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Post COVID-19 conditions (PCC) present with a wide range of symptoms. Headache is one of the most frequently reported neurological symptoms by patients with PCC. We aimed to assess the prevalence of headache in patients with PCC who attended the Post-COVID LMU outpatient department at LMU University Hospital in Munich. We hypothesized that headaches occur more frequently in patients with PCC than in the control group. Patients answered a questionnaire containing sociodemographic characteristics, their current symptoms, and prior psychiatric and somatic diagnoses, the WHO Quality of Life assessment (WHOQOL-BREF), 9-item Patient Health Questionnaire (PHQ-9), and the Fatigue Severity Scale (FSS). 188 PCC patients were included in this study and compared to a control group of patients with a history of COVID-19 or a different infectious disease - but no consecutive post-infectious condition (n c =27). 115 (61%) of our PCC patients were female. The median age was 41 years. 60 (32%, p = 0.001) had a pre-existing psychiatric diagnosis. PCC was associated with worse outcomes in all four domains of the WHOQOL-BREF (p < 0.001), high levels of fatigue (FSS; p < 0.001), and a higher likeliness for symptoms of depression (PHQ-9; p < 0.001). We were able to confirm that psychiatric disorders are more frequently associated with headaches in PCC patients. Headache should be assessed and treated in the context of PCC not only by neurologists but by multi-professional teams and regarding all PCC symptoms., (© 2024. The Author(s).)

In the study of biological populations, the Allee effect detects a critical density below which the population is severely endangered and at risk of extinction. This effect supersedes the classical logistic model, in which low densities are favorable due to lack of competition, and includes situations related to deficit of genetic pools, inbreeding depression, mate limitations, unavailability of collaborative strategies due to lack of conspecifics, etc. The goal of this paper is to provide a detailed mathematical analysis of the Allee effect. After recalling the ordinary differential equation related to the Allee effect, we will consider the situation of a diffusive population. The dispersal of this population is quite general and can include the classical Brownian motion, as well as a Lévy flight pattern, and also a "mixed" situation in which some individuals perform classical random walks and others adopt Lévy flights (which is also a case observed in nature). We study the existence and nonexistence of stationary solutions, which are an indication of the survival chance of a population at the equilibrium. We also analyze the associated evolution problem, in view of monotonicity in time of the total population, energy consideration, and long-time asymptotics. Furthermore, we also consider the case of an "inverse" Allee effect, in which low density populations may access additional benefits., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Background: Innate lymphoid cells (ILCs) are key organizers of tissue immune responses and regulate tissue development, repair, and pathology. Persistent clinical sequelae beyond 12 weeks following acute COVID-19 disease, named post-COVID syndrome (PCS), are increasingly recognized in convalescent individuals. ILCs have been associated with the severity of COVID-19 symptoms but their role in the development of PCS remains poorly defined., Methods and Results: Here, we used multiparametric immune phenotyping, finding expanded circulating ILC precursors (ILCPs) and concurrent decreased group 2 innate lymphoid cells (ILC2s) in PCS patients compared to well-matched convalescent control groups at > 3 months after infection or healthy controls. Patients with PCS showed elevated expression of chemokines and cytokines associated with trafficking of immune cells (CCL19/MIP-3b, FLT3-ligand), endothelial inflammation and repair (CXCL1, EGF, RANTES, IL-1RA, PDGF-AA)., Conclusion: These results define immunological parameters associated with PCS and might help find biomarkers and disease-relevant therapeutic strategies., (© 2024. The Author(s).)

Cognitive symptoms (CS) belong to the most common manifestations of the Post COVID-19 (PC) condition. We sought to objectify CS in PC patients using routine diagnostic assessments: neurocognitive testing (NCT) and brain imaging (BI). Further, we investigated possible associations of CS with patient reported outcomes (PROs), and risk factors for developing CS. Clinical data and PROs of 315 PC patients were assessed at a mean of 6 months after SARS-CoV-2 infection. 231 (73.3%) patients reported any sort of CS. Among them, 78 underwent NCT and 55 received BI. In NCT, the cognitive domains most affected were the working memory, attention, and concentration. Nonetheless, pathological thresholds were exceeded only in few cases. Neurocognitive performance did not differ significantly between patients complaining of severe (n = 26) versus non-severe (n = 52) CS. BI findings were abnormal in 8 (14.5%) cases with CS but were most likely not related to PC. Patients reporting high severity of CS scored worse in the PHQ-9, FSS, WHOQOL-BREF, were more likely to report impaired sleep, and had a higher prevalence of psychiatric diagnoses. Overall, NCT could confirm mild impairment in some but not all PC patients with CS, while BI studies were abnormal in only few cases. CS severity did not affect NCT results, but severe CS were associated with symptoms of depression (PHQ-9), fatigue (FSS), reduced quality of life (WHOQOL-BREF) and higher prevalence of psychiatric illnesses. These findings support the importance of NCT, BI, and neuro-psychological assessment in the work-up of PC patients reporting CS. TRIAL REGISTRATION: Trial registration number and date of registration: DRKS00030974, 22 Dec 2022, retrospectively registered., (© 2024. The Author(s).)

Patient-reported outcome measures (PROMs) such as the Numeric Pain Rating Scale (NPRS) or Likert scales addressing various domains of health are important tools to assess disease severity in Post COVID-19 (PC) patients. By design, they are subjective in nature and prone to bias. Our findings reveal substantial differences in the perception of disease severity between patients (PAT), their attending internists (INT) and psychiatrists/psychologists (PSY). Patients rated almost all aspects of their health worse than INT or PSY. Most of the differences were statistically highly significant. The presence of fatigue and mood disorders correlated negatively with health perception. The physical health section of the WHO Quality of Life Assessment (WHOQoL-BREF) and Karnofsky index correlated positively with overall and mental health ratings by PAT and INT. Health ratings by neither PAT, PSY nor INT were associated with the number of abnormal findings in diagnostic procedures. This study highlights how strongly perceptions of disease severity diverge between PC patients and attending medical staff. Imprecise communication, different experiences regarding health and disease, and confounding psychological factors may explain these observations. Discrepancies in disease perception threaten patient-physician relationships and pose strong confounders in clinical studies. Established scores (e.g., WHOQoL-BREF, Karnofsky index) may represent an approach to overcome these discrepancies. Physicians and psychologists noting harsh differences between a patient's and their own perception of the patient's health should apply screening tools for mood disorders (i.e., PHQ-9, WHOQoL-BREF), psychosomatic symptom burden (SSD-12, FCV-19) and consider further psychological evaluation. An interdisciplinary approach to PC patients remains imperative. Trial Registration Number & Date of Registration: DRKS00030974, 22 Dec 2022, retrospectively registered., (© 2023. The Author(s).)

We consider a forager diffusing via a fractional heat equation and we introduce several efficiency functionals whose optimality is discussed in relation to the Lévy exponent of the evolution equation. Several biological scenarios, such as a target close to the forager, a sparse environment, a target located away from the forager and two targets are specifically taken into account. The optimal strategies of each of these configurations are here analyzed explicitly also with the aid of some special functions of classical flavor and the results are confronted with the existing paradigms of the Lévy foraging hypothesis. Interestingly, one discovers bifurcation phenomena in which a sudden switch occurs between an optimal (but somehow unreliable) Lévy foraging pattern of inverse square law type and a less ideal (but somehow more secure) classical Brownian motion strategy. Additionally, optimal foraging strategies can be detected in the vicinity of the Brownian one even in cases in which the Brownian one is pessimizing an efficiency functional., (© 2022. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of "smoothing" the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.

We study the viability of a nonlocal dispersal strategy in a reaction-diffusion system with a fractional Laplacian operator. We show that there are circumstances-namely, a precise condition on the distribution of the resource-under which the introduction of a new nonlocal dispersal behavior is favored with respect to the local dispersal behavior of the resident population. In particular, we consider the linearization of a biological system that models the interaction of two biological species, one with local and one with nonlocal dispersal, that are competing for the same resource. We give a simple, concrete example of resources for which the equilibrium with only the local population becomes linearly unstable. In a sense, this example shows that nonlocal strategies can invade an environment in which purely local strategies are dominant at the beginning, provided that the resource is sufficiently sparse. Indeed, the example considered presents a high variance of the distribution of the dispersal, thus suggesting that the shortage of resources and their unbalanced supply may be some of the basic environmental factors that favor nonlocal strategies.