ABSTRACT
An epidemic multi-group model formed by interconnected SEIR-like structures is formulated and used for data fitting to gain insight into the COVID-19 dynamics and into the role of non-pharmaceutical control actions implemented to limit the infection spread since its outbreak in Italy. The single submodels provide a rather accurate description of the COVID-19 evolution in each subpopulation by an extended SEIR model including the class of asymptomatic infectives, which is recognized as a determinant for disease diffusion. The multi-group structure is specifically designed to investigate the effects of the inter-regional mobility restored at the end of the first strong lockdown in Italy (June 3, 2020). In its time-invariant version, the model is shown to enjoy some analytical stability properties which provide significant insights on the efficacy of the implemented control measurements. In order to highlight the impact of human mobility on the disease evolution in Italy between the first and second wave onset, the model is applied to fit real epidemiological data of three geographical macro-areas in the period March-October 2020, including the mass departure for summer holidays. The simulation results are in good agreement with the data, so that the model can represent a useful tool for predicting the effects of the combination of containment measures in triggering future pandemic scenarios. Particularly, the simulation shows that, although the unrestricted mobility alone appears to be insufficient to trigger the second wave, the human transfers were crucial to make uniform the spatial distribution of the infection throughout the country and, combined with the restart of the production, trade, and education activities, determined a time advance of the contagion increase since September 2020.
ABSTRACT
This paper addresses the problem of describing the spread of COVID-19 by a mathematical model introducing all the possible control actions as prevention (informative campaign, use of masks, social distancing, vaccination) and medication. The model adopted is similar to SEIQR, with the infected patients split into groups of asymptomatic subjects and isolated ones. This distinction is particularly important in the current pandemic, due to the fundamental the role of asymptomatic subjects in the virus diffusion. The influence of the control actions is considered in analysing the model, from the calculus of the equilibrium points to the determination of the reproduction number. This choice is motivated by the fact that the available organised data have been collected since from the end of February 2020, and almost simultaneously containment measures, increasing in typology and effectiveness, have been applied. The characteristics of COVID-19, not fully understood yet, suggest an asymmetric diffusion among countries and among categories of subjects. Referring to the Italian situation, the containment measures, as applied by the population, have been identified, showing their relation with the government’s decisions;this allows the study of possible scenarios, comparing the impact of different possible choices.
ABSTRACT
The paper presents a new mathematical model for the SARS-CoV-2 virus propagation, designed to include all the possible actions to prevent the spread and to help in the healing of infected people. After a discussion on the equilibrium and stability properties of the model, the effects of each different control actions on the evolution of the epidemic spread are analysed, through numerical evaluations for a more intuitive and immediate presentation, showing the consequences on the classes of the population.