Mrs Paustella G. AZOKPOTA has defended her master thesis on 29/12/2022
Topic: Assessing the dynamics of COVID-19 in the face of vaccination in African countries: mathematical analysis
ABSTRACT
Africa has been hit hard by the SARS-Cov-2, with considerable damages on global health and economics. The COVID-19 vaccine has been available in many African countries since 2020. However, the cost of implementation and vaccine skepticism might lead to the spread of the disease. Thus far, mathematical models have been helpful for understanding disease dynamics, and this study proposed an extended deterministic susceptible-exposed-infectious-recovered (SEIR)-type model including vaccination to examine the dynamics of the disease in ten (10) African countries that are Benin, Nigeria, Rwanda, South Africa, Lybia, Democratic Republic of Congo, Namibia, Gabon, Algeria and Kenya. We verified some basic properties of the model and also derived the control and basic reproduction number Rc and R0 respectively. We, further, utilized the Schur decomposition and the Castillo-Chavez method to investigate the local and global stability of the model at the disease-free equilibrium point under the condition Rc < 1. Moreover, we conducted a sensitivity and elasticity analysis in our COVID-19 Vaccination model to determine the potential importance of model parameters to disease transmission. In order to do so, we used certain parameter values from the literature corresponding to the third wave of the pandemic to compute the sensitivity and elasticity indices of the control reproduction number Rc with respect to the vaccination rate, the proportion of unvaccinated and vaccinated individuals following the control measure, the infection probabilities and the relative infectiousness related to the vaccinated individuals. As a result, the infection probabilities and the relative infectiousness of vaccinated individuals have a low effect on Rc. However, the vaccination rate, the percentage of unvaccinated people following the control measures and the one of the vaccinated have almost severe negative effects, with the effect of the unvaccinated people following the control measure being more significant than that of the vaccinated individuals. A 10% increase in those parameters lead to the highest indices in South Africa, Rwanda and lowest in Namibia and Democratic Republic of Congo. In addition, we performed a sensitivity analysis to examine the effect of parameter changes on the incidences and mortality. Our analysis found that the vaccination rate is the most sensitive parameter to the number of confirmed and deaths cases. As a means to stem the pandemic trend, it is necessary to maintain a high vaccination rate for the susceptible, the pre-symptomatic, the exposed, and those who have recovered, while the unvaccinated respect the control measures.
Keywords: mathematical model, COVID-19, vaccine, elasticity analysis, control reproduction number, sensitivity analysis, stability analysis