key: cord-256843-05m50voc
authors: Rovetta, Alessandro; Bhagavathula, Akshaya Srikanth
title: Modelling the epidemiological trend and behavior of COVID-19 in Italy
date: 2020-03-23
journal: nan
DOI: 10.1101/2020.03.19.20038968
sha: 
doc_id: 256843
cord_uid: 05m50voc

As of March 16, 2020, over 185,000 across the world, Italy became the red hotspot for the COVID-19 pandemic after China. With over 35,000 cases and 2900 deaths reported in the month of March in Italy, it is necessary to stimulate epidemic trend to understand the behavior of COVID-19 in Italy. By S.E.I.R. simulation, we estimated the most representative epidemic parameters occurred from March 1 to 14, 2020, thus being able to evaluate the consistency of the containment rules and identify possible Sars-Cov-2 local mutations. Our estimations are based on some assumptions and limitations exited.

The current surge of COVID-19 pandemic is devastating globally, with over 200,000 cases and more than 8600 deaths reported [1] . In Europe, COVID-19 cases are most dramatically started to increase from the first week of March 2020. Of these, Italy is grappling with the worst outbreak, with over 35,713 confirmed cases and around 3000 deaths by March 18, 2020 [1] [2] [3] [4] [5] . This exponential increase in COVID-19 positive cases in Italy raised turmoil, and the government decree to a lockdown of the entire country [1] . Given the seriousness of the situation, it is absolutely necessary not only an immediate intervention but also a criterion for assessing its effectiveness.

Article on modeling epidemic transition of COVID-19 have been published [1] [2] [3] [4] [5] [6] [7] [8] and based on the previous publication from China, South Korea, Iran, and Japan presented the estimation of epidemic trends and transmission rates [1] [2] [3] [4] [5] [6] [7] [8] . Through this research, we evaluated the consistency of the containment rules and identified possible SARS-CoV-2 local mutation using the S.E.I.R mathematical model. We used the most representative epidemic parameters that occurred during the first half of March 2020 to predict the trend of infections. Therefore, to assess the effectiveness of the containment measures, it will signal the presence of a plausible evolutionary mutation. To do this, it will be sufficient to compare the general trend foreseen by the S.E.I.R. with the real Italian population.

To carry out this study, we used the most recent data, found in the scientific literature relating to COVID-19 total and active cases, deaths, recoveries, and all epidemic parameters, have been . CC-BY-NC 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.03.19.20038968 doi: medRxiv preprint used. Since the Chinese situation has provided the most information, great statistical importance was given to the Sars-Cov-2 evolution in the Hubei region, with the implicit assumption of "very significant local mutations" absence necessary for generalizing the reports through classical inference. The statistics collected on virus mortality were first divided by age group and then recalibrated on the Italian demography, in order to be as representative as possible. To do this, we considered the most representative population of COVID-19 cases reported between March, 1-14, 2020, the number of infected persons necessary to approach the required mortality rate was added to the correct values.

To obtain a more realistic trend and assuming true the probable "non-relapse patients", and we applied S.E.I.R. model to predict the virus progress in Italy. As a note, it is not possible to estimate the containment measures taken by the government. However, at the same time, assuming that only half of the population was susceptible to the virus precisely due to the above containment measures. Thanks to the comparison between real and theoretical evolution, it is likely to estimate the presence of essential mutations and/or the limitation strategy effectiveness through similarities, anomalies, or substantial deviations from each other. We used S.E.I.R. differential equations and non-linear methods to resolve the gaps analytically. An interactive algorithm was developed using C++ software (version) to find a solution through a finite discretization method. The total population number has been considered constant because of the very low deaths/population ratio.

. CC-BY-NC 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.03.19.20038968 doi: medRxiv preprint By entering the initial values for the incubation time 1/σ, recovery time 1/γ, basic reproduction number R0, and number of infected I 0 on March 1, 2020, the software prints the S.E.I.R. values day by day. The best epidemic parameters were estimated through continuous iteration until the "closest values to the real ones" were reached until March 14, 2020. The number of initial incubates was calculated with the formula E 0 =R0·I 0 .

After the reconstruction of the real data on COVID-19 in Italy in the period March 2020, 1-14, through the above methods, the best estimates obtained for the Italian epidemic parameters are 1/σ = (3±1) days, 1/γ = (15±3) days, R0 = 3.51 ± 5%, I 0 = 3350 ± 20%.

The model predicts the following values for the next 7 days (March 2020, 15-22) with "D " . CC-BY-NC 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . These values obviously refer to the population with the constant mortality rate of 3.2%; however, the real number of deaths must be strictly less than the theoretical one expected or we will talk about mutation. Thus, thanks to the results obtained from the application of the S.E.I.R. model we can foresee three possible scenarios: If, in Italy, the real next-days trend of the total infected number will be lower than that shown in figure 1, we can assume the following events set out in order of probability: the containment measures adopted 10 days ago are taking effect; Sars-Cov-2 has undergone a significant anti-evolutionary mutation. If, in Italy, the real next-days trend of the total infected number will be equal than that shown in figure 1. We assume the following events set out in order of probability: the containment measures adopted 10 days ago are not taking effect; the containment measures adopted 10 days ago are taking effect and Sars-Cov-2 has undergone a significant evolutionary mutation. If, in Italy, the real next-days trend of the total infected number will be higher than that shown in figure 1. We assume the following events set out in order of probability: the containment measures adopted 10 days ago are not taking effect and Sars-Cov-2 has undergone a significant evolutionary mutation; the S.E.I.R model is no-more representative of the COVID-19 Italian case and we should utilize the S.E.I.R.S. model. Even considering an admissible "theoretical-estimates statistical error" of ± 5% these values could not be accepted since the trend indicates a faster growth than that predicted by the model with a breakeven point between 15 and 16 March and a percentage difference in net growth.

Deepening the discussion and going to analyze the cases region by region, a very significant result turns out: with the exception of Lombardy, the trend in the number of infected is very good 

Given that · It seems unlikely that the virus, without significantly changing, could infect a patient again [1, 2] [12], . CC-BY-NC 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.03.19.20038968 doi: medRxiv preprint · the mortality rate in Italy is too low to be significant in the short term [8] , · young children appear to have a secondary role in the spread of the infection [8] [17], We will investigate the possible scenarios through S.E.I.R. model. Using the discretization carried out in the previous study "Mathematical-statistical modeling of COVID-19 on the restricted population" [8] , a new C++ software was created to print the values of the S.E.I.R. day by day until a specific date and/or situation (2) . However, unlike the aforementioned study, the prediction period will be extended to a certain number of days in order to verify the effectiveness of the containment measures in Italy.

Since no European or international standard for data collection has been established, one of the crucial points of this analysis is the interpretation of the information available. On February 27, in Italy, a real "communicative turnaround" was announced so that only the most important symptomatic cases would be publicly counted from then on [6] . Since there do not appear to have been significant large-scale mutations and that a good amount of data is now available, we expect the WHO mortality data to be valid in Italy as well [13] [ Table 1 ].

The more recent study about Sars-Cov-2 mortality on symptomatic and asymptomatic COVID-19 patients in the Hubei region shows the following Sars-Cov-2 mortality per age-groups [3] [ Table 2 ].

. CC-BY-NC 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org /10.1101 /10. /2020 Since the Italian population is distributed according to the following age-percentages [15] [3] [ Table 3 ] Σ i P i · DR i / 100 = 3.2%

For this reason, it makes sense to conclude that the Italian COVID-19 death rate is exaggeratedly overestimated if we rely on Ministry of Health data. On the other side, the true-infect number (as the aforementioned "communicative turn" announced) must necessarily be higher. Trying to respect the percentage just calculated we obtain the following table 4.

Citing the adapted system of non-linear differential equations and their discretization [8] 

Legend:

. CC-BY-NC 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.03.19.20038968 doi: medRxiv preprint · 1/γ is the asymptomatic incubation time; · 1/σ is the recovery time; · R0 is the basic reproduction number; · S is the number of susceptible people; · E is the number of active exposed people (people in incubation); · I is the number of active infected people; · R is the number of recovered people (no longer infectable). · X n is the number of day-n "X-category" people; · X t is the number of table 4 "X-category" people;

Significant Discussion: in order for the supposed data to be representative of reality, we should admit the existence of many more cases than expected. All this is consistent both with the idea the infection had been present on the territory for some time, in the form of a less aggressive strain, than with the time course of the disease [1] . The number of people healed is also in line with international percentages [16].

Validity grade: plausible and supported by empirical evidences.

Warning level: high.

Assumptions: 1/σ = 3 days, 1/γ = 35 days, R0 = 6.05.

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is the (which was not peer-reviewed) The copyright holder for this preprint Warning level: high.

Since test 3 turned out to be the most likely, we focus on it.

Peak-day: 80.

Peak value: Imax = 8.86694·10 5 people (almost 9 million people); I < 10 -day: 333 (almost one year);

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is the (which was not peer-reviewed) The copyright holder for this preprint . I = 0 -day: 386.

We can also fit the curve through a convenient Gaussian f(x) = y0 + Gauss(A,x0,σ) (x) function, useful for modeling the initial trend of the virus.

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is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.03.19.20038968 doi: medRxiv preprint

The model is approximate as a direct consequence of the uncertainty of the data it was supposed to fit but it can act as a valid comparison for the identification of any Sars-Cov-2 genetic mutations as well as for the evaluation of the containment measures effectiveness. Observed the comparison between the predictions of the S.E.I.R. and the actual trends highlighted above, as well as between the trends of Lombardy and the other Italian regions, there are valid reasons to assert that in Lombardy, in particular in the cities of Brescia, Bergamo and Milan, a very significant evolutionary mutation of the virus may be underway, which would require immediate containment.

. CC-BY-NC 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.03.19.20038968 doi: medRxiv preprint . CC-BY-NC 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.03.19.20038968 doi: medRxiv preprint . CC-BY-NC 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.03.19.20038968 doi: medRxiv preprint . CC-BY-NC 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.03.19.20038968 doi: medRxiv preprint . CC-BY-NC 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.03.19.20038968 doi: medRxiv preprint

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