Studying Disease Reinfection Rates, Vaccine Efficacy and the Timing of Vaccine Rollout in the context of Infectious Diseases

Qatar has undergone distinct waves of COVID-19 infections, compounded by the emergence of variants, posing additional complexities. This research uniquely delves into the varied efficacy of existing vaccines and the pivotal role of vaccination timing in the context of COVID-19. Departing from conventional modeling, we introduce two models that account for the impact of vaccines on infections, reinfections, and deaths. Recognizing the intricacy of these models, we use the Bayesian framework and specifically utilize the Metropolis-Hastings Sampler for estimation of model parameters. The study conducts scenario analyses on two models, quantifying the duration during which the healthcare system in Qatar could have potentially been overwhelmed by an influx of new COVID-19 cases surpassing the available hospital beds. Additionally, the research explores similarities in predictive probability distributions of cumulative infections, reinfections, and deaths, employing the Hellinger distance metric. Comparative analysis, employing the Bayes factor, underscores the plausibility of a model assuming a different susceptibility rate to reinfection, as opposed to assuming the same susceptibility rate for both infections and reinfections. Results highlight the adverse outcomes associated with delayed vaccination, emphasizing the efficacy of early vaccination in reducing infections, reinfections, and deaths. Our research advocates prioritizing early vaccination as a key strategy in effectively combating future pandemics. This study contributes vital insights for evidence-based public health interventions, providing clarity on vaccination strategies and reinforcing preparedness for challenges posed by infectious diseases. The data set and implementation code for this project is made available at \url{https://github.com/elizabethamona/VaccinationTiming}.