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Abstract Background Estimating real-world vaccine effectiveness is challenging as a variety of population factors can impact vaccine effectiveness. We aimed to assess the population-level reduction in cumulative severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) cases, hospitalizations, and mortality due to the BNT162b2 mRNA coronavirus disease 2019 (COVID-19) vaccination campaign in Israel during January–February 2021. Methods A susceptible-infected-recovered/removed (SIR) model and a Dynamic Survival Analysis (DSA) statistical approach were used. Daily counts of individuals who tested positive and of vaccine doses administered, obtained from the Israeli Ministry of Health, were used to calibrate the model. The model was parameterized using values derived from a previous phase of the pandemic during which similar lockdown and other preventive measures were implemented in order to take into account the effect of these prevention measures on COVID-19 spread. Results Our model predicted for the total population a reduction of 648 585 SARS-CoV-2 cases (75% confidence interval [CI], 25 877–1 396 963) during the first 2 months of the vaccination campaign. The number of averted hospitalizations for moderate to severe conditions was 16 101 (75% CI, 2010–33 035), and reduction of death was estimated at 5123 (75% CI, 388–10 815) fatalities. Among children aged 0–19 years, we estimated a reduction of 163 436 (75% CI, 0–433 233) SARS-CoV-2 cases, which we consider to be an indirect effect of the vaccine. Conclusions Our results suggest that the rapid vaccination campaign prevented hundreds of thousands of new cases as well as thousands of hospitalizations and fatalities and has probably averted a major health care crisis. 

In this paper, we explore the interplay of virus contact rate, virus production rates, and initial viral load during early HIV infection. First, we consider an early HIV infection model formulated as a bivariate branching process and provide conditions for its criticalityR₀ > 1. Using dimensionless rates, we show that the criticality conditionR₀ > 1 defines a threshold on the target cell infection rate in terms of the infected cell removal rate and virus production rate. This result has motivated us to introduce two additional models of early HIV infection under the assumption that the virus contact rate is proportional to the target cell infection probability (denoted by). Using the second model, we show that the length of the eclipse phase of a newly infected host depends on the target cell infection probability, and the corresponding deterministic equations exhibit bistability. Indeed, occurrence of viral invasion in the deterministic dynamics depends onR₀and the initial viral loadV₀. If the viral load is small enough, eg,V₀ ≪ θ, then there will be extinction regardless of the value ofR₀. On the other hand, if the viral load is large enough, eg,V₀ ≫ θandR₀ > 1, then there will be infection. Of note,V₀≈θcorresponds to a threshold regime above which virus can invade. Finally, we briefly discuss between‐cell competition of viral strains using a third model. Our findings may help explain the HIV population bottlenecks during within‐host progression and host‐to‐host transmission.