Importance of Interaction Structure and Stochasticity for Epidemic Spreading: A COVID-19 Case Study

Backenkoehler

Wolf

2021

Preprint

Self Cite

In the recent COVID-19 pandemic, mathematical modeling constitutes an important tool to evaluate the prospective effectiveness of non-pharmaceutical interventions (NPIs) and to guide policy-making. Most research is, however, centered around characterizing the epidemic based on point estimates like the average infectiousness or the average number of contacts. In this work, we use stochastic simulations to investigate the consequences of a population's heterogeneity regarding connectivity and individual viral load levels. Therefore, we translate a COVID-19 ODE model to a stochastic multi-agent system. We use contact networks to model complex interaction structures and a probabilistic infection rate to model individual viral load variation. We observe a large dependency of the dispersion and dynamical evolution on the population's heterogeneity that is not adequately captured by point estimates, for instance, used in ODE models. In particular, models that assume the same clinical and transmission parameters may lead to different conclusions, depending on different types of heterogeneity in the population. For instance, the existence of hubs in the contact network leads to an initial increase of dispersion and the effective reproduction number, but to a lower herd immunity threshold (HIT) compared to homogeneous populations or a population where the heterogeneity stems solely from individual infectivity variations.

Section: Related Workmentioning

confidence: 99%

Why ODE models for COVID-19 fail: Heterogeneity shapes epidemic dynamics

Backenkoehler

Wolf

2021

Preprint

Self Cite

“…We apply our method to an SEIR (susceptible-exposed-infected-removed) model. This is widely used to describe the spreading of an epidemic such as the current COVID-19 outbreak [23,20]. Temporal snapshots of the epidemic spread are mostly only available for a subset of the population and suffer from inaccuracies of diagnostic tests.…”

Section: Recursive Bayesian Estimationmentioning

confidence: 99%

Analysis of Markov Jump Processes under Terminal Constraints

Backenköhler

Bortolussi

Tools and Algorithms for the Construction and Analysis of Systems

et al. 2021

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Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely used class of population-structured Markov jump processes. The method is based on a state-space lumping scheme that aggregates states in a grid structure. The resulting approximate bridging distribution is used to iteratively refine relevant and truncate irrelevant parts of the state-space. This way, the algorithm learns a well-justified finite-state projection yielding guaranteed lower bounds for the system behavior under endpoint constraints. We demonstrate the method’s applicability to a wide range of problems such as Bayesian inference and the analysis of rare events.

“…We calibrate the only unknown parameter λ accordingly (the relationships from the previous section remain valid). We explain the relation to R 0 when taking C and I into account in the Appendix (available at [16]). Substituting β by μ c gives…”

Section: A Network-based Covid-19 Spreading Modelmentioning

confidence: 99%

Importance of Interaction Structure and Stochasticity for Epidemic Spreading: A COVID-19 Case Study

Backenköhler

Wolf

2020

Preprint

Self Cite

In the recent COVID-19 pandemic, computer simulations are used to predict the evolution of the virus propagation and to evaluate the prospective effectiveness of non-pharmaceutical interventions. As such, the corresponding mathematical models and their simulations are central tools to guide political decision-making. Typically, ODE-based models are considered, in which fractions of infected and healthy individuals change deterministically and continuously over time.In this work, we translate an ODE-based COVID-19 spreading model from literature to a stochastic multi-agent system and use a contact network to mimic complex interaction structures. We observe a large dependency of the epidemic's dynamics on the structure of the underlying contact graph, which is not adequately captured by existing ODEmodels. For instance, existence of super-spreaders leads to a higher infection peak but a lower death toll compared to interaction structures without super-spreaders. Overall, we observe that the interaction structure has a crucial impact on the spreading dynamics, which exceeds the effects of other parameters such as the basic reproduction number R0. We conclude that deterministic models fitted to COVID-19 outbreak data have limited predictive power or may even lead to wrong conclusions while stochastic models taking interaction structure into account offer different and probably more realistic epidemiological insights.