Deterministic nonlinear epidemiological model for COVID-19 infection with double-dose vaccination

Abstract

COVID-19 remains relevant public health concern, and vaccinations play central role in reducing transmission and severity. While vaccination has been incorporated into several epidemic models, it is often represented as a single-dose process, with explicit modeling of double vaccination receiving limited consideration. Therefore, in this work, we have formulated and analyzed a new SEIR-type dynamic model that incorporates double-dose vaccination with a standard incidence force of infection to examine the spread of COVID-19 disease in Ghana. The proposed dynamic mathematical model, constructed within the framework of deterministic compartmental modeling, is new and different from those previously developed for COVID-19 infection. Analytical results include the derivation of the model equilibria, the basic reproduction number, and conditions for both the local and global asymptotic stability of the disease-free equilibrium point. Extensive analytical investigation of bifurcation analysis considered in this study demonstrates that complete vaccine efficacy leads to guaranteed forward bifurcation dynamics. The outcome of the bifurcation analysis is a significant contribution to this study, as it establishes the conditions under which forward or backward bifurcation can occur for the proposed model. Using appropriate data fitting techniques, the mathematical model is fitted to the real reported infected COVID-19 cases in Ghana from March 1, 2021, to May 9, 2023. In addition, we carried out global sensitivity analysis on the basic reproduction number by using the efficient Latin hypercube sampling (LHS) and partial rank correlation coefficient (PRCC) statistical methods. Results from the numerical illustrations indicate that enhanced vaccination efforts in the population decrease the prevalence of COVID-19 infection. The results highlight the need to incorporate the strategy of multi-dose vaccination into nonlinear epidemic models to facilitate sound policy decisions and to increase the preparedness against present and future infectious diseases.