Curve fitting and Least Square analysis to extrapolate for the case of COVID-19 status in Ethiopia.

On 30 January 2020 World Health Organization (WHO), declared the novel coronavirus as a Public Health Emergency of International Concern (PHEIC), COVID-19 virus as an epidemic transmitted virus. It was on 31 December 2019, the WHO China Country office informed the cases of pneumonia with unknown aetiology detected in Wuhan city, Hubei Province of China. Just after WHO’s declaration, Ethiopia has taken different measures to protect from this public health emergency problem. The disease is human to a human transmitted virus. It comes from outside of the country so it opens checkpoints at different entrances of the country. However, on 13 March 2020, the first positive case was reported from a Japanese man. The virus is continuing the transmission to the public progressively. While this research has been working, within 90 days from the first case, the country reported 2,506 positive cases and 35 deaths. The research has done after collecting the first 90 days of data in the Ethiopian case. The daily report announced by Ethiopian MoH is based on the test. And hence, the reported data as positive cases with COVID-19 is not actual positive case data in the country. Therefore, this paper has contributed to the planning and taking further measures on the viruses by demonstrating the next 90 days of predictive data.

3. Covid-19 in the case of Ethiopia

3.1. Analytical Result

The first case reported in Ethiopia was on 13th March 2020, [11], [12]. Just when one Japanese man has the virus, MoH and the Ethiopian Government has immediately taken action against this patient, his friends and coworkers who are suspected to be infected with the virus. In the first 30 days from the total test of 3,178, there were 69 cases have been reported as positive. With the first one month registered dead 3, 10 recovered and 54 were hospitalized.

In the first 30 days, only 69 cases were reported from 3,178 tests. Which is 2.17% of this number 14.49% were recovered and 78.26% were hospitalized and 4.35% death was reported. For the second 30 days, the number of tests increased from 3,178 to 36,606, which is 33,428 tests, which have been done within one month. From this number 181 new cases were reported which is 0.54% of the test.

after the second month, within fifteen days, 50,658 tests have been done which is 58.05% of the total test 87,264. This is a great change in the testing capacity of the ministry. In the second month, there was a declination of reporting positive cases. In the first month, 2.17% are reported as a positive case, whereas the second month reduces to 0.68% from the total test and 0.54% within the second month. In the third month at 75 days reported cases increased from 0.68% to 0.80% and within 15 days 0.89% of the tests were reported as positive cases. This may show that it is the time the virus spreads highly in the population. Not only this, during the next fifteen days of the third month, but there are also 71,257 tests have been done, from this 1,805 reported as positive cases.

This is 2.53% of the test. Generally within 90 days, (end of three months), a total of 158,521 tests have been done and 2,506 cases reported as positive. This is 1.58% of the total test. This is a signal for the government, MoH and for the nation to work more on the protection of the virus. At the end of 90 days from the day where the first case was reported, there are 2,506 cases reported, 16% of the case recovered, 82.52% in hospital and 1.40% of the total case dead.

On the ninth day averagely, from the total test, 1.72 % of cases were reported as positive, 20.67% recovered, 75.56% in hospital and 1.61% dead from the total cases.

Figure 1: Recovered, hospitalized and dead population in per cent withCOVID-19 in Ethiopia for the last 90 days.

From figure 1, the recovered rate is increased and the hospitalized rate is decreased. Which is the number of the population infected by the virus decreased until the fifty-third day of the first report was registered. The death rate is almost constant. But after fifty-third days it comes the reverse, hospitalized rate was increased and the recovery rate decreased dramatically.

3.2. Curve fitting and least square analysis result from python polyfit code

After taking the first ninety-day data, I am working on the curve fit analysis. I used and prefer the python Polyfit algorithm, with polynomial degree 4. For comparison purposes, I tested with the MS-Excel Trend line, which has R 2 = 0.99 for total cases. This determines the accuracy is very good. Also, it has the same equation with an equal coefficient to my python code result. Figures 2 and 3, the graphs generated from collected data and predicted with curve fitting. As I have said, above since it has R 2 = 0.99, the closer to one the more accurate the prediction.

Figure 2: 90 days COVID-19 total cases, new cases, hospitalized, recovered and death status in Ethiopia with actual data.

Figure 3: 90 days COVID-19 total cases, new cases, and hospitalized, recovered and dead status in Ethiopia with predicted data.

Figure 4: 90 days COVID-19 total cases, new, hospitalized, recovered and dead status in Ethiopia with real and predicted data.

Figures 2, 3 and 4 showed that the prediction value is almost the same as the real data. To visualize more the difference sees figure 4.

Figure 5: COVID-19 Status in Ethiopia for the Next 180 days.

From figure 5 and tables 8 and 9, the number of total cases increased from 2,524 on the 90th day to 124,775 on the day of the 180th. The death is an increase from 32 on the 90th day to 2,469 on the day of the 180th. The rate of death with the total case was, during the 90th day 1.61% on averagely, whereas from the data 1.98% of the total case will pass away.

4. Best Curve fitting Analysis

From the data that I have in Tables 8 and 9, the total number of positive COVID-19 virus cases would be around 124,775 on the 180th day, (after six months after the first case was reported in Ethiopia). From these positive cases, 13,066 recovered, 109,297 in hospital and 2,469 patients will die.

Figure 6: 90 days COVID-19, total case, daily new case and death status rate in Ethiopia

Figure 7: 90 days estimated COVID-19 total case, daily new cases and death status rate in Ethiopia.

From figure 6 from actual reported data and figure 7 from estimated data, the daily reported positive case is highly oscillated, between 0.001 and 0.14 for the first 20 days. This is probably; the test was taken from already highly exposed populations. Then after it becomes, a stable format between 0.005 and 0.02 up to the 75th day, it increases the rate to 0.04 while the rate of the total case with the total test is below 0.02. In Tables 8 and 9 the total number of patients in the hospital decreases while the recovery rate increase for about the first 55 days, and then the rate of hospitalisation is increased dramatically. On the 90th day, almost more than 80% of the cases are in hospital and the recovery rate is less than 20.

Figure 8: 90 days COVID-19 Recover and Hospital cases status rate in Ethiopia with real reported cases.

Figure 9: 90 days Estimated COVID-19 Recover and Hospital case rate in Ethiopia with predicted data.

From figure 8 using actual reported data and figure 9 using predicted data, the upper curve shows the rate of hospitalized cases. In the beginning, it was almost the rate is one. Which is almost all of the patients are in hospital, after ten days slowly decrease until fifty-five days or when the time near fifty-five days from 1 to 0.55 or below to 0.6, and then it increases with in the next 35 days the rate is above 0.8. This implies that the number of reporting cases as positive COVID-19 is increased. On the nineteenth day, 85% of reported positive case patients are hospitalized. The bottom curve shows the recovered rate. As shown in the figure, after 60 days the recovered rate is decreased from 0.4 to below 0.2 or near to 0.14. This means in the nineteenth day the total recovered population is almost 14% of the total reported cases, compared with table 5 above.

Figure 10: 180 days predicted COVID-19 Status rate in Ethiopia.

Figure 11: 180 days predicted COVID-19 total case, daily new and death Status rate in Ethiopia

Figure 12: 180 days predicted COVID-19 Status rate in Ethiopia

Based on the data from which we have to get after executing the python code generating ployfit curve as shown in figures 10, 11 and 12. The figure shows that the rate of the total case, new daily case, recovery and death all are more than 1. This means the rate of testing with the rate of the spread of the virus is incompatible. The virus is transmitted into the population faster than the capacity of testing the case. Even the recovery rate is very high, without knowing or testing the virus, already the patients recover from the disease, or dead.