arXiv subjects

Marius Bargo

Publications and source records attributed to Marius Bargo.

3 recordsLinked to original sources

arXiv2025

Global stabilization and emergence tracking via aquatic control in an age-structured mosquito model

This paper presents an age-structured, non-autonomous logistic model describing the aquatic and adult stages of the dynamics of malaria-vector mosquitoes. We propose a biological control strategy targeting the aquatic compartment and implement a tracking control for its emergence. A feedback control law guarantees stabilization of the emergent population density, specifically the global asymptotic stability of the logistic model. Additionally, a feedforward controller combined with feedback is introduced to steer the emergent density toward a time-varying reference trajectory. The analytical findings are corroborated and illustrated by numerical simulations.

math.AP↗

arXiv2025

Stabilization by Harvesting in Age-Structured Trophic Networks

We propose and analyze a nonlinear age-structured multi-species model that serves as a unifying framework for ecological and biotechnological systems in complex environments (microbial communities, bioreactors, and others). The formulation incorporates nonlocal intra- and interspecific interactions modulated by environmental covariates. Under general assumptions on mortality, reproduction rates, and interaction kernels, we establish existence, uniqueness, and positivity of solutions. We illustrate the model's practical relevance along two lines. First, multi-species examples, notably a non-transitive (cyclic) competition model, for which we show that, under the model assumptions, a control applied to a single species can achieve global stabilization of the system. Second, the population dynamics of malaria-vector mosquitoes, for which we develop two control strategies (biological and genetic). In the biological-control scenario, we prove global asymptotic stability of the aquatic compartment by constructing an explicit Lyapunov function. Numerical simulations validate the theoretical results and compare the effectiveness of the proposed strategies in reducing vector density and malaria transmission.

math.AP↗

arXiv2024

Birth control and turnpike property of Lotka-McKendrick models with diffusion

In this paper, we study the turnpike property in age structured population dynamics with birth control. These models describe the temporal evolution of one or more populations, incorporating age dependence and spatial structure. To this end, we first establish the null controllability of the system: we prove that for any T > A and any initial datum in L2(Omega x (0,A)), the population can be driven to zero using control functions that are spatially localized in time but act only at age a = 0. We then show that although this control is initially applied only at birth, it can be reformulated as a distributed control, and we demonstrate that the resulting control operator is admissible in the state space. Thus, to prove the turnpike property we combine our null controllability results with Phillips' theorem on exponential stability to design a suitable dichotomy transformation based on solutions of the algebraic Riccati and Lyapunov equations. Finally, we present numerical examples that substantiate our analytical findings.

math.OC↗