Epidemic spreading and control strategies in spatial modular network

The use of networks in spatial and temporal computational models for outbreak spread in epidemiology: A systematic review

OBJECTIVES

To examine recent literature in order to present a comprehensive overview of the current trends as regards the computational models used to represent the propagation of an infectious outbreak in a population, paying particular attention to those that represent network-based transmission.

METHODS

a systematic review was conducted following the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) guidelines. Papers published in English between 2010 and September 2021 were sought in the ACM Digital Library, IEEE Xplore, PubMed and Scopus databases.

RESULTS

Upon considering their titles and abstracts, 832 papers were obtained, of which 192 were selected for a full content-body check. Of these, 112 studies were eventually deemed suitable for quantitative and qualitative analysis. Emphasis was placed on the spatial and temporal scales studied, the use of networks or graphs, and the granularity of the data used to evaluate the models. The models principally used to represent the spreading of outbreaks have been stochastic (55.36%), while the type of networks most frequently used are relationship networks (32.14%). The most common spatial dimension used is a region (19.64%) and the most used unit of time is a day (28.57%). Synthetic data as opposed to an external source were used in 51.79% of the papers. With regard to the granularity of the data sources, aggregated data such as censuses or transportation surveys are the most common.

CONCLUSION

We identified a growing interest in the use of networks to represent disease transmission. We detected that research is focused on only certain combinations of the computational model, type of network (in both the expressive and the structural sense) and spatial scale, while the search for other interesting combinations has been left for the future.

Front propagation in a spatial system of weakly interacting networks

We consider the spread of epidemic in a spatial metapopulation system consisting of weakly interacting patches. Each local patch is represented by a network with a certain node degree distribution and individuals can migrate between neighboring patches. Stochastic particle simulations of the SIR model show that after a short transient, the spatial spread of epidemic has a form of a propagating front. A theoretical analysis shows that the speed of front propagation depends on the effective diffusion coefficient and on the local proliferation rate similarly to fronts described by the Fisher-Kolmogorov equation. To determine the speed of front propagation, first, the early-time dynamics in a local patch is computed analytically by employing degree based approximation for the case of a constant disease duration. The resulting delay differential equation is solved for early times to obtain the local growth exponent. Next, the reaction diffusion equation is derived from the effective master equation and the effective diffusion coefficient and the overall proliferation rate are determined. Finally, the fourth order derivative in the reaction diffusion equation is taken into account to obtain the discrete correction to the front propagation speed. The analytical results are in a good agreement with the results of stochastic particle simulations.