Modeling the Effects of Vaccination and Incubation on Covid-19 Transmission Dynamics

Abstract

The Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-COV-2) is a strain of Coron- avirus that causes Coronavirus Disease 2019 (COVID-19). The respiratory illness responsible

for the COVID-19 pandemic began in December 2019 in Wuhan city, China. Mathematical modeling has enabled the epidemiologist to understand the dynamics of the disease, its impact and future predictions in order to provide the governments with the best policies and strategies

to curb the spread of the virus. Deterministic susceptible-vaccinated-asymptomatic-infectious- recovered (SVAIR) model was formulated incorporated with time delay. The delay accounts

for the time lapsed between exposure and infectious period. In this study delay differential equations (DDEs) were formulated for the purposes of determining the stability of both disease free equilibrium (DFE) and endemic equilibrium point (EEP). It was found that the model was stable at both Disease Free Equilibrium (DFE) and Endemic Equilibrium Point (EEP) and was attained whenever R0 < 1 and R0 > 1 respectively. Calculations based on secondary data from various works of literature and the WHO dashboard was used. The basic reproduction number (R0) was computed using the next generation matrix (NGM) approach. The sensitivity analysis was carried out, it was found out that for all model parameters under study, the signs of the sensitivity indices of R0 were all negative. This implied that the model parameters under consideration contributed to the decline in the spread of the COVID-19 infection. It was noted that the rate of progression from asymptomatic to infectious δ1 was more sensitive than other model parameters since it contributed the most negative sensitivity index of -0.9265. Finally, numerical simulation was done using MATLAB for validation of the analytical results. Graphical representation shows that stability is achieved when τ >5 days and that R0 = 0.95 at DFE. Furthermore at EEP it was noted that R0 = 1.02 hence stability was guaranteed.