In this work we deal with global stability properties of classic SIS, SIR and SIRS epidemic models with constant recruitment rate, mass action incidence and variable population size. The usual approach to determine global stability of equilibria is the direct Lyapunov method which requires the construction of a function with specific properties. In this work we construct different Lyapunov func...

BACKGROUND Despite its widespread use in equine medicine, the clinical value of the systemic inflammatory response syndrome (SIRS) concept in horses remains unknown. OBJECTIVES To study the prognostic value of measures of SIRS in horses and identify the best model of severe SIRS to predict outcome. ANIMALS A total of 479 consecutive adult horse emergency admissions to a private primary refe...

In this paper, we prove a functional central limit theorem (FCLT) for stochastic epidemic model with varying infectivity and general infectious periods recently introduced in R. Forien et al. [Epidemic models infectivity, SIAM J. Appl. Math. 81 (2021), pp. 1893–1930]. The process (total force of infection at each time) is composed the independent random functions individual, which starts time i...

Stochastic SIRS models play a key role in formulating and analyzing the transmission of infectious diseases. These reflect environmental changes diseases their biological mechanisms. Therefore, it is very important to study uniqueness existence global positive solution investigate asymptotic properties model. In this article, we dynamics stochastic epidemic model with saturated incidence rate. ...

Abstract Containment of epidemic outbreaks entails great societal and economic costs. Cost-effective containment strategies rely on efficiently identifying infected individuals, making the best possible use available testing resources. Therefore, quickly optimal strategy is critical importance. Here, we demonstrate that machine learning can be used to identify which individuals are most benefic...

Traditional epidemic models consider that individual processes occur at constant rates; an infected has a probability per unit time of recovering from infection after contagion. This assumption indeed fails for almost all infectious diseases, in which the usually follows distribution more or less spread around mean value. We presented some years ago general treatment SIRS model both and immune ...

The ubiquity of oscillations in epidemics presents a long standing challenge for the formulation of epidemic models. Whether they are external and seasonally driven, or arise from the intrinsic dynamics is an open problem. It is known that fixed time delays destabilize the steady state solution of the standard SIRS model, giving rise to stable oscillations for certain parameters values. In this...