Mathematical analysis and simulation of COVID-19 model with booster dose vaccination strategy in Bangladesh

Abstract

The control of COVID-19 transmission remains a crucial issue despite the administration of multiple doses of vaccines, given the ongoing emergence of new variants. This study proposes a mathematical model of COVID-19 with multiple doses of vaccinations. We find disease-free equilibrium (DFE) and disease-endemic equilibrium (DEE) and perform their stability analysis to explore in which parameters space the disease will be fade-out or persists in the population. This study derives mathematical expressions for the basic reproductive numbers (R0) using the Next-Generation Matrix method. Using surface and contour plots, we brought to light the exciting consequences of disease transmission rate and other parameter values on the basic reproduction number (R0). It demonstrates that the disease-free equilibrium point is locally stable when R0 < 1, whereas the disease-endemic equilibrium point is locally stable for R0 > 1. We also perform bifurcation analysis to demonstrate in which conditions the disease will be stable or unstable when R0 = 1. Numerical simulations show that increasing first dose vaccination rate is more effective than second and booster doses vaccination rate for reducing the number of asymptomatic and symptomatic cases in Bangladesh. We use COVID-19 incidence data from WHO between January and December 2022 and estimate parameters using the least-squares technique. We perform the sensitivity index of symptomatic and asymptomatic cases to identify the most significant parameter for disease outbreaks and found that transmission rate had the highest impact on disease prevalence. This research provides insight to prevent and control of COVID-19 transmission with booster-dose vaccination in Bangladesh.