Covid 19: How Really is the Epidemiological Curve? Epidemiological Curve Growth Rate is Less than One

the Epidemiological Curve? Epidemiological Curve Growth Rate is Less than One. Biomed This paper shows some views on the mathematical structure of the diffusion of the Coronavirus (COVID-19), often claimed to have a positive exponential structure. However, we ﬁnd that the exponential growth rate is past the inﬂection point and that growth is much slower than this implication. It presents conclusions on the future ex-pected outcome of the current situation-not only in terms of diffusion of the disease but also for the hysteria that have been created around it.


Introduction
In the last three months, fear has emerged about the spreading of the virus SARS-CoV-2 and the related illness COVID-19, often leading to irrational consumers behaviour [1]. The virus has alleged generated tens of thousands of death worldwide, starting from China and moving to South Korea, Iran, and Italy. Then, it has started a spread toward their European countries, and onto trials, control, counselling, documentation and training for public health. The Institute is under the supervision of the Ministero della Salute (Ministry of Health). The discrepancy between such reports lies in the counting methodology. ISS declares that only 12 people were not affected by co morbidities. At the moment, authorities are not able to distinguish patients who are dying because of the virus from those who were already affected by serious pathologies and did not die because of COVID-19. Also, different countries may follow different approaches to this regard.
Another source of uncertainty concerns the computation of fatality rate, i.e., the proportion of deaths from a particular disease compared to the total number of people diagnosed with the disease for a specified period. At the beginning, the media hyper confuses fatality rate and mortality rate. Mortality rate is instead a measure of the number of deaths scaled to the size of the population per unit of time, and it is typically expressed in units of deaths per 1,000 individuals per year [9]. The fatality rate is a ratio between a numerator and a denominator that are both difficult to measure accurately in current circumstances [10]. The numerator depends on how deaths are attributed to COVID-19 in case of co morbidities.
The denominator is the total number of people diagnosed with the disease and it depends on the effort deployed to test the population (that varies among countries and it is the result of different prevention strategies), and on the accuracy of the test, which has been shown to be inaccurate (from the results of a recent study [11], false positives could be at least 50%). With these premises, fatality rate cannot be reliably computed at the moment. In addition to the case of co morbidities, we need to consider the case of confections, that is, when the COVID-19 acts together with another virus, for instance of a "more regular" flue, which may cause a death attributed to the COVID-19, while it is due to a multitude of causes; just to give an example associating an infection of Staffifloccus Aureus to a fluse increases the risk of death of a factor up to 4 [12].
With such statement we do not intend to claim that recommendations from health authorities should be ignored. Indeed, the virus is hazardous and demands attention and containment measures. The regulation announced by public health authorities must be rigorously followed to limit the spread. Also, the "regular" flu is dangerous and need to be handled with care, which is supported by the aforementioned data. Still, it is essential to reduce the uncertainty and to put the phenomena into perspective, to make reliable forecasts of the future, and to moderate the panic that is spreading, which, for instance, is leading people in the US to buy more weapons [13]. We need to acknowledge that the spread of the news of the viral spread is positive for many market sectors. The virus enlarges their potential customer base and, indeed, without any desire to spread the fear, their growth and diffusion spread the panic. The first of such market is social media, as the primary vehicle of news, and also of meaning for people to communicate while they are separated one another [14]. Then there are health care companies, tools to work from home, entertainment services to be used from home, and online stores [15].
To reinforce the importance of a reliable prediction, we should review the case of the emergence of the swine flu in England, which generated a tremendous fear, resulting then in public spending of 473 million pounds for a supposedly healing drug that ended up being as useful as paracetamol [16]. This short study has the goal of limiting the uncertainty and contributes to a rational understanding of the current virus outbreak. To this end, we present a rigorous model of the virus' spread and a hypothesis for the model. Our evidence supports the claim that the spreading is not in the exponential growth phase but it has slowed to an infections growth rate below 1. This paper is organized as follows. Section 2 proposes some mathematical models describing the diffusion of the virus in South Korea, Italy, and Iran, and Section 3 discusses the results we have achieved and their implications on our society. Section 4 discusses the limitations of the findings while Section 5 attempts to draw some conclusions. We welcome comments and alternative analyses. The datasets that we have used are the public ones distributed by WHO. Still, we make them directly available online for other people to validate our results and to produce alternative models.

Modeling the Spread of the Virus
There has been a growing number of statements that the COVID-19 has an "exponential growth" [5], meaning that it has a daily growth that is an almost constant proportion of the number of people who are infected -such situation would be so that in a matter of months the whole population of the world or a significant portion of it would be infected. However, our analysis does not confirm such findings, and instead shows we are past the inflection point of the bimodal or logistical curve, as the rate of new infections is less than 1. We have analysed the data of the diffusion of the virus in three countries, Iran, Italy, and South Korea. These countries have taken different strategies to cope with such situation as it is widely discussed in the media [17]. We have considered the data from the day of the first apparent propagation of the virus in such countries, and we have used the data coming from the World Health Organization, all occurring after the 24 th February 2020, the day zero in our plots. Let us emphasize again that the term "exponential diffusion" as used in the media means that the diffusion in one day is proportional to the number of cases present in the day before.
In other words, if xi represents the number of cases at time i, then we have that xi+1 = (a + 1) xi where a is a constant real number which ought to be strictly positive if we want a positive exponential diffusion. We have started to analyse such factor in the three countries and how it has evolved (Figure1), and we have observed that it is far from being a constant but rather it is a value decreasing overtime, which implies that the curve is past the inflection point.  (Figure 1). In all the cases, if we compute the robust Spearman rank correlation coefficient, we find an evident downward moving trend overall. The results rounded to the second significant decimal are for Italy a correlation of -0.84, with p < 10-6, for Iran -0.88, with p < 10-8, and for South Korea -0.95, with p < 10-13. This is a contradictory statement that in the days under consideration, there has been a positive exponential diffusion of the virus. Moreover, we can try to consider a linear model; the Pearson correlation coefficient rounded to the second decimal for Italy is-0.70, with p < 10-3, for Iranis-0.84, with p < 10-6, and for South Korea is -0.92, with p<10-10 . Indeed, the plot shows also that at the beginning, the regression over estimates air, and toward the end, it tends to underestimate it. However, this is explainable by the fact that the growth rate can never become negative, and the model is worth only at the time of expansion of the disease, that is, as long as there is a significant growth in the number of patients.
We have translated this into a differential equation to understand the implication of the model better, proposing a structure of the evolution of the kind: The third derivative is the trend of the variation, so it can tell us whether we are in front of an upward moving variation or a downward moving variation: It is now interesting to look at the shape of this function. Please, remember that we will consider it only when the derivative has a positive sign. As an example, we can consider the case for Italy. In  The main aspect to be noted is the trend disregard specific numbers, which could contain significant errors due to the mathematical operations performed on them. The data is publicly available at [23,8].

Short Analysis of the Results
The prediction of the course of an epidemic/pandemic is crucial for properly organizing the necessary response of the  [19]. Out of them, three people died (about 3.3% of the infected). As a result, panic has spread; causing the city has been locked, which makes it an ideal case to analyze. A further and more in-depth analysis has shown that the spread was about two to four times as much [20] and that the people who died had generally is coherent with our findings (Figure 2).

1.
Many patients are asymptomatic. Tracing them, as initially suggested, is difficult and costly, so this policy was not applied after some initial attempts.

2.
Symptoms requiring medical attention are present in a minority of patients. Also, they can closely resemble those of the flu, with which COVID-19 can coexist. have played an unexpectedly significant negative impact in the clinical course of the Italian patients living in the regions mentioned above [19]. If the prediction presented in this study is correct, the clinical course of the COVID-19 infection will be less dramatic in the rest of Italy, which is a welcoming scenario. The disease will take longer to subside. In the meantime, there will be unavoidably Still, if the hypotheses shown in this study prove to be reliable, the public health authorities could take additional (and perhaps cheaper and more effective) measures to handle such diffusion.

3.
If the spread is so fast and hard to handle, steps should also be taken to minimize its impact. First, it is surprising that there is substantial evidence that ascorbic acid (vitamin C) helps reducing viral infections, up to even 85% [25]. This has not been taken into account into the overall recommendation, even though if vitamin C is quite inexpensive. In essence, a regular cost in a pharmacy is  [27]. Such an approach would not have as harming economic effects in case of a false alarm.
It is interesting to observe how now the situation will evolve, especially in Italy, from which we hope to receive new data soon. Italy

Limitations of the Findings
Where N is the total population and a and b are factors that consider that not all the population will be affected by the virus and that some people can be infected multiple times. The model would have a solution: Where k is a constant, leading to the typical logistic structure, which is a model used to predict the spreading of diseases for at least almost a century [28]. Indeed, we could then move further and also consider the time dimension. All of these new and important matters deserve a further reflection, being outside the limited scope of this first communication.

Conclusions
The beginning of 2020 has seen an outbreak of the virus SARS-CoV-2 and the related illness COVID-19. Initially originated from China has then seen the spread over other countries such as Italy, Iran and South Korea for then having cases appearing in virtually all European countries. On 11 th of March, Tedros Adhanom Ghebreyes us, the director general of WHO, declared:"We have therefore made the assessment that COVID-19 can be characterized as a pandemic" [29]. Since then, all countries started actively taking stricter countermeasures, even those that were previously acting mildly. Mass media started to publicize the situation extensively, and panic took over worldwide. Reliable sources have made several statements about the potential exponential growth of the disease [5], increasing further a sense of phobia and worldwide run to the supermarket to stock items related to basic needs. This hype and panic made it more difficult for the authorities to act and for citizens to behave rationally and collaboratively. Rational decisions necessitate looking at facts.
The diffusion of the virus does not follow an purely exponential trend as promoted by the mass media, but a traditional epidemiological curve, typical of seasonal flu, for example. Stricter measures could help in flattening the peak to avoid overloading the healthcare system. However, even before the more stringent containment measures adopted in Italy on 10 th of March this year, the phenomenon did not appear to be in the exponential phase. The data requires a sober reflection after the crisis, with the emergency managed. Curve-flattening policies and containment measures have immediate economic consequences on the country that may

Volume 27-Issue 5
impose further cuts on the healthcare system, leading to a potential financial break down in the future. Policymakers should start from these considerations to design the future, especially when creating monetary policies.