On the mathematical modeling of COVID-19 pandemic disease with some non-pharmaceutical interventions: Nigerian case study

Abstract

This paper is devoted to deriving a mathematical model depicting the dynamics of COVID-19 infection and the inclusion of some essential features of the disease dynamics and Non - Pharmaceutical Interventions (NPIs), with Nigeria as a case study. The model is analyzed in a region where COVID-19 transmission is positively invariant. The time - independent COVID-19 absent and present equilibrium solutions are obtained to show that if the transmission threshold describing the COVID-19 spread, called the basic reproduction number Rcν is below unity, the COVID-19 - absent equilibrium is locally and globally asymptotically stable, leading to the elimination of the disease, while the COVID-19 present equilibrium is locally and globally asymptotically stable whenever Rcν is above unity, leading to the persistence of the disease. Data on COVID-19 disease prevalence in Nigeria published by the Nigerian Center for Disease Control (NCDC) as at July 31, 2020 is fitted to the model, which showed a good fit with low residual/error approximation. The fitted and estimated parameters are employed to estimate Rcν and it is observed that Rcν ≈ 3.186 with 95% Confidence Interval (CI : 2.186 - 4.186). This implies that a COVID-19 infected individual infects at least three people on the average. The associated confidence intervals of the fitted parameters are shown, while the sensitivity analysis of the model parameters of Rcν reveals that the effective COVID-19 transmission parameters β 1 , β 2 , β 4 , a and ω are most sensitive to Rcν . The sensitivity results show that human individuals in Nigeria needs to strictly make use of face mask, appear for proper screening and comply with other NPIs to minimize the disease. Further simulations of the fitted parameters showed that the infection peaks around 40 - 50 days but continue to rise further within 150 days. This predicts that in the absence of mitigation measures and urgent response from the Nigerian government and public health institutions, a second deadly wave of the pandemic is imminent.