arXiv subjects

Carlos Muñoz-Moncayo

Publications and source records attributed to Carlos Muñoz-Moncayo.

4 recordsLinked to original sources

arXiv2026

Compartmental epidemiological models with infection-driven immune escape

We propose and study a compartmental epidemiological model that incorporates both waning immunity and mutation-driven immune escape into a single-strain framework. The model, termed SIRCm, extends the SIRC (Susceptible-Infected-Recovered-Cross-immune) model, in which recovered individuals pass through an intermediate cross-immune class before returning to full susceptibility. In SIRCm, both the rate of immune waning and the rate of immune escape are amplified by a feedback function tied to the current level of infection. We study two formulations of this feedback, a transmission-driven model, in which mutation opportunities arise at the point of new infection, and a prevalence-driven model, in which they arise in proportion to the infected population alone. For both models and any feedback strength, we prove existence of an endemic equilibrium using persistence theory, and characterize its behavior analytically in the weak and strong-feedback limits, recovering the SIRC and SIS models, respectively, as limiting cases. Unlike the SIRC model, we show that the SIRCm endemic equilibrium is unstable in certain parameter regimes. This leads to novel behavior, even in the absence of seasonal forcing.

math.DS↗

arXiv2026

Adaptive, efficient, and scalable water wave modeling with dispersive hyperbolic systems

Accurate modeling of tsunamis (such as those generated by landslides) requires capturing both wave dispersion in the deep ocean and wave breaking near the shore. The shallow water equations are often preferred for working with tsunamis, but neglect dispersion and may be inaccurate in scenarios where dispersive effects are significant. In this work, we develop an approach that seeks to incorporate the best aspects of both hyperbolic and dispersive models by combining either of two hyperbolic reformulations of the Serre-Green-Naghdi equations away from the shore with the non-dispersive shallow water equations near the shore. The model is discretized and implemented within the GeoClaw software, and incorporates adaptive mesh refinement as well as shared-memory parallelism. We validate it through comparison with benchmarks and real tsunami data. The results and performance compare favorably with the existing dispersive water wave solvers, including a speedup of about 2x relative to GeoClaw's existing dispersive solver for a large-scale tsunami simulation.

physics.flu-dyn↗

arXiv2025

A Unified Framework for Sponge-Layer Relaxation Methods and Damping Operators for Conservation Laws: Application to the Piston Problem of Gas Dynamics

This work addresses the imposition of outflow boundary conditions for one-dimensional conservation laws. While a highly accurate numerical solution can be obtained in the interior of the domain, boundary discretization can lead to unphysical reflections. We investigate and implement some classes of relaxation methods and far-field operators to deal with this problem without significantly increasing the size of the computational domain. We formulate these methods within a framework that allows to reveal relationships among them, and to propose novel extensions. In particular, we introduce a simple and robust relaxation method with a matrix-valued weight function that selectively absorbs outgoing waves. As a challenging model problem, we consider the Lagrangian formulation of the Euler equations for a polytropic gas with inflow boundary conditions determined by an oscillating piston.

math.NA↗

arXiv2025

A Hyperbolic Approximation of the Nonlinear Schrödinger Equation

We study a first-order hyperbolic approximation of the nonlinear Schrödinger (NLS) equation. We show that the system is strictly hyperbolic and possesses a modified Hamiltonian structure, along with at least three conserved quantities that approximate those of NLS. We provide families of explicit standing-wave solutions to the hyperbolic system, which are shown to converge uniformly to ground-state solutions of NLS in the relaxation limit. The system is formally equivalent to NLS in the relaxation limit, and we develop asymptotic preserving discretizations that tend to a consistent discretization of NLS in that limit, while also conserving mass. Examples for both the focusing and defocusing regimes demonstrate that the numerical discretization provides an accurate approximation of the NLS solution.

math.AP↗