This study proposes a nonlinear mathematical model of virus transmission based on the SEIR model. In this study, the interaction between viruses and immune cells is investigated using phase-space analysis of a mathematical model. Specifically, it is focused on the dynamics and stability behavior of the mathematical model of a virus spread in a population and its interaction with human immune systems cells. The endemic equilibrium points are found and local stability analysis of all equilibria points of the related model is obtained. Further, the global stability analysis either, at disease-free equilibria, or in endemic equilibria is discussed by constructing the Lyapunov function which shows the validity of the concern model exists. Finally, a simulated solution is achieved and the relationship between viruses and immune cells is highlighted.

Perceptual and statistical evidence has underlined voice characteristics of individuals affected by genetic syndromes different from that of normophonic subjects. In this paper we propose a procedure for the systematic collection of such pathological voices and the development of AI-based automatic tools to support differential diagnosis. Guidelines are provided concerning most suitable recording devices, vocal tasks and acoustical parameters, in order to simplify, speed up and make the whole procedure homogenous and replicable. The proposed procedure was applied to a set of 56 subjects, affected by Costello syndrome (CS), Down syndrome (DS), Noonan syndrome (NS) and Smith-Magenis syndrome (SMS). The whole database has been divided into three groups, respectively called: paediatric subjects (PS, individuals < 12 years of age), female adults (FA) and male adults (MA) subjects. In line with literature results, the Kruskal-Wallis test and post-hoc analysis with Dunn-Bonferroni test highlighted several significant differences in acoustical features not only between healthy subjects and patients, but also across syndromes within PS, FA and MA groups. Machine learning provided for the PS group a k-nearest neighbour classifier with 75% accuracy, for the FA group a support vector machine (SVM) model with 84% accuracy and for the MA group a SVM model with 97% accuracy. These preliminary results suggest that the proposed procedure, based on acoustical analysis and AI, might be helpful for an effective non-invasive automatic characterization of genetic syndromes.