Infectious modelling to the rescue

As mentioned last fall, the first part of this project mainly consisted on identifying the availability of primary sources: the necrology registers of the Archivio di Stato in Venice. Therefore, we asked to a collaborator based in Venice to have a look at the archive. The presence of 205 necrology registers dating from 1537 to 1805 was confirmed. Here is a small extract from these registers, taken from the thesis of Mr Carlo Salmistraro, written in Italian and entitled: Il sistema sanitario a venezia nel cinquecento: analisi del Necrologio dei provveditori alla sanità 1568 more Veneto e considerazioni su alcune patologie epidemiche riscontrate.

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Basically, the registers contain for each death:

  • The date and place of the registration
  • The name of the deceased
  • The name of the deceased’s father (in case of homonym, also the grandfather’s name)
  • In case of women, the husband’s name and the civil status (married or widow)
  • The age
  • The description of the death cause
  • The place of death and eventually the transportation
  • The name of the doctor examining the body and validating death
  • The burial place

Although this kind of data is very interesting, it appears that these documents are not considered as a priority for digitization as part of the Venice Time Machine project, and thus these sources would not be available for the timespan of this project.

With a lack of primary sources, we now have to re-orientate the project.

We still think that a dynamic representation of the evolution of the Plague epidemics in Venice, using a map of Venice as background, would be useful. Therefore, we will now try to simulate this evolution using several models related to the propagation of epidemics, adapted to the spatial context of Venice and to the plague itself as this disease has characteristics (prevalence and high fatality) that could lead to a rather simple model.

In a first approach, the urban modelling of Venice will be defined as a small-world network, where nodes, i.e. parishes, are connected by edges:

venice_network

We would use the Watz-Strogatz procedure to rewire nodes knowing their spatial localization and the prevailing disposition for infections (islands are more prone to harvest the infection burden). All this information will be contained in a connectivity matrix of size #nodes x #nodes. Edges will be given a certain coefficient proportional to the potential of the infection route. Different centrality measures (see Centrality Measures in Spatial Networks of Urban streets, Peolo Cruciti et al.) and other simpler characteristics such as distance between parishes, their connections, size and estimated population will allow us to weight the edges in a proper way. On this network, we are planning to apply a spatio-temporal decaying coefficient providing us with the probability of someone being infected at time t+1 knowing that a previous infection occurred at a certain location at time t. Differential equations of models provided in the literature will be able to provide us with a dynamic environment representing the live evolution of the infection.

 

For now, we plan to run this simulation under MATLAB and show the results in a web-based visualization tool. The code for the simulation would be available so that everyone can run it or tweak it. Ideally our visualization tool will be able to take in the results of the simulation easily. We found a few scripts in the D3.js online library that could serve this purpose.

Since the necrology registers will be available under a digital form at some point in the future, it would be interesting to be able to incorporate the actual data in our visualization tool in some way, so that one could confront or complete the epidemics model. Another approach would be to build a tool that could help comparing the results of our simulation with the actual data. This feature could be relevant as it would allow to verify if a simple model is capable of estimating the propagation of the plague in a more complex population, but also help adjusting the model.