[01063] Challenges in biomathematical modeling and control
Session Time & Room : 1C (Aug.21, 13:20-15:00) @A206
Type : Proposal of Minisymposium
Abstract : In biomathematics, theoretical and data modeling showed to be big challenges, both at the macroscopic and microscopic levels. Complex networks are proved to be a rather powerful theoretical tools in epidemics, neuroscience, protein functions, ecology and cancer. When considering space-time analysis of big data, we have at our disposal a variety of methods, wavelets, Bayesian, Topological Data Analysis, Cross-entropy, Fuzzy logic, among others. The choice of a method is linked to the kind of questions we want to target.
The emergency experienced with pandemics showed also the importance of being able to make predictions and to develop methods of control.
Organizer(s) : Stefanella Boatto, Bernard Cazelles, Ludovick Gagnon
[05271] Analyzing infectious disease dynamics: the challenge of non-stationarity
Author(s) :
Bernard Cazelles (IBENS CNRS INSERM)
Abstract : The spread of disease through human populations is complex. The characteristics of disease propagation evolve with time, as a result of a multitude of environmental and anthropic factors, including social distancing. This non-stationarity is a key factor in the complexity of disease propagation.
In the absence of appropriate external data sources, to correctly describe disease propagation, I propose a flexible methodology, based on stochastic models for disease dynamics, and on Brownian processes for parameter evolution. Using such a diffusion process has the advantage of not requiring a specific mathematical function for the parameter dynamics. Coupled with Bayesian inference using particle MCMC, this approach allows us to reconstruct both the time evolution of some key parameters of an epidemiological dynamic and its incidence.
I will demonstrate the efficiency of this methodology on toy epidemiological models where the parameters and the observation process are known, and also on more complex epidemics, such as flu, dengue and COVID-19.
[05319] Models of mosquito population control strategies for fighting against arboviruse
Author(s) :
Michel Duprez (Inria)
Luis Almeida (Inria)
Yves Dumont (CIRAD - University of Pretoria)
yannick Privat (Université de Strasbourg)
Nicolas Vauchelet (Université Paris 13)
Abstract : In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of the vector, Aedes mosquitoes in this case. Among possible actions, a technique consist in releasing sterile mosquitoes to reduce the size of the population (Sterile Insect Technique). This talk is devoted to studying the issue of optimizing the dissemination protocol for each of these strategies, in order to get as close as possible to these objectives. Starting from a mathematical model describing the dynamic of a mosquitoes population, we will study the control problem and introduce the cost function standing for sterile insect technique. In a second step, we will consider a model with several patchs modeling the spatial repartition of the population. Then, we will establish some properties of these two optimal control problems. Finally, we will illustrate our results with numerical simulations.
