Aim
Contribution to the deconfinement with modelling and simulation tools to measure the choices impact of the public decision-makers

The aim of the project is to contribute to the gradual phasing out of total deconfinement, by proposing the implementation of modelling and simulation tools to measure the short and medium-term impact of the choices made by public decision-makers. In addition, the project aims to contribute to the development of digital tools for monitoring and pandemic alert on a territorial scale. The aim is to ensure the early detection of a resurgence or a new pandemic risk or to estimate or predict in the longer term the spread of the existing pandemic.

Short-term objective of the project
horizon of 2 months

=> Development of a model and implementation of a simulator based on available data.  The aim is to be able to assess the impact of the public authorities' deconfinement strategy on the evolution of the pandemic.  Our approach is based on multi-zone modelling to better take into account the heterogeneity of the territory (population density, employment areas, tourism, etc.) and external (international) and inter-zone mobility flows.

Longer-term objective

=> Introduction in our multi-zone model of a differentiation according to the age and gender of the populations, taking into account the studies showing a strong disparity of the pandemic dynamics according to these categories.

=> Study of an optimal surveillance system for pandemics
On the basis of the model thus developed, study of an optimal surveillance system for pandemics within the framework of an alert system based on detailed multi-zone modelling. We will work, on the one hand, on the optimization of the "instrumentation" (selection of populations to be screened, optimal location and frequency of screening, use of smartphone data ...) and, on the other hand, on the study of algorithms for detection / prediction of pandemic evolution on the national territory.
 

Methodology
A detailed multizone model

Most of the dynamic models [1,3] proposed today are based on an aggregation on a very macroscopic scale of susceptible, exposed, infected or immunized populations. On the contrary, we are working on a more detailed multizone model, integrating the mobility graph, which can be modulated in spatial resolution.

We have already started to work at the scale of the 18 regions, but our ambition is to develop a relevant model up to the scale of municipalities, including 101 departments or 332 districts. This detailed model will integrate mobility and social interactions, and take into account age and gender categories. This has never been done at the scale of a spatially distributed model to our knowledge. We will perform a sensitivity analysis to determine which parameters are influential on the outputs of interest (number of infected people at the peak of the pandemic, duration above a certain threshold, slope at the origin... or even the entire trajectory of the density of infected people). The proposed model will be enriched by a multi-agent approach allowing a more detailed analysis at the level of individual interactions, for example for a better knowledge of the transmission rate and therefore of the R0.  Observation and control approaches for large systems or partial differential equations will be used (optimal control, observers, analysis and observability optimization). We will also implement, on the basis of the proposed model, a statistical method to estimate the model parameters from the observations, by proposing a random observation model and calculating the maximum likelihood (see [2]).

Covid-19 pandemic simulator at the municipal level,
currently under development (source Seepia project)

Références

• [1] M. J. Keeling, and P. Rohani, “Modeling Infectious Diseases in Humans and Animals”, Princeton University Press, 2008.
• [2] Lionel Roques, Etienne Klein, Julien Papaïx et Samuel Soubeyrand, Modèle SIR mécanistico-statistique pour l'estimation du nombre d'infectés et du taux de mortalité par COVID-19, arXiv:2003.10720v2 [q-bio.PE] 25 Mar 2020.
• [3] Reza Sameni, Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus, https://arxiv.org/abs/2003.11371 25 Mar 2020.
• [4] Van Tri Nguyen, Didier Georges, Gildas Besançon, State and parameter estimation in 1-D hyperbolic PDEs based on an adjoint method. Automatica, Elsevier, 2016, 67, pp.185-191. <10.1016/j.automatica.2016.01.031>.
  
• [5] Mathias Dus, Francesco Ferrante, Christophe Prieur, « On L_infty Stabilization of Diagonal Semilinear Hyperbolic Systems by Saturated Boundary Control ». ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2020, 26 (23). ? hal-02384422 ?
  
• [6] Laurence Yeung, Lee. Murray, Patricia Martinerie, Emmanuel Witrant, Huanting Hu, et al.. Isotopic constraint on the twentieth-century increase in tropospheric ozone. Nature, Nature Publishing Group, 2019, 570 (7760), pp.224-227. ? 10.1038/s41586-019-1277-1 ?. ? hal-02179376 ?
  
• [7] Julius Bañgate, Carole Adam, Elise Beck, Julie Dugdale. Review of agent based modelling of social attachment in crisis situations. International Journal of Information Systems for Crisis Response and Management (IJISCRAM). IGI Global. Volume 11, Issue 1, Article 3. 2019.
  
• [8] Clémentine Prieur, L. Viry, E. Blayo and J.-M. Brankart (2019), A global sensitivity analysis approach for marine biogeochemical modeling. Ocean Modelling Volume 139, 101402.
  
• [9] M. Selva, F. Gruber, D. Sampaio, Ch. Guillon, L.-N. Pouchet , F. Rastello, Building a Polyhedral Representation from an Instrumented Excution : Making Dynamic Analyses of Non-Affine Programs Scalable, ACM Transaction on Architecture and Code Optimization, 2019, 16 (4), pp.1-26.