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

Abstract

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.

Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model

“…During the revision of this paper, we became aware of [14,16,17]. Superspreaders and superspreading events are known to play an essential role in the propagation of Covid-19 according to [1,3,19,20,27,38,39]. Incorporating these considerations in compartmental models will anyway require further studies.…”

Preventing COVID-19 outbreaks through surveillance testing in healthcare facilities: a modelling study

“…Indeed, we could see in our study that the impact of the parameter controlling the extent of heterogeneity in the contact structure was negligible. Therefore, only the variation of individual transmissibility needed to be incorporated into the model, but not necessarily an explicit contact structure as employed in many other studies [ 7 – 9 , 31 ] including commonly encountered models with contact structure dictated by a network. This can be attributed to the fact that on average, the first few transmissions rely on the more general epidemiological parameters such as the reproduction number rather than the contact structure.…”

“…Heterogeneity in the transmission structure has been found to play a key role in infection spread, e.g. by application of infection models on networks [ 31 ] or age-stratified contact matrices [ 32 ]. In order to implement a relevant heterogeneous transmission structure into our model, the four agent classes—patients, low-risk staff, average-risk staff and high-risk staff—were defined.…”

COVID-19 Spatial Diffusion: A Markovian Agent-Based Model

“…Moreover, the Italian government promoted an app for smartphones, namely Immuni [14], to collect anonymous information about contacts based on Bluetooth proximity, with some minor results, and there is a request for properly organizing the existing data about the pandemics and its treatment in the spirit of the OpenData initiative, to disclose information for community-based research efforts, including network-based modeling. SIR is a family of models that is widely explored and used in literature, and is the base for many variants, such as SIS, after Susceptible, Infected, and Susceptible, SEIR, that adds a Exposed stage, or, for example, the recent SIDARTHE [1] (Susceptible, Infected, Diagnosed, Ailing, Recognized, Threatened, Healed, and Extinct) and SECIHURD [15] (Susceptible, Exposed, Carrier, Infected, Hospitalized, in intensive care Unit, Dead, and Recovered) specifically developed for COVID-19. The model described in Reference [1] deals with data about Italy, uses a larger number of stages for the evolution of COVID-19 to provide a closer representation of the phenomenon, and is a case that represents how researchers evolved the basic idea into different custom variants, while the model described by Großmann et al [15] shows how an SIR-like model can be translated into a meanfield model for solution.…”

“…SIR is a family of models that is widely explored and used in literature, and is the base for many variants, such as SIS, after Susceptible, Infected, and Susceptible, SEIR, that adds a Exposed stage, or, for example, the recent SIDARTHE [1] (Susceptible, Infected, Diagnosed, Ailing, Recognized, Threatened, Healed, and Extinct) and SECIHURD [15] (Susceptible, Exposed, Carrier, Infected, Hospitalized, in intensive care Unit, Dead, and Recovered) specifically developed for COVID-19. The model described in Reference [1] deals with data about Italy, uses a larger number of stages for the evolution of COVID-19 to provide a closer representation of the phenomenon, and is a case that represents how researchers evolved the basic idea into different custom variants, while the model described by Großmann et al [15] shows how an SIR-like model can be translated into a meanfield model for solution. Another recent example of application of SIR models, using data from China, is provided by Chen et al [16], in which interested readers can find a good step-by-step description of the approach, that we found useful to get insights into this modeling technique, while Reference [8] provides a very good introduction to modeling of epidemic processes in complex networks in general.…”