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Register a new userOptimal Control to Limit the Spread of COVID-19 in Italy
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Added by
Delfim F. M. Torres
Publication date
2021
fields
Biology
and research's language is
English
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We apply optimal control theory to a generalized SEIR-type model. The proposed system has three controls, representing social distancing, preventive means, and treatment measures to combat the spread of the COVID-19 pandemic. We analyze such optimal control problem with respect to real data transmission in Italy. Our results show the appropriateness of the model, in particular with respect to the number of quarantined/hospitalized (confirmed and infected) and recovered individuals. Considering the Pontryagin controls, we show how in a perfect world one could have drastically diminish the number of susceptible, exposed, infected, quarantined/hospitalized, and death individuals, by increasing the population of insusceptible/protected.
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The ongoing COVID-19 pandemic has created a global crisis of massive scale. Prior research indicates that human mobility is one of the key factors involved in viral spreading. Indeed, in a connected planet, rapid world-wide spread is enabled by long-distance air-, land- and sea-transportation among countries and continents, and subsequently fostered by commuting trips within densely populated cities. While early travel restrictions contribute to delayed disease spread, their utility is much reduced if the disease has a long incubation period or if there is asymptomatic transmission. Given the lack of vaccines, public health officials have mainly relied on non-pharmaceutical interventions, including social distancing measures, curfews, and stay-at-home orders. Here we study the impact of city organization on its susceptibility to disease spread, and amenability to interventions. Cities can be classified according to their mobility in a spectrum between compact-hierarchical and decentralized-sprawled. Our results show that even though hierarchical cities are more susceptible to the rapid spread of epidemics, their organization makes mobility restrictions quite effective. Conversely, sprawled cities are characterized by a much slower initial spread, but are less responsive to mobility restrictions. These findings hold globally across cities in diverse geographical locations and a broad range of sizes. Our empirical measurements are confirmed by a simulation of COVID-19 spread in urban areas through a compartmental model. These results suggest that investing resources on early monitoring and prompt ad-hoc interventions in more vulnerable cities may prove most helpful in containing and reducing the impact of present and future pandemics.
Several European countries have suspended the inoculation of the AstraZeneca vaccine out of suspicion of causing deep vein thrombosis. In this letter we report some Fermi estimates performed using a stochastic model aimed at making a risk-benefit analysis of the interruption of the delivery of the AstraZeneca vaccine in France and Italy. Our results clearly show that excess deaths due to the interruption of the vaccination campaign injections largely overrun those due to thrombosis even in worst case scenarios of frequency and gravity of the vaccine side effects.
During the current Covid-19 pandemic in Italy, official data are collected with medical swabs following a pure convenience criterion which, at least in an early phase, has privileged the exam of patients showing evident symptoms. However, there are evidences of a very high proportion of asymptomatic patients (e. g. Aguilar et al., 2020; Chugthai et al, 2020; Li, et al., 2020; Mizumoto et al., 2020a, 2020b and Yelin et al., 2020). In this situation, in order to estimate the real number of infected (and to estimate the lethality rate), it should be necessary to run a properly designed sample survey through which it would be possible to calculate the probability of inclusion and hence draw sound probabilistic inference. Some researchers proposed estimates of the total prevalence based on various approaches, including epidemiologic models, time series and the analysis of data collected in countries that faced the epidemic in earlier time (Brogi et al., 2020). In this paper, we propose to estimate the prevalence of Covid-19 in Italy by reweighting the available official data published by the Istituto Superiore di Sanit`a so as to obtain a more representative sample of the Italian population. Reweighting is a procedure commonly used to artificially modify the sample composition so as to obtain a distribution which is more similar to the population (Valliant et al., 2018). In this paper, we will use post-stratification of the official data, in order to derive the weights necessary for reweighting them using age and gender as post-stratification variables thus obtaining more reliable estimation of prevalence and lethality.
The spread of pandemics such as COVID-19 is strongly linked to human activities. The objective of this paper is to specify and examine early indicators of disease spread risk in cities during the initial stages of outbreak based on patterns of human activities obtained from digital trace data. In this study, the Venables distance (D_v), and the activity density (D_a) are used to quantify and evaluate human activities for 193 US counties, whose cumulative number of confirmed cases was greater than 100 as of March 31, 2020. Venables distance provides a measure of the agglomeration of the level of human activities based on the average distance of human activities across a city or a county (less distance could lead to a greater contact risk). Activity density provides a measure of level of overall activity level in a county or a city (more activity could lead to a greater risk). Accordingly, Pearson correlation analysis is used to examine the relationship between the two human activity indicators and the basic reproduction number in the following weeks. The results show statistically significant correlations between the indicators of human activities and the basic reproduction number in all counties, as well as a significant leader-follower relationship (time lag) between them. The results also show one to two weeks lag between the change in activity indicators and the decrease in the basic reproduction number. This result implies that the human activity indicators provide effective early indicators for the spread risk of the pandemic during the early stages of the outbreak. Hence, the results could be used by the authorities to proactively assess the risk of disease spread by monitoring the daily Venables distance and activity density in a proactive manner.
We present a data-driven optimal control approach which integrates the reported partial data with the epidemic dynamics for COVID-19. We use a basic Susceptible-Exposed-Infectious-Recovered (SEIR) model, the model parameters are time-varying and learned from the data. This approach serves to forecast the evolution of the outbreak over a relatively short time period and provide scheduled controls of the epidemic. We provide efficient numerical algorithms based on a generalized Pontryagin Maximum Principle associated with the optimal control theory. Numerical experiments demonstrate the effective performance of the proposed model and its numerical approximations.
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