Stochastic dynamics on a Normally Hyperbolic Invariant Manifold arising in a simple model of viral genomes replication [ Back ]

15:30 to 16:30
UAB - Dept. Matemàtiques (C1/-128)
Josep Sardanyés
Centre de Recerca de Matemàtiques


We will discuss the concept of Normally Hyperbolic Invariant Manifolds (NHIMs) in a biological model of viral genomes amplification under different replication modes. NHIMs involve the presence of so-called quasi-neutral coexistence scenarios in which the asymptotic population states entirely depend on the initial conditions. This is due to the presence of invariant manifolds being neutrally stable, with a normal hyperbolic direction. NHIMs involve coexistence of competing species in the deterministic limit. However, under stochasticity, the trajectories diffuse on this NHIM until an absorbing or an asymptotic state is achieved. We will discuss recent theory on stochastic diffusion on one-dimensional NHIMs studied in biological models. Then, we will extend these developments to a dynamical system of viral RNAs under different replication modes. The theoretical diffusive approach,  in agreement with Gillespie simulations, will be discussed for this system. Finally, we will explain a novel mechanism for noise-induced bistability tied to NHIMs under stochasticity.
Joint work with Tomás Alarcón, Santiago F. Elena and Andreu Arderiu.