Danesi, Davide (2020) A SIR-based approach for describing the time evolution of Covid-19 pandemic. [Magistrali biennali]
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In this thesis, we developed a framework to analyze and better understand the dynamics of the Covid-19 spread, mainly in terms of estimating the effective reproduction number as a time-dependent quantity. We considered and tried to highlight some problems that are usually ignored. For example, we modelled the inefficiencies in the testing system and the delay in spotting and reporting infected people. We also tried to address the challenge of finding a way to compare the number of new cases registered in different days, that is a difficult task because every day a different number of tests is analyzed. Solving this problem is essential to understand the real state of an ongoing epidemic. For each of these issues, we proposed a possible approach. We reported some useful insight we discovered, as the possibility of double-checking the estimates of the reproduction number in periods of exponential growth presented in section 4.3 or how visualizing the time series of new cases in a semi-logarithmic scale is often better to be able to understand changes in the trends of the epidemic. In 3.1,3. we made an estimate of the distribution of the time between the onset of the symptoms and the registration of a case for the Italian scenario. In literature, we have not found any better estimate of this quantity. In 3.2, we presented a method to simulate the evolution of an epidemic, a stochastic process describing the relationships between our variables of interest. Such a tool has been essential to test and build up our fitter on some data for which we knew the parameters that generated them. Also, we used it to understand how much different two epidemics characterized by the same parameters can be, and consequently to estimate the statistical uncertainties on the parameters caused by this aspect. In 3.3 we turned this stochastic process into a system of recursive equations, describing the average scenario related to a set of variables. Our method to estimate the parameters of the epidemic is finding values for the parameters for which the profiles obtained through this system of recursive equations are similar to the real ones. In chapter 4, we described this method. We introduced an error function, to calculate the similarity between an observed and an estimated profile, and a minimization algorithm. We used a genetic algorithm, differential evolution, to minimize the mean squared error between the two time series. We also developed an algorithm to estimate the uncertainties on these estimated variables, and we presented it in 4.4. Finally, in chapter 5 and 7, we applied the algorithms developed in the previous chapters to model the epidemic in the Italian regions and in a few foreign states.
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