A non-linear deterministic mathematical model for investigating the population dynamics of COVID-19 in the presence of vaccination

Abstract

COVID-19 has been a significant threat to many countries worldwide. COVID-19 remains a threat even in the presence of vaccination. The study formulates and analyzes a non-linear deterministic mathematical model to investigate the dynamics of COVID-19 in the presence of vaccination. Numerical results show that increasing the treatment rates with a relatively high vaccination rate might subdue the virus in the population. Also, decreasing the vaccine inefficacy increases the vaccine efficacy, and this may result in a population free of the virus. We further show that increasing the vaccination rate as against the vaccine inefficacy, the effective contact rate for COVID-19 and the modification parameter that accounts for increased infectiousness for COVID-19, the virus responsible for COVID-19 can be eradicated from the population. The sensitivity analysis results deduce that hidden factors are driving the model dynamics. These hidden factors must be given special attention and minimized. These factors includes the incubation periods for vaccinated and unvaccinated individuals, the fractions for vaccinated and unvaccinated individuals, and the transition rates for vaccinated and unvaccinated individuals