A bifurcation analysis and model of Covid-19 transmission dynamics with post-vaccination infection impact

• Published in: Healthcare analytics (New York, N.Y.) N.Y.), 2023-11, Vol.3, p.100157-100157, Article 100157
• Main Authors: Idisi, Oke I., Yusuf, Tunde T., Owolabi, Kolade M., Ojokoh, Bolanle A.
• Format: Article
• Language: English
• Subjects: Backward bifurcation; Control reproduction number; Coronavirus; Metzler matrix; Sensitivity analysis; Stability analysis
• ISSN: 2772-4425; 2772-4425
• DOI: 10.1016/j.health.2023.100157

SARS COV-2 (Covid-19) has imposed a monumental socio-economic burden worldwide, and its impact still lingers. We propose a deterministic model to describe the transmission dynamics of Covid-19, emphasizing the effects of vaccination on the prevailing epidemic. The proposed model incorporates current information on Covid-19, such as reinfection, waning of immunity derived from the vaccine, and infectiousness of the pre-symptomatic individuals into the disease dynamics. Moreover, the model analysis reveals that it exhibits the phenomenon of backward bifurcation, thus suggesting that driving the model reproduction number below unity may not suffice to drive the epidemic toward extinction. The model is fitted to real-life data to estimate values for some of the unknown parameters. In addition, the model epidemic threshold and equilibria are determined while the criteria for the stability of each equilibrium solution are established using the Metzler approach. A sensitivity analysis of the model is performed based on the Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCCs) approaches to illustrate the impact of the various model parameters and explore the dependency of control reproduction number on its constituents parameters, which invariably gives insight on what needs to be done to contain the pandemic effectively. The foregoing notwithstanding, the contour plots of the control reproduction number concerning some of the salient parameters indicate that increasing vaccination coverage and decreasing vaccine waning rate would remarkably reduce the value of the reproduction number below unity, thus facilitating the possible elimination of the disease from the population. Finally, the model is solved numerically and simulated for different scenarios of disease outbreaks with the findings discussed. •A deterministic model is formulated to offer insight into the transmission dynamics of Covid-19 disease.•The study discusses current findings on reinfection, vaccination, pre-symptomatic, and waning of vaccine immunity.•Metzler Approached is applied to determine the criteria for stability of each of the model equilibria.•The research finding reveals that increasing vaccination coverage and decreasing vaccine waning rate facilitate the elimination of Covid-19.•The model reveals the existence of backward bifurcation and conditions at which forward bifurcation will occur. which by inplication driving the reproduction number below unity may n