeneously mixed.…”