Countries around the world are working to “flatten the curve” of new cases of Coronavirus pandemic. I derived inferences related to flattening of COVI19 curve by analyzing data up to 08th May (http://www.dailynews.lk) and inferences on estimator for R0 at different time intervals which will be useful for medical and public health professionals and other decision makers for data driven decision making. This is the second analysis on the same subject which is a continuation of my previous article available at the following link (http://www.dailynews.lk/2020/04/22/features/216965/covid19-curve-sri-lan...

**Countries Flattening the Covid19 Curve**

As per 08st May, I noted (https://virusncov.com) that the covid19 curves of New Zealand, Australia, Hong Kong and Taiwan have been flattening to a smaller number depending on the country. The corresponding trends are shown in Figures 1- 4.

In New Zealand (Fig. 1) total number of COVID19 as at 08th May was 1491. The number of new cases has been exponentially decaying since 04th April and in fact it has been less than 20 since 15th April and in fact less than 10 since 19th April.

In Australia (Fig. 2 ) total number of COVID19 as at 08th May was 6929. The number of new cases has been exponentially decaying since 28th March and it has been less than 25 since 20th April.

In Hong Kong (Fig. 3) total number of COVID19 as at 08th May was 1045. The daily number of new cases has been less than 10 since 12th April, and also it has been exponentially decaying too since 28th March.

In Taiwan (Fig. 4) total number of COVID19 as at 08th May was 440. Since 13th February, a number greater than 20 positive cases were found only for five days and the number of COVID19 cases has been decreasing sine 31st March. The number has been less than 20 cases per day since 25th March and less than 10 since 01st April with an exceptional value of 22 cases on 19th April. In fact this 22 can be considered as an influential point with respect to the numbers in Taiwan.

However, in Sri Lanka the pattern (Fig. 5) of confirmed cases has slightly deviated from the above patterns, but it can come back to decaying shape soon. Based on distribution free method, the probability of getting (i) less than or equal to 10 new and (ii) less than or equal to 25, during the period from 11th March to 08th May are 0.58 and 0.89. The corresponding probability for more than 25 cases is 0.20. This was due to the observing more than 25 cases consecutively for seven days (23 April to 29 April). I believe it was an unusual phenomenon that happened against the natural course of the disease. If the number of covid19 cases per day is assumed to be poison distribution, the probabilities of COVID19 cases per day greater than 15 and 25 per are 0.331 and 0.003 respectively.

In fact, the unexpected situation during (23-29) April, has been realized by the government appropriately and immediate remedial measures were taken by the government to avoid a resurgence. Those points are considered as outliers in statistics which impact to the natural pattern that we have been observing. Thus we can expect a delay in the flattening of the curve by few weeks. The new period of flattening would be from middle of May.

**Trend in 5-day median**

To reduce the noise, the trend was plotted for 5-day median (Fig.6). This is a better outlier resistant smoothing technique than 5-day moving averages. It can be seen that the median has been decreasing from 52 (25 April) to 27 (04 May) in spite of outliers. It has slight gone up on 05th May and 6th May. The pattern is an indication that the new cases will convergent to smaller number of cases from middle of May.

**Trend in % increase of cumulative values**

In spite of sudden spikes, the flattening the curve can be further justified by the trend of percentage increase in cumulative daily new cases (Fig. 7).

Fig. 7 has a clear exponentially decreasing trend and in fact most of percentage are very low (< 10%) in particularly as the time passes. Let the cumulative values of daily new cases on (t-1)th day and day tth day and be yt-1 and yt respectively. Then the percentage increase at day t is:

Thus as the percentage value is low (say < 10%), it can be concluded that the cumulative value at time t tends to be the cumulative value at time t-1, which is good indication of flattening the curve soon. Our observed percentage increases are low and somewhat decreasing with time, therefore it can be concluded that the curve would be flattening from middle of May.

**Case Fatality Rate (CFR) and Recovery Rate (RR) as on 01st May**

The COVID19 cases are categorized into two as ‘active’ and ‘closed’ in almost all the data bases on COVID19 across the world. The closed cases are further divided into two cases namely recovery and death. The active cases are also divided in to ‘mild’ and ‘critical’ based on their clinical condition.

The CFR is the ratio between confirmed deaths and confirmed cases (COVID19 cases). This is an indicator to compare the mortality rates in different outbreaks and also to compare the mortality rates among the different regions and the countries in a given outbreak situation. Generally, it is better to see a trend of CFR over time. Also it needs to be related to the demographic profile of the patients. Since my intention was to compare the CFR in Sri Lanka with the corresponding values in other countries, I have selected several countries based on the covid19 curves of the countries (Fig. 8)

**Fig.8 - CFR and RR as on 02nd May in different countries**

It can be seen that four countries whose COVID19 curve has been flattening, CFR is also very low and less than 2.0. The CFR is the lowest in Singapore (0.09) followed by Hong Kong (0.38). The CFR in Sri Lanka (0.99) is also below the corresponding values of Australia (1.40) and New Zealand (1.34). I believe the value of Sri Lanka reflects that we are out of danger for a greater extent than we would expect thus COVID19 is not a very series epidemic with respect to the number of deaths. The CFR values are greater than 10 in Spain, Sweden, Italy and France, but it is 5,81% in USA though confirmed cases are the highest in UA.

The recovery rate (RR) is defined as the ratio of recovery cases and total number of COVID19 cases. The recovery rate is the highest in Australia followed by New Zealand (> 85%). The RR in Hong Kong (83%) and in Taiwan (85%). However, in Sri Lanka RR is very low and equals to 25.8%. It is not easy to explain without having more medical parameters of the patients. However, if it can be increased government can reduce the number of beds required for COVID patients in the hospitals. As the both indicators: CFR and RR vary with time, it is necessary to study those two variables along with the demography of patients.. Doctors can get wealth of information if such data is analyzed statistically and the results would be immensely useful for various decision making process.

This analysis clearly indicates that the NZ, Australia, Hong Kong and Taiwan have a very low CFR with a very high RR. The COVID curve in those four countries have already started flattening. No doubt that Sri Lanka will also reach that level from middle of May, if unexpected things did not occur and people adhere to guidelines given by the Health Authority. .

**Estimating RO Based on Case Count Approach**

R0 is an important quantification that tells the rate of spread of a virus from one patient to the others without any restriction. In other words, if R0 is 2.5, one infected person would infect another 2.5 on average. Initially, the expected number of COVID19 cases were estimated by varying R0 value from 2.0 to 3.5 and consequently the results obtained were misleading the public as well as the decision makers. The R0 greater than 1 indicates that the number of cases is growing, perhaps necessitating of the lockdowns or other appropriate measures. The R0 below 1 suggests that the number of cases is shrinking, possibly allowing the communities back to their normal routines. Based on our data with time it is obvious that R0 cannot be greater than one.

Of course there can be various methods to estimate R0 in our context. Though the spread has not gone to community level. Using a simple Excel sheet, I estimated the number of Freely Moving Infected (FMI) cases and Currently Infected cases (CI). The main assumptions were: (a) each FMI case roams for 5 days and (b) the total number of CI cases was assumed as three times of the actually infected cases during that period.

My proxy estimator for R0 is the ratio between CI and FMI. The values computed are shown in the Table below.

It is clear that the rate of spreading COVID19 in Sri Lanka has been decreasing with time, It provided people follow the instructions given by health authority. This is a good inference to conclude that the probability of community transmission of COVID19 is almost zero.

**Present Sampling Method**

Initially we used to test lesser number of people for COVD19 due to lack of facility. However, at that time, the probability of identifying a COVID19 case from a suspect group of people is high. Due to increase number of PCR machines more samples are tested now, but I am worrying about the sampling method because the probability of not detecting COVID19 patient among the suspect group is high. Of course, we do not have to access real data, but I am explaining the situation based on the information given by the media.

Even though, the relevant authorities stated that the random samples are taken for testing, it sort of misused of the name of the technique. Random sampling is correct if all the subjects are given equal chance to be a sample in a homogeneous population. The concept of random is misused by many people. My feeling is that, we are doing purposive random sampling because we take samples only from suspect groups. However, we need to worry, even under this situation, if the probability of not confirming on COVID19 among the suspect group is high. I wonder it may be due to lack of training on tracing suspect cases. If we study past data, we may be able to stratify the suspect group based on age group, health condition etc to increase the efficiency of sampling. Nevertheless, a good dialog must be taken place between health experts and good applied statisticians to come precise and efficient sampling scheme to assess the condition.

**Conclusions and Recommendations**

COVID 19 curve in Sri Lanka should flatten from Mid-May.

Case Fatality Rate is very low in Sri Lanka indicating with respect to number of deaths, COVID19 is not very serious in Sri Lanka like most of other countries.

Recovery rate is also low which needs to study by the health authorities. This would help to reduce the number of beds for COVID19 patients.

As R0 has been less than one over time, we do not want to worry that large number of COVID19 patients (say, 40000-45000) are in Sri Lanka and also it can be concluded the chance of spreadingCOVID19 to community level is not high.

Government can relax most restrictions irrespective of the type of employee so that all categories can come back to normal life. However, people should follow the “intra vires” instructions given by the health authorities even after the situation back to normal.

We cannot expect to get rid of COVID19, even though an effective vaccination is found because at any time there can be some probability that a COVID19 patient may be in the society. Data driven decision making (DDDM) is a more powerful tool for effective decision making rather than making decisions that are intuitive or based on observations alone.

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