Stability Criteria for SIS Epidemiological Models under Switching Policies

We study the spread of disease in an SIS model. The model considered is a time-varying, switched model, in which the parameters of the SIS model are subject to abrupt change. We show that the joint spectral radius can be used as a threshold parameter for this model in the spirit of the basic reproduction number for time-invariant models. We also present conditions for persistence and the existence of periodic orbits for the switched model and results for a stochastic switched model

A study on the effects of containment policies and vaccination on the spread of SARS-CoV-2

This paper presents a method to predict the spread of the SARS-CoV-2 in a population with a known age-structure, and then, to quantify the effects of various containment policies, including those policies that affect each age-group differently. The model itself is a compartmental model in which each compartment is divided into a number of age-groups. The parameters of the model are estimated using an optimisation scheme and some known results from the theory of monotone systems such that the model output agrees with some collected data on the spread of SARS-CoV-2. To highlight the strengths of this framework, a few case studies are presented in which different populations are subjected to different containment strategies. They include cases in which the containment policies switch between scenarios with different levels of severity. Then a case study on herd immunity due to vaccination is presented. And then it is shown how we can use this framework to optimally distribute a limited number of vaccine units in a given population to maximise their impact and reduce the total number of infectious individuals

Global and Local Weighted Homogeneity for Time-Delay Systems

International audienceThe notion of weighted homogeneity is extended to the time-delay systems. It is shown that the stability/instability of homogeneous functional systems on a sphere implies the global stability/instability of the system. The notion of local homogeneity is introduced, a relation between stability/instability of the locally approximating dynamics and the original time-delay system is established using Lyapunov-Razumikhin approach. An implication between homogeneity and input-to-state stability is investigated. Examples of application of the proposed theory are given