Mathematical Analysis of the Dynamics of COVID-19 in the Face of Vaccination in African Countries

Abstract

(1) Background: The ongoing COVID-19 pandemic has posed significant global challenges; its impact in Africa, in particular, has been a subject of increasing concern. Vaccination against COVID-19 started in many African countries in 2020. Despite the remarkable progress made by a selected number of countries initiating vaccination campaigns in 2020, the global vaccination coverage against the targeted disease remains inadequate. This study aimed to assess the dynamics of COVID-19 in the face of vaccination in Africa. (2) Methods: We used an extended deterministic Susceptible-Exposed-Infectious-Recovered (SEIR)-type model stratified by vaccination status to mathematically analyze the effect of vaccination on the dynamics of COVID-19 in ten African countries, namely: Benin, Namibia, South Africa, Rwanda, Lybia, DRC, Nigeria, Algeria, Gabon and Kenya. We studied some basic properties of the model and derived the control and basic reproduction numbers R_c and R₀, respectively. We further utilized the Castillo-Chavez method to investigate the global stability of the model at the disease-free equilibrium point under the condition R_c < 1. In addition, we developed the expressions of the sensitivity and elasticity of the control reproduction number (R_c) with respect to vaccination coverage, level of adherence to control measures (ψ_u and ψ_v), infection probabilities, and relative infectiousness of different compartments of Infected. The model was fitted using cumulative daily COVID-19 case data corresponding to each country's third wave of the pandemic. The unknown parameters are estimated using the non-linear least square method. We used the resulting parameter values to compute the sensitivity and elasticity indices. (3) Results: The study demonstrates the importance of sustaining high vaccination coverage and control measures to mitigate COVID-19 transmission in Africa. Results identify vaccination rates and population compliance to control measures as most influential based on sensitivity analysis. (4) Conclusions: By generating evidence tailored to the African context, this research provides crucial insights to inform resource allocation and interventions to combat COVID-19, where needs are greatest.