A Numerical Analysis of Kenya’s Scenario Tracing turning points on the curves and providing key interpretations

How is mathematics socialising COVID-19 projections?

The novel coronavirus has made social distancing, or better still, physical distancing, the most widely used phrases this period. Mathematics has used the occasion to claim its rightful place as the language of science, socialising all discussions on the scenario of possibilities for policy and planning interventions against COVID-19. “Flattening the curve” has become every country’s anxiously awaited visitor. When will it knock on the door? Similarly, statistics and graph theory are no longer just abstract topics relegating maths teachers to monologue. No! We always need them for proper planning, but most political governance systems trivialise their place in decision making – inviting stealthy, mostly slow, but exponentially damaging consequences in the long run. 

Derived to project the worldwide growth in coronavirus infections starting from 21^st March 2020, the global equation  was shared here on 4^th April 2020. It gave good estimates for policy and planning. The projection of 1.5 million in global cases by 7^th April was not far from the reported 1.4 million. The projection of 2 million cases by 12^th April still stands to be tested even as the graph shows a slight drop starting from 5^th April 2020 towards a new projection equation:  as shown in the graph. This newly developing equation with a lower daily growth rate of 6%, however, still projects the global total cases to hit 1.8 million by 11^th April and 2.3 million by 15^th April 2020.

The slight change in the curve of reported global coronavirus cases from an exponential rate of 10% (March 21 – April 04) to 6% (April 05 – 09). Data source: Worldometer.

Rising recovery rates and Germany’s classic consistency among the big five

By today (10^th April 2020), the top-five countries today in the order of their total COVID-19 cases were the USA, Spain, Italy, Germany, and France. The global recovery rate has improved slightly from 21% the week before to 22% on 10^th April 2020.  The global death rate has increased slightly from the previous week’s 5% (7 deaths per million) to today’s 6% (12.5 deaths per million). The rise in recovery rates has also been evident in the trends among the leading country cases. Germany has recorded a high increase from the previous week’s 23% to 44% by 10^th April 2020, far ahead of the other countries in the league, which have also recorded an increase since last week’s release as follows: Spain (from 20% to 35%); Italy (from 15% to 20%); France (from 18% to 20%); and the USA (from 3% to 6%).

Though above the 1% reported before, Germany’s death rate at 2% as reported by 10^th April 2020 was still the lowest among the top-five countries, translating into 31 deaths per million. This death rate was below the USA’s at 4% (50 deaths per million) and the rest in this group, which by the same date have been recording 10-13% death rate. For France, the figure becomes 187, for Italy 302 and Spain 340 deaths per million.  At 15,730 tests per million by 10^th April 2020, Germany has posted the highest index in this group, three times the score of France, more than double for Spain or the USA, and still higher than Italy’s 14,114 tests per million.

Kenya: Curious questions, cautious optimism on flattening the curve

In Kenya, the Easter weekend has started with a figure of 189 COVID-19 cases reported on 10^th April 2020. Till 10^th April 2020, the tests have been manual and slow. On this date, the reported death rate was 4% and the recovery rate was 12%. Going by the model of scenarios that this thought-leadership series shared the week before (link), the reported figure of 184 on 9^th April 2020 falls below the model prediction of 211 under the optimistic scenario and 404 under the business-as-usual (BAU) scenario. It is, however, important to note that mass testing has yet to begin, with the possibility of unveiling more cases that could have been escaping the routine checks within a few quarantine facilities. By 10^th April 2020, the tests were still below 6,200 in total.

In addition to the dusk-to-dawn curfew is the partial lockdown of Nairobi and coastal counties, being the observed hotspots of growing COVID-19 cases. Since 27 March 2020, two weeks after the first reported case, a significant respite from the high rise in the curve appeared on 4^th April 2020, which is eight days later. Two questions arise:

1. Are the measures the government is taking to restrict movements and raise awareness about precautionary measures already paying off?

• When is the curve likely to flatten so that citizens can go back to routine work and school?

The two questions have their fundamental answer in flattening Kenya’s COVID-19 curve.

Here is how:

• March 13 – 26: This was Kenya’s slow and rugged phase, a learning curve of sorts.

• March 27 – April 03: This was a fast-rising phase, mimicking a simulation curve simplified as  .
• April 04 – 09: Kenya’s trajectory of total cases were declining, tracing a gentle simulation curve governed by a quadratic polynomial, simplified as

 . This downward curve leads us to Kenya’s most probable optimistic path to containing COVID-19 cases, but if and only if no substantial cases that can tip the balance exist within the larger share of the yet to be tested population. The respite may just as well be the lull before the storm.

Three curves for the different growth phases in Kenya’s reported coronavirus cases. Data source: Worldometer.

Theoretically, the curve in (iii) above reaches its maximum at 187 cases on 10^th April 2020, after which it goes down to 181 cases on 12th April 2020. This downturn in numbers can be interpreted as having no more new cases but instead subtracting recoveries to have reduced active cases. The total cases reported on 10^th April 2020, however, came to 189, which is slightly higher than the theoretical expectation of 187 for a flattening trend. The unveiled innovation for automated mass testing by the Kenya Medical Research Institute (KEMRI) should lead to faster tests to map out the actual prevalence of cases across Kenya, a vast country of 50 million inhabitants over a land area of more than 580,000 sq.km.

Conclusion

Kenya’s experience with the slow manual testing for COVID-19 from 13^th March to 10^th April means we are still far from achieving a fair spatial stratification of samples across the vast country with socially active populations. The total cases reported by 10^th April 2020 cannot provide a sufficient answer to the curious question on if Kenya’s coronavirus curve has started flattening.

Germany offers a good example on the power of efficient testing protocols, healthcare intervention mechanisms and adequate containment strategies, which are evident in her high score on parameters such as high recovery and low death rates. The innovation of automated mass testing by the Kenya Medical Research Institute (KEMRI) could be a game changer in revealing the actual prevalence of COVID-19 in Kenya.

Since the planned mass testing is likely to unveil more coronavirus cases in the next few weeks, extra care and precaution in the war against COVID-19 must still remain the better part of the trademark Kenyan optimism.