Mathematical modeling of the combined influence of psychological fear and imperfect vaccination on the spectrum of COVID-19.

Numerous studies have demonstrated that during an epidemic, fear can significantly influence human behavior, leading to a reduction in new infection cases. This investigation introduces an SVIRS framework that accounts for the influence of psychological fear and imperfect vaccination. The dynamic interplay between these factors opens up novel avenues for analyzing disease progression and control. After formulating the model and establishing fundamental properties such as positivity and boundedness, we derive the basic reproduction number ℛ0 and identify equilibrium points. We prove the local and global stability of the disease-free equilibrium when ℛ0<1, we also prove that the unique endemic equilibrium is locally/globally asymptotically stable whenever ℛ0>1. The model is validated against reported data from Kerala between April 2021 to December 2021 to ensure its empirical applicability. A sensitivity analysis is conducted to identify the parameters that most significantly influence disease dynamics, followed by numerical simulations that validate and vividly illustrate the theoretical insight. It is found that fear factor when combined with the imperfect vaccination is capable to substantially suppress the peaks of the infection of COVID-19.