# Comparison of the Evolution of the COVID-19 Disease between Romania and Italy
## 5 Conclusions  
Since at the time of the outbreak of the COVID epidemic in Europe, many Romanian citizens returned to Romania en masse from Italy, Spain, Great Britain, etc. when the first wave of the epidemic started in Romania, the first wave was relatively more pronounced in Romania than in Italy. However, the number of deaths in Romania during the first wave was far from being as high as in Italy. The proposed model answers the questions asked in the introduction and forecasts about the same extend of the second peak (maximum at about 8%) for both countries (in relative terms). Note that the proposed model cannot answer the question when (if) will the epidemics end--it just rises up the question on the relation between the time and extent of the 1 st and 2 nd peak. Neither the prevalence of the disease can be considered by SIR models. To explain how \(R_{0}\) changes, note that in the SIR model the population is assumed to be closed, and \(N\) cannot change, neither the rate of recovery \(\gamma\). Therefore, the real change appears on the parameter \(\beta\). A simple application of the definition of conditioned probability yields \(\beta=\ pc\), where \(c\) is a contact parameter (i.e., the probability of contact between a single infected and a single susceptible) and \(p\) is a contagion parameter (i.e., the probability that if a contact occurs, then the susceptible becomes infected). However, \(p\) cannot change with restrictions, since it depends on the infectivity of the disease. Therefore, a lockdown-type restriction makes \(c\) smaller, since it reduces the contacts. The duration of restrictions (i.e., \(\Delta t\)) and the social distance approach as considered in the model is reflected linearly in terms of the fraction of the maximal extent and in terms of the expected datum of the 2 nd peak. On the other hand, the relation \(T_{2}=T_{2}(R_{2})\) seems to be exponential. The model predicts the influence of the beginning and duration of the restrictions to the extent and duration of the 2 nd wave. The number of total infected in the 2 nd wave seems to be much higher than the number infected in the 1 st wave (note that the 1 st peak is measured in per mils while the 2 nd peak in per cents). A reasonable question is of course also how many waves will occur. That depends, of course, on the duration of the actual immunity and on whether/when we will have a coronavirus vaccine. Similar to the assessment of the duration of immunity, the answer to this question should be compared with cases from real-life. From history we know of cases where the virus has decimated the population, so caution is more than appropriate in combating COVID-19. One of the most affected diseases in Europe was Spanish flu. In 1918, the Spanish flu infected 500 million people with the H1N1 flu virus in four waves, which was one third of the world's population at that time (and killed 17-50 million people). If there are many waves, and if the immunity to SARS-CoV-2 is as strong as the immunity to SARS-CoV-1, the next waves will not be as strong as the 2 nd wave. However, this is left for the future work. To conclude we give answers to the questions (Q1)-(Q7):  
* Answer to (Q1): In Italy, the final \(R_{2}\)=0.4, however the average \(R_{2}=2.017\), with \(\frac{1}{\gamma}=13\) days. * In Romania, the final R2 = 0.83, however the average \(R_{2}=2.14\), with \(\frac{1}{\gamma}=14\) days. * Answer to (Q2): The time delay \(\Delta T\) varies with \(R_{2}\) and \(t_{2}\), as it can be seen in Figures 16 and 23. Varying of \(R_{2}\) makes sense for the future evolution, while varying of \(t_{2}\), once the restrictions were eased, has just a theoretical meaning. For Italy, \(\Delta T\) varies from 2.5 months (if \(R_{2}=3\)) to 7.3 months (if \(R_{2}=1.5\)). * Answer to (Q3): From Figures 13 and 20 we see that the relation is linear and ascending. For \(R_{2}>1.2\) the extent fraction is higher than 10.