Multiplicity of solutions of asymptotically linear Dirichlet problems associated to second order equations in R^{2n+1}

We present a result about multiplicity of solutions of asymptotically linear Dirichlet problems associated to second order equations in R^(2n+1), n \geq 1. Under an additional technical condition, the number of solutions obtained is given by the gap between the Morse indexes of the linearizations at zero and in nity. The additional condition is stable with respect to small perturbations of the vector eld. We show with a simple example that in some cases the size of the perturbation can be explicitly estimated

A note on stability criteria in the periodic Lotka–Volterra predator-prey model

We present a stability result for T-periodic solutions of the periodic predator–prey Lotka–Volterra model. In 2021, R. Ortega gave a stability criteria in terms of the L1 norm of the coefficients of a planar linear system associated to the model. Previously, in 1994, Z. Amine and R. Ortega proved another stability criteria formulated in terms of the L∞ norm. The present work gives a Lp criterion, building a bridge between the two previous results.Grant “Margarita Salas” funded by the Spanish Ministerio de Universidades with NextGenerationEU funds of the European UnionFCT projects UIDB/04621/2020 and UIDP/04621/2020 of CEMAT at FC-Universidade de Lisbo

Connected Branches of Initial Points for Asymptotic BVPs, With Application to Heteroclinic and Homoclinic Solutions

Abstract We consider the second order nonlinear ODE uʺ – f(t, u) = 0 and assume that f(·, υ0) ≡ 0; for some υ0 ∈ ℝ. We prove the existence of closed connected sets Γ ⊆ ℝ2 of initial points such that for each (α, β) ∈ Γ there exists a solution u(·) of the given differential equation, with (u(t0), uʹ(t0)) = (α, β) and (u(t), uʹ(t)) → (υ0, 0) as t → –∞ (or as t → +∞). These results are then applied to the search of heteroclinic and homoclinic solutions

Heterogeneity in disease risk induces falling vaccine protection with rising disease incidence

This paper is concerned with the analysis of phase 3 vaccine trials. In a randomized controlled trial, a representative sample of a population is given a vaccine and a matched sample is given a placebo. These individuals are followed for a stipulated length of time, while infection (or disease) occurrences are registered. Vaccine efficacy is then calculated to measure the reduction in disease rate (or risk) attributed to the vaccine. Seemingly very reasonable, this procedure often results in the most disparate estimates when conducted in different parts of the world. Here, we argue that this is due to cohort selection acting on the trial participants as follows. The more susceptible individuals are infected first, leaving behind a pool whose mean susceptibility decreases over time. As a result, infection rates decrease, and this effect is stronger in the control group, provided that the vaccine reduces susceptibility. Therefore, any direct measure of vaccine efficacy is expected to decrease as the trial progresses, and this happens faster in settings where the intensity of pathogen exposure is higher. We propose an analytical scheme that takes this phenomenon into account while estimating efficacy more consistently across settings. We provide analytical results concerning the dependence of vaccine efficacy on the intensity of pathogen exposure as well as on the mean and variance of the distribution of disease risk

Vector-borne disease outbreak control via instant releases

This paper is devoted to the study of optimal release strategies to control vector-borne diseases, such as dengue, Zika, chikungunya and malaria. Two techniques are considered: the sterile insect one (SIT), which consists in releasing sterilized males among wild vectors in order to perturb their reproduction, and the Wolbachia one (presently used mainly for mosquitoes), which consists in releasing vectors, that are infected with a bacterium limiting their vector capacity, in order to replace the wild population by one with reduced vector capacity. In each case, the time dynamics of the vector population is modeled by a system of ordinary differential equations in which the releases are represented by linear combinations of Dirac measures with positive coefficients determining their intensity. We introduce optimal control problems that we solve numerically using ad-hoc algorithms, based on writing first-order optimality conditions characterizing the best combination of Dirac measures. We then discuss the results obtained, focusing in particular on the complexity and efficiency of optimal controls and comparing the strategies obtained. Mathematical modeling can help testing a great number of scenarios that are potentially interesting in future interventions (even those that are orthogonal to the present strategies) but that would be hard, costly or even impossible to test in the field in present conditions

A missing dimension in measures of vaccination impacts

Immunological protection, acquired from either natural infection or vaccination, varies among hosts, reflecting underlying biological variation and affecting population-level protection. Owing to the nature of resistance mechanisms, distributions of susceptibility and protection entangle with pathogen dose in a way that can be decoupled by adequately representing the dose dimension. Any infectious processes must depend in some fashion on dose, and empirical evidence exists for an effect of exposure dose on the probability of transmission to mumps-vaccinated hosts [1], the case-fatality ratio of measles [2], and the probability of infection and, given infection, of symptoms in cholera [3]. Extreme distributions of vaccine protection have been termed leaky (partially protects all hosts) and all-or-nothing (totally protects a proportion of hosts) [4]. These distributions can be distinguished in vaccine field trials from the time dependence of infections [5]. Frailty mixing models have also been proposed to estimate the distribution of protection from time to event data [6], [7], although the results are not comparable across regions unless there is explicit control for baseline transmission [8]. Distributions of host susceptibility and acquired protection can be estimated from dose-response data generated under controlled experimental conditions [9]–[11] and natural settings [12], [13]. These distributions can guide research on mechanisms of protection, as well as enable model validity across the entire range of transmission intensities. We argue for a shift to a dose-dimension paradigm in infectious disease science and community health

A influência da prática deliberada na reparação de ruturas na aliança terapêutica e a sua auto-avaliação

Dissertação de Mestrado realizada sob a orientação do Professor Doutor Daniel Cunha Monteiro de Sousa, apresentada no Ispa – Instituto Universitário para obtenção de grau de Mestre na especialidade de Psicologia Clínica.A prática deliberada (PD) tem-se demonstrado uma aliada em diversas áreas para que os profissionais alcancem a expertise, no entanto, observa-se ainda uma lacuna na área da psicologia. Este estudo vem reforçar a necessidade de investigação que aprofunda a experiência e o uso da PD na formação de psicoterapeutas. Objetivos: Verificar o impacto da PD na capacidade de resposta na reparação de ruturas na aliança terapêutica e noutras competências. Pretende também observar como os terapeutas se autoavaliam nessas mesmas competências. Métodos: Realizou-se um estudo quantitativo onde um grupo de terapeutas em formação frequentou sessões semanais de PD durante 3 meses. Foram submetidas respostas a vídeos-estímulo na plataforma SkillSetter e respostas a um questionário auto avaliativo (FIS-SR) no Qualtrics. Resultados: Os participantes apresentaram uma pequena melhoria entre o primeiro e o último vídeo na dimensão reparação de ruturas na aliança (RRA) e noutras dimensões da FIS. Adicionalmente, observaram-se algumas diferenças na comparação entre os valores da FIS e da FIS-SR na dimensão RRA, mas coerência no valor médio. Conclusão: Os resultados obtidos neste estudo reforçam os benefícios da PD direcionada para os psicoterapeutas, como esta pode ser importante a combater a sobrevalorização que os terapeutas tendem a ter sobre as suas competências, e sugerem que perante novos e mais elevados desafios vêm também novas dificuldades. Observam-se vantagens e melhorias que se forem consideradas poderão impactar de forma ainda mais positiva a prática clínica e a obtenção de expertise nos psicoterapeutas.ABSTRACT: Deliberate practice (DP) has proven to be an ally in several areas for professionals to achieve expertise, however there is still a gap in the psychology area. This study reinforces the need for further investigation that deepens the experience and the use of DP in psychotherapists training. Objectives: Verify the impact of DP on the capacity of responsiveness in repairing ruptures in the therapeutic alliance and in other skills. It also aims to see how therapists evaluate themselves in those same skills. Methods: A quantitative study was conducted, where a group of therapist students attended weekly DP sessions for 3 months. Responses were submitted to stimulus videos on the SkillSetter platform and responses to a self-evaluative questionnaire (FIS-SR) on the Qualtrics platform. Results: Participants showed a slightly improvement between the first and last video in the ability to respond to the alliance rupture-repair dimension (RRA) and in other dimensions. Additionally, the were some differences when comparing the value of FIS and FIS-SR ratings in the RRA dimension but consistency in the average value. Conclusion: The results in this study reinforce the benefits of DP aimed at psychotherapists, how it can be relevant to work on the overvaluation that therapists tend to have regarding their skills and imply that with new and greater challenges also comes new difficulties. There are advantages and improvements that if considered, could have an even more positive impact on clinical practice and in the acquisition of expertise in psychotherapists