Estimating the role of heterogeneities in the first-wave dynamics of COVID-19 in Nigeria.

Heterogeneity, defined as variation in individual-specific traits such as susceptibility or connectivity that are not subject to short-term change, can strongly influence epidemiological dynamics. In particular, it can reduce the effective reproduction number and the herd immunity threshold, thereby increasing the potential to control infectious disease outbreaks. However, heterogeneities at the epidemic level are extremely challenging to observe directly and difficult to estimate indirectly from epidemiological data. This study develops a methodology to estimate heterogeneities in COVID-19 transmission from under-reported incidence data. We estimate the parameters of a modified Susceptible Infected Recovered model using Bayesian Markov Chain Monte Carlo techniques, first testing the proposed method on simulated data to determine its effectiveness before applying it to incompletely reported time-series data from ten Nigerian states. We estimate the average basic reproduction number to be 1.360 (95% credible intervals (CrI): 1.356-1.366), the heterogeneity parameter representing the coefficient of variation in susceptibility to be 2.561 (95% CrI 2.247-2.884), and the reporting probability to be 0.005 (95% CrI 0.004-0.006). Information criteria indicated that the model with heterogeneity was better supported than a homogenous model. The herd immunity threshold with this estimated level of heterogeneity for the best model drops from 0.26 to 0.04 compared to the homogenous model and the percentage of individuals infected in the first wave from over 20% to about 8%. Underestimating the impact of heterogeneities would lead to overestimating the extent of interventions required to bring the effective reproduction number below 1, important when considering the design of control programs that combine different, partially effective interventions.