arXiv subjects

Maria Soledad Aronna

Publications and source records attributed to Maria Soledad Aronna.

9 recordsLinked to original sources

arXiv2026

A structured model of vector-borne disease with within-host viral load and antibody dynamics

We present an epidemiological model for vector-borne diseases that includes within-host viral load and antibody dynamics using structured transport equations. By incorporating the internal dynamics into the infected and recovered host compartments, the formulation introduces nonlinearities and nonlocalities. We establish analytical properties, including well-posedness and mass conservation, and characterize its characteristic curves. Furthermore, we derive a simplified Uniform Host Response (UHR) model featuring delay-type terms. For both the full and UHR frameworks, the basic reproduction number is determined and shown to serve as a threshold for the existence of an endemic equilibrium, and is related to the linear stability of the disease-free state. Finally, numerical experiments, parameterized specifically for Dengue fever, demonstrate how within-host mechanisms influence population-level epidemiological outcomes.

math.AP↗

arXiv2025

Bang-Bang Optimal Control of Vaccination in Metapopulation Epidemics with Linear Cost Structures

This paper investigates optimal vaccination strategies in a metapopulation epidemic model. We consider a linear cost to better capture operational considerations, such as the total number of vaccines or hospitalizations, in contrast to the standard quadratic cost assumption on the control. The model incorporates state and mixed control-state constraints, and we derive necessary optimality conditions based on Pontryagin's Maximum Principle. We use Pontryagin's result to rule out the possibility of the occurrence of singular arcs and to provide a full characterization of the optimal control.

math.OC↗

arXiv2025

Singular Arcs on Average Optimal Control-Affine Problems

In this paper we address optimal control problems in which the system parameters follow a probability distribution, and the optimization is based on average performance. These problems, known as Riemann-Stieltjes optimal control or optimal ensemble control problems, involve uncertainties that influence system dynamics. Focusing on control-affine systems, we apply the Pontryagin Maximum Principle to characterize singular arcs in a feedback form. To demonstrate the practical relevance of our approach, we apply it to the sterile insect technique, a biological pest control method. Numerical simulations confirm the effectiveness of our framework in addressing control problems under uncertainty.

math.OC↗

arXiv2020

On nonlinear pest/vector control via the Sterile Insect Technique: impact of residual fertility

We consider a minimalist model for the Sterile Insect Technique (SIT), assuming that residual fertility can occur in the sterile male population.Taking into account that we are able to get regular measurements from the biological system along the control duration, such as the size of the wild insect population, we study different control strategies that involve either continuous or periodic impulsive releases. We show that a combination of open-loop control with constant large releases and closed-loop nonlinear control, i.e. when releases are adjusted according to the wild population size estimates, leads to the best strategy in terms both of number of releases and total quantity of sterile males to be released.Last but not least, we show that SIT can be successful only if the residual fertility is less than a threshold value that depends on the wild population biological parameters. However, even for small values, the residual fertility induces the use of such large releases that SIT alone is not always reasonable from a practical point of view and thus requires to be combined with other control tools. We provide applications against a mosquito species, \textit{Aedes albopictus}, and a fruit fly, \textit{Bactrocera dorsalis}, and discuss the possibility of using SIT when residual fertility, among the sterile males, can occur.

q-bio.PE↗

arXiv2018

Interval observer for uncertain time-varying SIR-SI epidemiological model of vector-borne disease

The issue of state estimation is considered for an SIR-SI epidemiological model describing a vector-borne disease such as dengue fever, subject to seasonal variations. Assuming continuous measurement of the incidence rate (that is the number of new infectives in the host population per unit time), a class of interval observers with estimate-dependent gain is constructed, and asymptotic error bounds are provided. The synthesis method is based on the search for a common linear Lyapunov function for monotone systems that represent the evolution of the estimation errors.

math.OC↗

arXiv2013

A shooting algorithm for problems with singular arcs

In this article we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method is used to compute a zero of the shooting function. This shooting algorithm is locally quadratically convergent if the derivative of the shooting function is one-to-one at the solution. The main result of this paper is to show that the latter holds whenever a sufficient condition for weak optimality is satisfied. We note that this condition is very close to a second order necessary condition. For the case when the shooting system can be reduced to one having the same number of unknowns and equations (square system) we prove that the mentioned sufficient condition guarantees the stability of the optimal solution under small perturbations and the invertibility of the Jacobian matrix of the shooting function associated to the perturbed problem. We present numerical tests that validate our method.

math.OC↗

arXiv2013

Convergence of the shooting algorithm for singular optimal control problems

In this article we propose a shooting algorithm for optimal control problems governed by systems that are affine in one part of the control variable. Finitely many equality constraints on the initial and final state are considered. We recall a second order sufficient condition for weak optimality, and show that it guarantees the local quadratic convergence of the algorithm. We show an example and solve it numerically.

math.OC↗

arXiv2012

Necessary conditions involving Lie brackets for impulsive optimal control problems; the commutative case

In this article we study control problems with systems that are governed by ordinary differential equations whose vector fields depend linearly in the time derivatives of some components of the control. The remaining components are considered as classical controls. This kind of system is called `impulsive system'. We assume that the vector fields multiplying the derivatives of each component of the control are commutative. We derive new necessary conditions in terms of the adjoint state and the Lie brackets of the data functions.

math.OC↗

arXiv2011

Quadratic order conditions for bang-singular extremals

This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we derive a second order sufficient condition for the scalar control case.

math.OC↗