An Analysis of the Italian Lockdown in Retrospective Using Particle Swarm Optimization in Machine Learning Applied to an Epidemiological Model

A critical analysis of the open data provided by the Italian Civil Protection Centre during phase 1 of Covid-19 epidemic—the so-called Italian lockdown—is herein proposed in relation to four of the most affected Italian regions, namely Lombardy, Reggio Emilia, Valle d’Aosta, and Veneto. A possible bias in the data induced by the extent in the use of medical swabs is found in relation to Valle d’Aosta and Veneto. Observed data are then interpreted using a Susceptible-Infectious-Recovered (SIR) epidemiological model enhanced with asymptomatic (infected and recovered) compartments, including lockdown effects through time-dependent model parameters. The initial number of susceptible individuals for each region is also considered as a parameter to be identified. The issue of parameters identification is herein addressed by a robust machine learning approach based on particle swarm optimization. Model predictions provide relevant information for policymakers in terms of the effect of lockdown measures in the different regions. The number of susceptible individuals involved in the epidemic, important for a safe release of lockdown during the next phases, is predicted to be around 10% of the population for Lombardy, 16% for Reggio Emilia, 18% for Veneto, and 40% for Valle d’Aosta

Modelling complex systems in the context of the COVID-19 pandemics

Systems biology is an interdisciplinary approach investigating complex biological systems at different levels by combining experimental and modelling approaches to understand underlying mechanisms of health and disease. Complex systems including biological systems are affected by a plethora of interactions and dynamic processes often with the aim to ensure robustness to emer- gent system properties. The need for interdisciplinary approaches became very evident in the recent COVID-19 pandemic spreading around the globe since the end of 2019. This pandemic came with a bundle of urgent epidemiological open questions including the infection and transmis- sion mechanisms of the virus, its pathogenicity and the relation to clinical symptoms. During the pandemic, mathematical modelling became an essential tool to integrate biological and healthcare data into mechanistic frameworks for projections of future developments and the assessment of different mitigation strategies. In this regard, systems biology with its interdisciplinary approach was a widely applied framework to support society in the COVID-19 crisis. In my thesis, I applied different mathematical modelling approaches as a tool to identify underlying mechanisms of the complex dynamics of the COVID-19 pandemic with a specific focus on the situation in Luxembourg. For this purpose, I analysed the COVID-19 pandemic at its different phases and from various perspectives by investigating mitigation strategies, consequences in the healthcare and economical system, and pandemic preparedness in terms of early-warning signals for re-emergence of new COVID-19 outbreaks by extended and adapted epidemiological Susceptible-Exposed-Infectious-Recovered (SEIR) models

Studying the course of Covid-19 by a recursive delay approach

In an earlier paper we proposed a recursive model for epidemics; in the present paper we generalize this model to include the asymptomatic or unrecorded symptomatic people, which we call {\em dark people} (dark sector). We call this the SEPAR$_d$-model. A delay differential equation version of the model is added; it allows a better comparison to other models. We carry this out by a comparison with the classical SIR model and indicate why we believe that the SEPAR$_d$ model may work better for Covid-19 than other approaches. In the second part of the paper we explain how to deal with the data provided by the JHU, in particular we explain how to derive central model parameters from the data. Other parameters, like the size of the dark sector, are less accessible and have to be estimated more roughly, at best by results of representative serological studies which are accessible, however, only for a few countries. We start our country studies with Switzerland where such data are available. Then we apply the model to a collection of other countries, three European ones (Germany, France, Sweden), the three most stricken countries from three other continents (USA, Brazil, India). Finally we show that even the aggregated world data can be well represented by our approach. At the end of the paper we discuss the use of the model. Perhaps the most striking application is that it allows a quantitative analysis of the influence of the time until people are sent to quarantine or hospital. This suggests that imposing means to shorten this time is a powerful tool to flatten the curvesComment: 66 pages, 67 figures Changes in v2:Correction of formulas pp. 5, 6, 7, 20, general case of dark model, p_c \neq p_d included, tautological model for eta_7 adde