Second meeting on mathematical modeling and control in epidemic spread

Laboratoire Jacques-Louis Lions, UPMC
May 23, 2016

        The aim of this meeting is to gather specialists in different fields of mathematics working on the mathematical modeling and control in epidemic spread.
        The meeting will be held in the Laboratoire Jacques-Louis Lions, on Monday May 23rd 2016, seminar room 15-16 309 (third floor) (Subway station: Jussieu, line 7 or 10, access).
        This meeting will be followed on May 24th by the workshop SIMBAD.

Invited speakers :
Matthieu Alfaro, Université de Montpellier, France
Anton Camacho, London School of Hygiene and Tropical Medicine, UK
Gael Raoul, CMAP, Ecole Polytechnique, France
David Salthouse, CNRS, Ecole Normale Supérieure Paris, France
Panagiotis Souganidis, Department of Mathematics, The University of Chicago, USA
Max Souza, Universidade Federal Fluminense, Rio de Janeiro, Brasil

Program :
  • 9:30 - 9:40   Welcome
  • 9:40 - 10:20   Max Souza
  • 10:20 - 10:45   Coffee Break
  • 10:45 - 11:25   Anton Camacho
  • 11:30 - 12:10   David Salthouse
  • 14:00 - 14:40   Gael Raoul
  • 14:45 - 15:25   Matthieu Alfaro
  • 15:30 - 16:00   Coffee Break
  • 16:00 - 16:40   Panagiotis Souganidis

Titles and abstracts :

Matthieu Alfaro: Pulsating fronts for a reaction diffusion system as a model in evolutionary epidemiology

Abstract: We discuss a Fisher-KPP system as a model in evolutionary epidemiology, where two types of pathogens compete in a heterogeneous environment while mutations can occur. The main result is the construction of pulsating fronts, the mathematical difficulty being that no comparison principe is available. This is a joint work with Q. Griette (Univ. Montpellier).

Anton Camacho: Explaining the past, predicting the future: two contributions from the mathematical modelling of Ebola outbreaks.

Abstract: In the first part of this talk, I will revisit data from the first known Ebola outbreak, which occurred in 1976 in Yambuku, DRC. By fitting mechanistic models to time series stratified by disease onset, outcome and source of infection, it becomes possible to estimate several epidemiological quantities that have previously proved challenging to measure, including the contribution of hospital and community infection to transmission.

Moving on to the recent Ebola virus disease outbreak in West Africa, I will present how we developed real-time modelling and forecasting tools for monitoring the evolution of the epidemic and informing the design of appropriate interventions. Due to limited data available in real-time, it was challenging to explain the dynamics of Ebola transmission as a mechanistic interplay between different factors. To tackle this issue, we used a stochastic SEIR model with a phenomenological approach for the transmission rate, which was modelled as a Brownian motion. I will close with a retrospective assessment of our forecasts in term of reliability, sharpness and bias.

Gael Raoul: Virulence evolution at the front line of an epidemics.

Abstract: We consider a pathogen population where two types are present: a wild type, and a more virulent type. Once the epidemics is set, the wild type is prevalent, but we will show that during an epidemics, the virulent type can drive the propagation of the disease. The first part of this talk will be devoted to the existence and qualitative properties of travelling waves for a PDE model, and in a second part, we will investigate (by the mean of numerical simulations and non-rigorous asymptotics) the impact of stochasticity.

David Salthouse: French Polynesian dengue epidemics : The coupling of phylogeny and mathematical models.

Abstract: As more and more virus sequences become available, phylogenetics is increasingly used to study infection history (who infected whom) through the reconstruction of phylogenetic trees. If enough mutations accumulate at the time scale of the population dynamics then the structure of the phylogenetic tree may be modified by the past dynamics. The field of phylodynamics is concerned with recovering information on the tree-shaping dynamics through statistical analysis. Luckily for epidemiologists, viral genetics have such high mutation rates that some information on the dynamics of viral epidemics can be retrieved through its phylogeny. Starting with coalescence theory [1], new phylodynamic methods [2,3,4] have been developed to estimate the parameters of increasingly complex stochastic non-linear dynamical models. Here we present the results of our study of the dengue epidemics in French Polynesia. Characterised by the absence of co-circulating dengue serotypes, these epidemics rapidly propagate between the different peninsular islands. The surveillance program was conducted by the Institute Louis Malardé who recorded the historic incidence and collected more than 500 genetic sequences of dengue strains emerging in french polynesia since 1982. Using methods derived from [2,4], an estimation of epidemiological parameters is obtained via bayesian inference coupling simultaneously genetic sequence and historic incidence data.

[1] Kingman J.F.C., 1982, "the coalescent", stochastic processes and their applications.
[2] Volz E.M., 2012, "complex population dynamics and the coalescent under neutrality", genetics.
[3] Stadler T., Bonhoeffer S., 2013, "uncovering epidemiological dynamics in heterogeneous host populations using phylogenetic methods." phil. trans. r. soc. b
[4] Rasmussen D. A., Volz E. M. and Koelle K., 2014, "phylodynamic inference for structured epidemiological models." plos comp. biol.

Panagiotis Souganidis: Front propagation: homogeneous, periodic and random media

Max Souza: Vector borne diseases on an urban environment

We consider a metapopulation model for an arboviral disease dynamics within a urban environment. The underlying dynamics is a coupled SIR (human)/SI (mosquito) system; notification districts are taken for patches. We focus on the role of human movement in sustaining the epidemics. It turns out that considering different aspects of urban districts leads to very heterogeneous networks, which might lead to very distinctive dynamics. In a worst case scenario, one might have local basic reproduction numbers all less than unity, but with the network basic reproduction number ($R_0$) larger than one. In particular, we can obtain a correction to the uniform R0 (aggregating the data as a single region). The correction factor is given by the principal singular value of an interaction matrix. We also completely analyse the model with respect to global stability. This is joint work with Abderrahman Iggidr, Jair Koiller, Maria Lúcia Penna, Gauthier Sallet and Moacyr Silva.

Organizers :
Luis Almeida
Benoit Perthame
Nicolas Vauchelet

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