# Modeling the effect of the vaccination campaign on the Covid-19 pandemic

arXiv: https://arxiv.org/abs/2108.13908 · HTML: https://mlsanity.com/paper/2108.13908/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 48 references that are in the map.
- First posted on arXiv 27 Aug 2021.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems](https://mlsanity.com/paper/2011.10616/) (2020)
- [Solving Differential Equations Using Neural Network Solution Bundles](https://mlsanity.com/paper/2006.14372/) (2020)
- [Semi-supervised Neural Networks solve an inverse problem for modeling Covid-19 spread](https://mlsanity.com/paper/2010.05074/) (2020)

## Built on by (most cited first, 2 of 2)

- [Approaching epidemiological dynamics of COVID-19 with physics-informed neural networks](https://mlsanity.com/paper/2302.08796/) (2023)
- [First principles physics-informed neural network for quantum wavefunctions and eigenvalue surfaces](https://mlsanity.com/paper/2211.04607/) (2022)

## Abstract (arXiv)

Population-wide vaccination is critical for containing the SARS-CoV-2 (Covid-19) pandemic when combined with restrictive and prevention measures. In this study, we introduce SAIVR, a mathematical model able to forecast the Covid-19 epidemic evolution during the vaccination campaign. SAIVR extends the widely used Susceptible-Infectious-Removed (SIR) model by considering the Asymptomatic (A) and Vaccinated (V) compartments. The model contains several parameters and initial conditions that are estimated by employing a semi-supervised machine learning procedure. After training an unsupervised neural network to solve the SAIVR differential equations, a supervised framework then estimates the optimal conditions and parameters that best fit recent infectious curves of 27 countries. Instructed by these results, we performed an extensive study on the temporal evolution of the pandemic under varying values of roll-out daily rates, vaccine efficacy, and a broad range of societal vaccine hesitancy/denial levels. The concept of herd immunity is questioned by studying future scenarios which involve different vaccination efforts and more infectious Covid-19 variants.