Short-Term Projection of COVID 19 Cases in Kenya using an Exponential Model

Introduction: The COVID-19 disease has spread to over 200 countries and territories since the first case was recorded in Wuhan, China in December 2019. In Kenya, the first case of COVID-19 was recorded on 13 th March 2020, since then over one hundred cases have been confirmed, and three deaths recorded as of 2 nd April 2020. With the rapid changing situation, timely and reliable data is required for monitoring, planning and rapid decision making with an aim of reversing the already deteriorating situation (economic, health, learning among others) in the country. Methods : The study used the exponential model to project the expected daily cumulative cases in Kenya within the first 40 days. The study opted to do a short time prediction owing to the fact that the scenario is rapidly changing. Data used in the analysis was obtained from the daily updates by the Kenya Ministry of Health, and analysis was done using Stata Version 15 and MS Excel 2010. Results : The Case Fatality Rate on day 21 was estimated as 2.7% (95% CI 0.01 – 7.80), with varying daily estimates as expected. The model estimated that the 1,000 confirmed cases will be reached by 14 th April 2020 while the 4,000 cases will be reached by 21 st April 2020. The results indicate that it will take 33 days for Kenya to reach the 1,000 confirmed cases and 40 days to reach the 4,000 cases Conclusion: Massive screening and contact tracing of all individuals who entered the country within 28 days prior to the mandatory screening should be planned and implemented immediately with an aim of increasing the chances of getting active cases, and possible transmission through such contacts. Continuous modeling of data is needed in order to cater for other factors which were not considered in this study such as the impact of mandatory quarantine, night curfews and suspension of international flights


Introduction
The World Health Organization (WHO) defines the Coronavirus Disease (COVID 19) as an infectious disease caused by a newly discovered coronavirus [1] and is characterized by several symptoms including fever, cough, fatigue, shortness of breath, sore throats and headache [2,3]. The disease was first reported in Wuhan, China and was declared a Public Health Emergency of International Concern on 30 th January 2020. The World Health Organization further recognized the disease as a pandemic on 11 th March 2020. As of 3 rd April 2020 (19:47 Hours GMT), the disease had spread in over 207 countries, with 976,586 confirmed cases and 50,492 confirmed deaths [4].
In Africa, the first case of COVID 19 was confirmed on 14 th February 2020 in Egypt and as of 3 rd April (15:40 Hours GMT), about 50 countries in the continent had reported the outbreak of the diseases ( Figure 1). As of the reference date, only four African countries had not reported any confirmed case of COVID 19 and they include Comoros, Lesotho, South Sudan and São Tomé and Príncipe. In the same period, 7,177 confirmed cases of COVID 19 had been recorded in Africa, with South Africa recording the highest number of 1,505 followed by Algeria with 986 cases [6]. Additionally, over 290 deaths and 650 recoveries respectively have been in continent.
Kenya recorded the first confirmed case of COVID 19 on 13 th March 2020, and as of 3 rd April 2020 (06:00 GMT ) 110 cases had been confirmed [7]. In the same duration, the Ministry of Health had confirmed three mortality cases and four recoveries from COVID 19. The confirmed cases of COVID 19 were spread in over five counties, with Nairobi recording the highest number (Figure 7).
To curb the spread of the disease in the country, the Kenya government instituted a number of measures including closure of school and all social and public gatherings in excess of 10 people. In addition, all international flights to and from the country were suspended as of 25 th March 2020. The government also instituted mandatory quarantine for all returning Kenyans and residents from 22 nd March 2020; and from 28 th March 2020, a night curfew (7.00 p.m. to 5.00 a.m.) was implemented.
Over the days, the government has also intensified contact tracing for all individuals who were exposed to infected cases.
To estimate the COVID 19 caseloads for coming days in Kenya, this paper has developed a statistical model based on the already available data. The projected data is critical for early preparedness, awareness creation and informed decision making in the country.

Methods
The statistical model for an epidemic has five phases as described in the Figure 3 adopted from Batista M. Phase 1 and Phase 2 are characterized by exponential growth. While phase 1 is characterized by a slow growth, phase 2 is characterized by an accelerated fast growth. Phase 3 and 4 are characterized by a negative growth, with phase 4 recording an accelerated negative growth.
Phase 5 is the ending phase where limited cases are recorded or are completely not there.
As noted by Chen et. al. [10], the coronavirus epidemic appear to be nonlinear and chaotic, as such, this paper focused on a short-term prediction of COVID-19 cases specifically under phase 1 and 2 of the epidemic in Kenya. Using data from the Ministry of Health on the reported COVID-19 cases, the model was developed to provide estimates until the 21 st of April 2020 which is the 40 th day since the 1 st case was confirmed in Kenya.
Assuming a continuous spread of the disease, the number of detected cases are expected to follow an exponential model [11]. The daily cumulative confirmed cases have been estimated using the exponential distribution (equation 1), by fitting the observed confirmed cases in Kenya, α is the number of expected COVID 19 cases at the beginning of the pandemic, β is the daily growth rate and t is the time, in this case day numbers from the 1 st day when COVID 19 was confirmed in Kenya (t:1,2,3……. Day 1 is 13 th March 2020) This paper also analyzed the COVID-19 Case Fatality Rate (CFR) in Kenya. The CFR also called case fatality ratio in epidemiology is the proportion of people who die from a specified disease among all individuals diagnosed with the disease over a certain period of time [12].
Data used in the analysis was compiled by the author from the daily updates given by the Ministry of Health from 13 th March to 2 nd April 2020; a total of 21 days. Data Analysis was done using Stata Version 15 and MS Excel 2010.

Descriptive Analysis
As of 2 nd April 2020, a total of 110 COVID 19 confirmed cases had been reported in Kenya. In addition, three mortality cases and four recoveries had also been reported in the same duration.  Worth to note is that Day 20 and 21 recorded over 20 new confirmed cases apiece and this could be attributed to the massive testing of individuals specifically those under the mandatory quarantine.
Further analysis indicated that a total of 51 cases were confirmed on day 20 and 21, and out of these, 44 were in the mandatory quarantine centers representing 86% of new cases confirmed in both days.  Figure 5).
Additionally, the CFR on closed cases (cases with an outcome) was calculated for Day 21 and recorded as 42.9% ranging from 50% in Day 14 to 25% in Day 20.

Projection of COVID 19 Cases in Kenya
The parameters of interest were estimated using a linear and non-linear exponential model (equation 1) and the parameters of interest are presented in Table 2 and 3 respectively.  The graphical presentation of both models against the actual number of reported in Kenya in the 21 days span is presented in Figure 6. As evidenced in Figure 6, there was a near perfection in estimation of cases by both models until day 16, when the linear model started to overestimate the cases. On the other hand, the non-linear model seems better in estimating the cases. Using the non-linear model, Kenya will record 1,000 confirmed cased of COVID-19 on 14 th April 2020, and 4,000 confirmed COVID 19 cases on 21 st April 2020. On the other hand, using the linear model, then 1,000 COVID-19 cases will be reached on 12 th April and 4,000 cases will be reached on 19 th April 2020. The daily predicted COVID-19 cumulative cases are presented in Table 4.  Projected COVID-19 Cases in Kenya (Until 21st April 2020)