The SEIR Covid-19 model described by fractional-order difference equations: analysis and application with real data in Brazil

Several efforts have been recently devoted to the studies on epidemic mathematical models based on fractional-order operators, by virtue of their capability to take into account memory effects and nonlocal features. The aim of this paper is to make a contribution to the topic by introducing a novel Covid-19 model described by non-integer-order difference equations. By conducting a stability analysis, the paper shows that the conceived system has two fixed points at most, i.e. a disease-free fixed point and an endemic fixed point. In particular, a theorem is proved, which assures the global stability of the disease-free fixed point, indicating that the pandemic will disappear when a simple condition on the system parameters is satisfied. Finally, simulation results are carried out with the aim to highlight the capability of the conceived approach.

A New Incommensurate Fractional-Order COVID 19: Modelling and Dynamical Analysis

Nowadays, a lot of research papers are concentrating on the diffusion dynamics of infectious diseases, especially the most recent one: COVID-19. The primary goal of this work is to explore the stability analysis of a new version of the (Formula presented.) model formulated with incommensurate fractional-order derivatives. In particular, several existence and uniqueness results of the solution of the proposed model are derived by means of the Picard–Lindelöf method. Several stability analysis results related to the disease-free equilibrium of the model are reported in light of computing the so-called basic reproduction number, as well as in view of utilising a certain Lyapunov function. In conclusion, various numerical simulations are performed to confirm the theoretical findings. © 2023 by the authors.

ELEVATED RESTING HEART RATE AS INDEPENDENT IN-HOSPITAL PROGNOSTIC MARKER IN COVID-19

Objective: SARS-CoV-2 infection could be complicated by serious autonomic imbalance caused directly by the virus or through secondary release of inflammatory cytokines. Some studies suggested that elevated resting heart rate (HR) and resting tachycardia, being markers of an increased adrenergic cardiac drive, are associated with poor prognosis in COVID-19 syndrome. Design and method: We performed a retrospective analysis in an inpatient cohort of 389 subjects diagnosed with SARS-CoV-2 infection to investigate the prognostic relevance of HR in predicting the maximum care intensity needed during hospitalization according to the following four severity outcome classes: I) no need for oxygen support/ need for low flow oxygen therapy;II) need for high flow oxygen therapy/continuous positive airway pressure;III) transfer to the Intensive Care Unit;IV) death. HR assessments were recorded on admission and during the first 3 and 7 days of hospitalization. Results: For each class increase in maximum care intensity we observed a corresponding significant increase in HR, considering both data collected on admission (average HR value: 90.1 ± 17 beats/minute, p-value trend = 0.0397), and during the first 3 days (p-value trend < 0.0006) or 7 days (p-value trend < 0.0001) of hospitalization. The significant trend was maintained after adjustment for age, sex, comorbidities and fever and in the subpopulation of patients (n = 118) not receiving drugs potentially active on HR both before and during hospitalization. Kaplan- Meier curves for survival based on HR displayed a significant decreased survival in patients with higher HR. Conclusions: The assessment of HR during hospitalization provides information on the clinical outcome of patients affected by SARS-CoV-2 infection independently of other confounders. HR as an in-hospital prognostic marker can be obtained both through a first assessment at the admission or mean values over the course of hospitalization with an increase of its accuracy by a 7-days longitudinal evaluation. Further studies might elucidate the association between SARS-CoV-2 infection with multiple autonomic abnormalities.

An inflammatory profile correlates with decreased frequency of cytotoxic cells in coronavirus disease 2019. (COVID special issue #2.)

Increased production of inflammatory cytokines and myeloid-derived suppressor cells occurs in patients with coronavirus disease 2019. These inversely correlated with perforin-expressing natural killer (NK) and CD3⁺ T cells. We observed a lower number of perforin-expressing NK cells in intensive care unit (ICU) patients compared with non-ICU patients, suggesting an impairment of the immune cytotoxic arm as a pathogenic mechanism.