Data sources

Daily counts of confirmed COVID-19 cases were extracted from publicly available data provided by the Nigeria Centre for Disease Control (NCDC) [4]. The NCDC daily situation reports include the number of local and imported cases. From 16 April 2020, all reported cases were classified as local cases by NCDC. This suggests that the travel ban imposed by the Nigerian Government on 20 March 2020 was effective. However, due to border porosity in Africa [Reference Okumu12], there is a high likelihood that some of the reported cases after 20 March 2020 were imported cases or some imported COVID-19 cases were unreported.

Effective reproduction number estimation

We adopted a likelihood-based approach that allows for the evaluation of the contributions of imported cases of COVID-19 [10, Reference Zhang11, Reference Liu13]. The locally acquired infections (L(t)) are assumed to be Poisson distributed with rate given as

(1)$$\lambda \lpar t \rpar = \left({R\lpar t \rpar \mathop \sum \limits_{s = 1}^t \psi \lpar s \rpar C\lpar {t-s} \rpar } \right)\comma \;$$

where C(t) is the number of daily new cases (locally acquired and importations) on day t = 0, …, T. ψ(s) is the distribution of the serial interval. We assumed that ψ(s) is lognormal distributed with a mean of 4.7 days and a standard deviation of 2.9 days [Reference Nishiura, Linton and Akhmetzhanov14]. The likelihood ${\cal L}$ of the observed times series of cases from day 1 to day T conditional on C(0) is thus given by

(2)$${\cal L} = \mathop \prod \limits_{t = 1}^T P\lpar {L\lpar t \rpar \semicolon \;\;\lambda \lpar t \rpar } \rpar $$

where P is the probability mass function of a Poisson distribution. The effective reproduction is estimated in a Bayesian framework using the Metropolis−Hasting Markov chain Monte Carlo (MCMC) method for sampling from the prior distribution of R(t). We assumed a non-informative prior, uniform (0, 5) for R(t) and performed 1 000 000 iterations with a burn-in of 10%.

The effective reproduction number shows how effective are the intervention strategies. The interventions put in place in Nigeria include disease surveillance to capture importations and local transmission, travel ban, contact tracing, isolation, quarantine and social distancing [4]. With a score of approximately 40% on the WHO Joint External Evaluation (JEE) mission report for Nigeria's capacity to prevent, detect and rapidly respond to public health risk [15], these metrics do not favour Nigeria's COVID-19 outcomes. Therefore, to obtain the proportion of symptomatic under-reported in the daily COVID-19 cases, we applied the delay-adjusted cases fatality ratio [Reference Riou16]. Detail explanation of the model can be found in Riou et al. [Reference Riou16].

Assumptions and sensitivity analysis

Previous work has shown that apporximately 50% of COVID-19 cases are asymptomatic [Reference Russell17]. Hence, we doubled the adjusted reported cases prior to estimating R(t). We used the following different assumptions about cases detection to test the sensitivity of the estimation of the effective reproduction number to assumptions.

1. (1) All importations are equally likely to cause infection as local cases.

2. (2) 40% of all importations contribute to transmission. Here, Im(t) = 40Im(t)/100. This is saying that the imported cases contributed less to the transmission and Im(t) is the number of imported cases per day.

In the case in which we assume 40% reporting proportion, we interpreted it as reporting probability to adjust for the under-reporting in COVID-19 cases as

(3)$${\rm report}\sim {\rm Binomial}\ \lpar {H\lpar t \rpar \comma \;p} \rpar $$

here, H(t) is the adjusted reported number of cases and p is the reporting proportion.

Modelling the dynamics of COVID-19

To forecast the number of COVID-19 cases, we estimate the basic reproduction number (R ₀) instead of R(t) using a compartmental model which was fitted in a Bayesian framework to the cumulative reported cases and deaths data. The compartmental model is a general SEIR-type model (S − susceptible, E – exposed, I – infectious and R − recovered). In the model, we divide the population into 10 compartments (see Table 1). The deterministic form of the model is given below

(4)$$\displaystyle{{{\rm d}S} \over {{\rm d}t}} = {-}\displaystyle{{\lpar {\beta \lpar t \rpar \lpar {I_1 + 2I_2 + I_3} \rpar } \rpar S} \over N}$$

$$\displaystyle{{{\rm d}E_1} \over {{\rm d}t}} = \displaystyle{{\lpar {\beta \lpar t \rpar \lpar {I_1 + 2I_2 + I_3} \rpar } \rpar S} \over N}-\sigma _1E_1$$

$$\displaystyle{{{\rm d}E_2} \over {{\rm d}t}} = \sigma _1E_1-\sigma _2E_2$$

$$\displaystyle{{{\rm d}I_1} \over {{\rm d}t}} = \rho _1\sigma _2E_2-\gamma _1I_1$$

$$\displaystyle{{{\rm d}I_2} \over {{\rm d}t}} = k_1C + \gamma _1I_1-\gamma _2I_2$$

$$\displaystyle{{{\rm d}I_3} \over {{\rm d}t}} = \lpar {1-\rho_1} \rpar \sigma _2E_2-\gamma _3I_3$$

$$\displaystyle{{{\rm d}R} \over {{\rm d}t}} = \rho _2\gamma _2I_2 + \gamma _3I_3$$

$$\displaystyle{{{\rm d}D} \over {{\rm d}t}} = \lpar {1-\rho_2} \rpar \gamma _2I_2$$

$$\displaystyle{{{\rm d}C} \over {{\rm d}t}} = k_1C$$

$$\displaystyle{{{\rm d}H} \over {{\rm d}t}} = \rho _3\lpar k_1C + \gamma _1I_1\rpar$$

where D is the death compartment, C is the importation compartment and H is the hospitalised compartment. The model is closed population model with no births or non-COVID-19 mortality.

Table 1. State variable description

The basic reproduction number estimated using the next-generation method [Reference Diekmann, Heesterbeek and Roberts18] is given as

(5)$$R_0 = \beta \left({\displaystyle{{\rho_1} \over {\;\gamma_1}} + \displaystyle{{2\rho_1} \over {\;\gamma_2}} + \displaystyle{{\lpar 1-\rho_1\rpar } \over {\;\gamma_3}}} \right)$$

The model parameters and estimates are described in Table 2. The analysis was performed in R [Reference Team19] and the codes for the estimation can be download from https://github.com/Shina-GitHub/COVID-19_Nig.

Table 2. Parameter descriptions

*CI-credible interval, estimated parameters are shown in bold. The state variables not shown in the table are set to zero.