Modeling the effect of non-pharmaceutical measures and vaccination on the spread of two variants of COVID-19 in India

Abstract

An RNA virus, SARS-CoV-2 is capable of mutation, and vaccines developed to combat its earlier strains are comparatively less effective against its new emerging variants of concern. Therefore, it is proposed to formulate a two-strain COVID-19 deterministic model that incorporates non-pharmaceutical preventive strategies along with an imperfect and leaky vaccine. The control reproduction number (denoted by Rc) of the model is calculated using the next-generation matrix method. Rigorous model analysis elucidates that its disease-free equilibrium (DFE) is locally asymptotically stable when Rc<1. Using the central manifold theorem, the occurrence of subcritical bifurcation is proved when the relevant conditions required for its existence hold. However, the model exhibits transcritical bifurcation when the vaccinated population does not get infected. Additionally, the DFE point of this reduced case is globally asymptotically stable when Rc is sufficiently less than 1. Moreover, the model is analyzed to reveal the presence and global asymptotic stability (using the Lyapunov function approach) of endemic equilibrium points. The introduced model is calibrated and cross-validated with observed daily and cumulative data of Delta (1 April 2021 to 30 November 2021) and Omicron variant (1 December 2021 to 15 February 2022). Data fitting depicts that competitive exclusion exists among the variants as the Omicron variant tends to extinct other variants prevalent in that duration within a restricted timeframe. The model is examined, using the known and calibrated parameter values corresponding to the Omicron variant, to examine the impression of vaccination, quarantine, isolation, and lockdown on the prevalence of illness in India. The impact of fluctuations in vaccine and infection-induced immunities on daily and cumulative cases is studied. It is observed that vaccine-derived immunity exerts a greater influence on the current wave of the pandemic as compared to subsequent waves while natural infection immunity has a significant impact on future waves of the pandemic. Furthermore, there is a possibility of a future wave of the Omicron variant but with a relatively low peak. The minimum percentage of vaccinated people required to reach community-wide herd immunity has been estimated with respect to vaccine efficacy and various non-pharmaceutical control parameters.