arXiv subjects

Carlos Doebeli

Publications and source records attributed to Carlos Doebeli.

3 recordsLinked to original sources

arXiv2026

Partial health status observability and time horizon uncertainty in mean-field game epidemiological models

We introduce Mean-Field Game (MFG) epidemiological models, in which immunity either wanes with time in a fully observable way or disappears instantaneously with no direct observation (making a previously recovered individual fully susceptible again without realizing it). Both interpretations create computational challenges for rational noninfected individuals deciding on their contact rates based on their personal current immunity state and the changing epidemiological situation. Both require solving a forward-backward MFG system that includes PDEs (an advection-reaction equation for the immunity-structured population and a Hamilton-Jacobi-Bellman equation for the corresponding value function). We show how this can be done efficiently by solving a two-point boundary value problem for a system of approximating ODEs. We also show how the same approach can be extended to handle an initial uncertainty in the planning horizon.

math.OC↗

arXiv2024

A polynomial approximation scheme for nonlinear model reduction by moment matching

We propose a procedure for the numerical approximation of invariance equations arising in the moment matching technique associated with reduced-order modeling of high-dimensional dynamical systems. The Galerkin residual method is employed to find an approximate solution to the invariance equation using a Newton iteration on the coefficients of a monomial basis expansion of the solution. These solutions to the invariance equations can then be used to construct reduced-order models. We assess the ability of the method to solve the invariance PDE system as well as to achieve moment matching and recover the steady-state behaviour of nonlinear systems with state dimension of order 1000 driven by linear and nonlinear signal generators.

math.OC↗

arXiv2022

On the evolutionary emergence of predation

In models for the evolution of predation from initially purely competitive species interactions, the propensity of predation is most often assumed to be a direct consequence of the relative morphological and physiological traits of interacting species. Here we explore a model in which predation ability is an independently evolving phenotypic feature, so that even when the relative morphological or physiological traits allow for predation, predation only occurs if the predation ability of individuals has independently evolved to high enough values. In addition to delineating the conditions for the evolutionary emergence of predation, the model reproduces stationary and non-stationary multilevel food webs with the top predators not necessarily having size superiority.

q-bio.PE↗