DOI: https://doi.org/10.21203/rs.3.rs-34391/v1
Background: The coronavirus disease 2019 (known as COVID-19) pandemic caused by Severe Acute Respiratory Syndrome coronavirus 2 (SARS-CoV-2) appeared in Wuhan, China has rapidly spread to over 200 countries and territories. In Nigeria, the Kano State Ministry of Health has confirmed its first case of COVID-19 on April 11, 2020, and since then there might have been issues of under-ascertainment that occurred roughly from 22 to 27 April 2020. In this work, we estimate the number of under-ascertainment cases and the basic reproduction number, B, of COVID-19 in Kano, Nigeria.
Methods: We employ the exponential growth and modelled the outbreak curve of COVID-19 cases, in Kano, Nigeria from 11 to 30 April 2020. We estimated the number of under-ascertainment cases using the maximum likelihood estimation. We adopted the SI estimated for Hong Kong as approximations of the unknown SI for COVID-19 in Kano to estimate the a. We use ARIMA model to provide a short term (15 days) prediction of the COVID-19 cases in Kano, Nigeria.
Results: We revealed that the initial growth phase mimic an exponential growth pattern. We found that the under-ascertainment was likely to have resulted in 213 (95% CI: 106−346) unreported cases from 22 to 27 April 2020. The reporting rate after 27 April 2020 increase up to 10-fold compared to the scenario from 22 to 27 April 2020 on average. We estimated the c of COVID-19 in Kano as 2.74 (95% CI: 2.53−2.96). We forecasted that the total number of COVID-19 cases in Kano to be 1067 (95% CI: 883, 2137) by June 6, 2020.
Conclusion: The under-ascertainment likely exists during the fourth week of April, 2020 and should be regarded in the future analysis/investigation.
Coronaviruses are a group of related Ribonucleic acid (RNA) viruses that belongs to the Coronaviridae family (and the order Nidovirales) and widely disseminated in human beings (Huang et al., 2020). Most of the coronavirus infections in human have mild symptoms. The outbreaks of the two other coronaviruses (known as beta-coronaviruses), which include severe acute respiratory syndrome coronavirus (SARS-CoV) and Middle East respiratory syndrome coronavirus (MERS-CoV), have caused more than 10,000 cumulative cases in the past two decades, with the death rates of about 10% for SARS-CoV and 37% for MERS-CoV (Huang et al., 2020). The novel coronavirus disease 2019 (named COVID-19) started in Wuhan, Hubei province of China and spread worldwide, have been declared a Public Health Emergency of International Concern by the WHO on January 30, 2020 (WHO, 2020a), and later named the 1st pandemic caused by coronaviruses on March 11, 2020 (WHO, 2020b). As of June 3, 2020, COVID-19 affected over 6.5 million people with more than 386000 fatalities worldwide (WHO, 2020c).
Nigeria has reported its first (imported) case of COVID-19 on February 27, 2020 following the case definition by the NCDC (NCDC, 2020; Ohia, 2020). After which community transmission takes place due to inadequate contacts tracing from index case and lack of early closure of boarders to prevent further spread. The fact that the control of COVID-19 pandemic rely heavily on a country’s health care system. Nigeria is currently witnessing a rapid increase of COVID-19 cases probably due to the poor health care system, making it more vulnerable to the virus especially with population of over 200 million people (the highest in Africa). In northern region, Kano state has confirmed its first case of COVID-19 on April 11, 2020 (NCDC, 2020), and since then there might have been issues of under-ascertainment that exists roughly from 22 to 27 April 2020. This is likely due to the lack of sufficient health care facilities (such as test kits, gowns, and facemasks), limited diagnostic testing of suspected patients, and some other unknown reasons. Being the commercial center and the most populace state in Nigeria (with more than 10 million people), Kano is likely the most vulnerable for COVID-19 in northern Nigeria (Gilbert, 2020). As of June 3, 2020, there have been 970 cases of COVID-19 infections confirmed in Kano, Nigeria including 45 deaths (NCDC, 2020). Further the fact that few COVID-19 diagnostic testing was done in Nigeria. In particular, As of May 26, 2020 only about 69,801 people were tested throughout the country (NCDC, 2020). This together with the fact that autopsies and testing of deceased individuals are not generally carried out in the country (in some cases, for traditional or religious reasons), clearly suggests a gross under-ascertainment of the true scenario of the pandemic in the country.
Recently, there were numerous researches focusing on mathematical and statistical modelling to study the dynamics transmission of COVID-19 pandemic since its emergence in Wuhan, China (Li, 2020; Zhao et al., 2020a; Zhao et al., 2020b; Ngonghala et al., 2020; Eikenberry et al., 2020; Tang et al., 2020; Wu et al., 2020; Musa et al., 2020; Gilbert et al., 2020; Lin et al., 2020). Some of these studies focused on estimation of basic reproduction number by using the serial intervals and intrinsic growth rate (Zhao et al.,2020a; Zhao et al., 2020b) or using ordinary differential equations and Markov Chain Monte Carlo methods (Ngonghala et al., 2020; Eikenberry et al., 2020; Tang et al., 2020; Lin, 2020). However, few studies have been done to understand the transmission of COVID-19 pandemic in Africa (Gilbert et al., 2020; Musa et al., 2020).
In this study, we aim to investigate the epidemiological patterns, and estimate the number of under-ascertainment cases and of the COVID-19 outbreak in Kano, Nigeria. We hope our results in this study will be useful to inform the world community of the under-ascertainment issues and the value of in order to help to curtail the spread of the virus. In addition, our study will make a short-term forecast of COVID-19 cases in order to predict possible scenario and informed decision makers in the country about the importance of sustaining stringent measures as recommended by the WHO and other health related organizations as the virus is yet to have effective treatment or vaccination. All measures are currently directed primarily to non-pharmaceutical interventions (NPIs), like social (physical) distancing, community lockdown, quarantine of suspected cases, contact tracing, isolation of confirmed cases and the use of facemasks in general public.
According to the NCDC report, the total cumulative number of COVID-19 cases in Kano stand at 73 between 22 to 24 April 2020, and stand at 77 between 25 to 27 April 2020 (after addition of four new cases), i.e., no new case was reported between 22 to 24 April 2020, as well as between 25 to 27 April 2020, which appears weird considering the rapid increase of the outbreak curve since the index case on 11 April 2020 in Kano (NCDC, 2020). We presume that the COVID-19 cases in Kano were under-ascertained probably from 22 to 27 April 2020. In this paper, we estimate the number of under-ascertainment cases and of COVID-19 in Kano, Nigeria from 22 to 27 April 2020 based on the available data during the early phase of the epidemic.
We used the time series data for cumulative confirmation compiled by the NCDC (2020) from 11 April to 30 April 2020. All cases data were confirmed from the laboratory according to the definition of COVID-19 cases by the NCDC which is available at https://covid19.ncdc.gov.ng/report/. The data chosen for this study was from 11 to 30 April 2020 instead of including up to the present date, this is due to the fact that the diagnostic testing have improved significantly since the end of April, 2020, and also sufficient personal protective equipment’s (PPEs) were provided to the health workers. We suspected that there was a number of under-ascertainment of COVID-19 cases, denoted by, likely from 22 to 27 April 2020. The cumulative confirmation of the total number of cases, represented by Ci, of the i-th day since 11 April 2020 is the summation of the cumulative cases reported, represented by , and cumulative unreported cases, represented by . Thus Ci = + , where is observed from the data, and is 0 for i before 22 April and for i after 27 April 2020.
We adopted the approach used in previous works (Zhao et al., 2020a; Zhao et al., 2020b; De Silva, 2009) and modelled the outbreak curve. The series, Ci, is used as an exponential growing Poisson process. The data from 22 to 27 April 2020 seems constant probably due to the poor testing facilities and some other unknown reasons, thus, these data were ignored in exponential growth fitting. The and the intrinsic growth rate (represented by γ) of the exponential growth were to be estimated using the log-likelihood estimation (ℓ), from the Poisson priors. We estimated the 95% confidence interval (95% CI) of based on the profile likelihood estimation technique with cutoff threshold computed by a Chi-square quantile, given by χ2pr = 0.95, df = 1 (Fan & Huang, 2005). We obtained the R0 based on the estimation of γ following similar approach as in (Zhao et al., 2020a; Zhao et al., 2020b; Musa et al., 2020). Therefore, given R0 as R0 = 1/(−γ) with 100% susceptibility presumed at the early stage for COVID-2019 outbreak. Also, the function (∙) denote the moment generating function of the probability distribution (i.e., Laplace transform) for the serial interval (SI) of the disease which is represented by h(), where is the SI (Zhao et al., 2020a; Zhao et al., 2020d; Wallinga & Lipsitch, 2007).
Since the transmission chain of COVID-2019 in Africa still remains fully uncovered, we adopted the SI information of COVID-19 from previous works, see for instance (Du et al., 2020; Nishura et al., 2020). The h(k) were modelled as a lognormal distribution with mean of 5.0 days and standard deviation (SD) of 1.9 days (Du et al., 2020; Nishura et al., 2020). It is important to note that slightly changing the SI information may not affect our main results and conclusion. In this work, we also aimed to evaluate the trends of the daily number of cases, in this case, represented by for the i-th day, and given as Ci = Ci−1 + . For the details of the simulations framework see (Zhao et al., 2020b).
Furthermore, we employed Autoregressive Integrated Moving Average (ARIMA) model (a time series model), which has been used in previous study to make short-term prediction (Maleki, 2020). The model consists of three parameters: p (autoregressive order), d (the degree of differencing) and q (moving average order). We estimated parameters for ARIMA model according to best AIC value (Akaike, 1998). The 95% confidence intervals are obtained based on the assumption that residuals of the model are normally distributed. Here, we only took the confidence interval of non-negative value here.
In Fig. 1a, we estimated the total number of COVID-19 under-ascertainment cases as 213 (95% CI: 106 − 346). Clearly, this result was notably greater than zero. Our result insinuated the existence of under-ascertainment cases likely from 22 to 27 April 2020. After considering the effect of under-ascertainment, we also estimated the R0 as 2.74 (95% CI: 2.53 − 2.96), see Fig. 1b, which is largely consistent with previous findings (Zhao et al., 2020a; Zhao et al., 2020b; Musa et al., 2020). In Fig. 2a, with the value of R0 as 2.74 and as 213, the exponential growing framework fitted the cumulative number of COVID-19 cases (Ci) eloquently well, considering the McFadden’s pseudo-R-squared value of 0.99. Figure 2b showed the fitting results using the exponential growth of the daily number of COVID-19 cases in Kano, Nigeria.
The estimation of rely hugely on the SI of COVID-19. In this study, we adopted the SI information of the COVID-19 from previous works (Du et al., 2020; Nishura et al., 2020) as approximations to that of Kano, considering the fact that the estimation of SI requires sufficient time. This is because the computation of SI needs the knowledge of disease transmission chain which requires adequate number of patient samples and time for follow-up (Cowling, 2009), and thus this is difficult to be done in a short period. However, using the SI of Hong Kong as approximation could provide a reasonable insight into the transmission potential and features of COVID-19 in Kano at the early phase of the outbreak. We found that changing the mean and SD of SI very slightly would not change our main results. The R0 of COVID-19 in Kano was estimated at 2.74 (95% CI: 2.53 − 2.96), and this is largely consistent with previously computed R0 (Zhao et al., 2020a; Zhao et al., 2020b).
In Fig. 2b, we provided the simulated daily number of COVID-19 cases (). We found that, the parameter equaled the observed daily number of cases after 27 April 2020, but was larger than the observations of cases from 22 to 27 April 2020. Our finding highlight that the under-ascertainment probably exists in the fourth week of April 2020. Thus, the reporting rate was estimated after 27 April 2020, which was found to have increased by up to 10-fold (95% CI: 5–16) compared to the scenario before 27 April 2020 on average. One possible reasons was due to the poor testing facilities for diagnosing daily new cases, and lack of adequate PPEs for the frontline health workers. The newly reported daily cases started increasing very fast after 27 April 2020, see Fig. 2b.
Under-ascertainment is difficult to be ameliorate for some diseases such as Infectious Intestinal Disease (IID), but that may not be the case for some other diseases such as COVID-19 (Sethi et al., 1999). In general, solving the problem of under-ascertainment, cases and controls need to be appropriately included in cases-control studies. In addition, knowing the exact number of ascertainment cases or maintaining a low risk under-ascertainment cases is very crucial in controlling disease pandemic (https://catalogofbias.org/biases/ascertainment-bias/). Considering the general asymptomatic (mild) nature of the COVID-19 infection, it is possible that different reporting controls have different criteria for finding the kind of strategies to be used in order to avoid or reduce under-ascertainment issues. We assert that our estimates should be considered for future analysis /investigation. Furthermore, estimation of key epidemiological parameters in populations during disease epidemics by using routine data requires knowledge of when, where and to what extent these data represent the true scenario of disease, and in some instances it is necessary to make some adjustment in order to avoid underestimation. Multiplication factors can also be used to adjust notification and surveillance data to provide more realistic estimates of incidence (Gibbons et al., 2014).
In Fig. 3a, we present the short-term time series prediction of the COVID-19 cases in Kano, Nigeria. The auto-correlation function (ACF) plots of the residuals presented in Fig. 3b indicate that the fitted models seems very appropriate. The histograms of the residuals based on the estimated densities are superimposed in Fig. 3c and show the good performance of the estimated models to the stationary series of the total confirmed and recovered number of cases. We conducted the first-order difference and Augmented Dickey-Fuller Test to the data. Data is proved to be the stationary time series (p value 0.0173). According to AIC, the best model is ARIMA (2,1,0). The Q-Q plot of residual (Fig. 1) revealed that the residuals were normally distributed, which means that the residuals are basically white noises. Further, we forecasted that the total number of COVID-19 cases will be 1067 (95% CI: 883, 2137) by June 6, 2020.
Under-ascertainment have probably exists and resulted in 213 (95% CI: 106 − 346) unreported cases likely from 22 to 27 April 2020. The reporting rate after 27 April 2020 was likely to have increased up to 10-fold (95% CI: 5–16) compared with the scenario from 22 to 27 April 2020 on average, and it should be regarded in future analysis/investigation. We estimated the of COVID-19 in Kano as 2.74 (95% CI: 2.53 − 2.96). Using ARIMA model, we forecasted that the total number of COVID-19 cases will be 1067 (95% CI: 883, 2137) by June 6, 2020.
R0: Basic reproduction number; SI: Serial interval; CI: Confidence interval; : number of under-ascertainment of COVID-19 cases; Ci: Cumulative number of cases; : Summation of the cumulative reported cases; : cumulative unreported cases; γ: Intrinsic growth rate; ℓ: log-likelihood estimation; (∙): moment generating function of the probability distribution for the serial interval; h(): Probability distribution for the serial interval; h(k): Lognormal distribution; : daily number of cases; p: Autoregressive order; d: Degree of differencing; q: Moving average order; AIC: Akaike information criterion
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Availability of data and materials
All data are publicly available at https://covid19.ncdc.gov.ng/report/.
Competing interests
All authors declare that they have no competing interests.
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Authors’ contributions
Conceptualization: Salihu S Musa, Shi Zhao, Nafiu Hussaini, Zian Zuang, Maggie H Wang & Daihai He; Formal analysis: Salihu S Musa, Shi Zhao, Nafiu Hussaini, Zian Zuang, Maggie H Wang & Daihai He; Writing – original draft: Salihu S Musa, Shi Zhao, Nafiu Hussaini, Zian Zuang, Maggie H Wang & Daihai He; Writing – review & editing: Daihai He.
Acknowledgements
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Authors’ information
aDepartment of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China. bDepartment of Mathematics, Kano University of Science and Technology, Wudil, Nigeria. cJC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China. dShenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China. eDepartment of Mathematical Sciences, Bayero Unuversity, Kano, Nigeria. Corresponding author: [email protected] (DH).