In this paper, the asymptotic behaviour of the numerical solution to the Volterra integral equations is studied. In particular, a technique based on an appropriate splitting of the kernel is introduced, which allows one to obtain vanishing asymptotic (transient) behaviour in the numerical solution, consistently with the properties of the analytical solution, without having to operate restrictions on the integration steplength

Despite the international guidelines on the containment of the coronavirus disease 2019 (COVID-19) pandemic, the European scientific community was not sufficiently prepared to coordinate scientific efforts. To improve preparedness for future pandemics, we have initiated a network of nine European-funded Cooperation in Science and Technology (COST) Actions that can help facilitate inter-, multi-, and trans-disciplinary communication and collaboration.

Background: Systems Medicine is a novel approach to medicine, i.e. an interdisciplinary field that considers the human body as a system, composed of multiple parts and of complex relationships at multiple levels, and further integrated into an environment. Exploring Systems Medicine implies understanding and combining concepts coming from diametral different fields, including medicine, biology, statistics, modelling and simulation, and data science. Such heterogeneity leads to semantic issues, which may slow down implementation and fruitful interaction between these highly diverse fields.

We consider a simple example of a partially dissipative hyperbolic system violating the Shizuta-Kawashima condition, ie such that some eigendirections do not exhibit dissipation at all. In the space-time resonances framework introduced by Germain, Masmoudi and Shatah, we prove that, when the source term has a Nonresonant Bilinear Form, as proposed by Pusateri and Shatah CPAM 2013, the formation of singularities is prevented, despite the lack of dissipation. This allows us to show that smooth solutions to this preliminary case-study model exist globally in time.

Drug research, therapy development, and other areas of pharmacology and medicine can benefit from simula- tions and optimization of mathematical models that contain a mathematical description of interactions between systems elements at the cellular, tissue, organ, body, and population level. This approach is the foundation of systems medicine and precision medicine. Here, simulated experiments are performed with computers (in silico) first, and they are then replicated through lab experiments (in vivo or in vitro) or clinical studies.