Computational applications of extended SIR models: A review focused on airborne pandemics

Epidemiological-Mathematical models are powerful tools for estimating the course of a pandemic and exploring different scenarios through pandemic intervention policies (PIPs). These models are commonly developed to provide decision-support tools for policymakers who are forced to make difficult decisions in a timely manner. Done properly, these models are able to provide a safe, quick, and cheap solution for this challenge. There are numerous types of mathematical models for epidemiological disease spread and control. However, in order to become applicative tools for decision-making, the modelers of these models are required to overcome three computational challenges: efficiently define the model, develop it as computer software, and fit it into historical data. Performed efficiently, one can use the obtained tool to explore possible scenarios and PIPs. In this paper, we present a critical review of models that extend the Susceptible–Infected–Recovered (SIR) model and explore the efficiency of these models, their software characteristics, and model performance on real-world data. We further provide a guide for epidemiological-mathematical model development and implementation, exploring several modeling approaches and their respective implementation options. Lastly, we outline the current trends, limitations, and opportunities in this field. In particular, we find that the spatial properties of a model play a critical role in its accuracy and ability to explain historical pandemic spread, especially in the context of airborne diseases. Moreover, we show that agent-based simulations are preferable over partial/ordinary differential solvers when considering a highly-realistic pandemic model or focusing on a relatively small population size.