arXiv subjects

Diego Vicencio

Publications and source records attributed to Diego Vicencio.

3 recordsLinked to original sources

arXiv2020

Monotonicity properties arising in a simple model of Wolbachia invasion for wild mosquito populations

In this paper, we propose a simplified bidimensional Wolbachia infestation model in a population of Aedes aegypti mosquitoes, preserving the main features associated with the biology of this species that can be found in higher-dimensional models. Namely, our model represents the maternal transmission of the Wolbachia symbiont, expresses the reproductive phenotype of cytoplasmic incompatibility, accounts for different fecundities and mortalities of infected and wild insects, and exhibits the bistable nature leading to the so-called principle of competitive exclusion. Since Wolbachia-based biocontrol is now accepted as an ecologically friendly and potentially cost-effective method for prevention and control of dengue and other arboviral infections, it is essential to have reduced models with the main biological characteristics of Aedes aegypti in the presence of Wolbachia-carriers because such models help to simplify the mathematical analysis for determining appropriate biocontrol strategies. Using tools borrowed from monotone dynamical system theory, in the proposed model, we prove the existence of an invariant threshold manifold that allows us to provide practical recommendations for performing single and periodic releases of Wolbachia-carrying mosquitoes, seeking the eventual elimination of wild insects that are capable of transmitting infections to humans. We illustrate these findings with numerical simulations using parameter values corresponding to the wMelPop strain of Wolbachia that is considered the best virus blocker but induces fitness loss in its carriers.

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arXiv2020

Optimal control of diseases in prison populations through screening policies of new inmates

In this paper, we study an optimal control problem of a communicable disease in a prison population. In order to control the spread of the disease inside a prison, we consider an active case-finding strategy, consisting on screening a proportion of new inmates at the entry point, followed by a treatment depending on the results of this procedure. The control variable consists then in the coverage of the screening applied to new inmates. The disease dynamics is modeled by a SIS (susceptible-infected-susceptible) model, typically used to represent diseases that do not confer immunity after infection. We determine the optimal strategy that minimizes a combination between the cost of the screening/treatment at the entrance and the cost of maintaining infected individuals inside the prison, in a given time horizon. Using the Pontryagin Maximum Principle and Hamilton-Jacobi-Bellman equation, among other tools, we provide the complete synthesis of an optimal feedback control, consisting in a bang-bang strategy with at most two switching times and no singular arc trajectory, characterizing different profiles depending on model parameters.

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arXiv2020

Comparison Theorem for Viability Kernels via Conic Preorders

In natural resource management, decision-makers often aim at maintaining thestate of the system within a desirable set for all times.For instance, fisheries management procedures include keeping thespawning stock biomass over a critical threshold.Another example is given by the peak control of an epidemic outbreakthat encompasses maintaining thenumber of infected individuals below medical treatment capacities.In mathematical terms, one controls a dynamical system.Then, keeping the state of the system within a desirable set for all times is possible when the initial state belongs to the so-called viabilitykernel. We introduce the notion of conic quasimonotonicity reducibility.With this property, we provide a comparison theorem by inclusion between two viabilitykernels, corresponding to two control systems in the infinite horizon case. Wealso derive conditions for equality. We illustrate the method with a model for thebiocontrol of a vector-transmitted epidemic.

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