Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus

TL;DR

This paper extends SIR models to analyze COVID-19 spread, demonstrating how social measures impact disease dynamics and providing MATLAB tools for simulation to aid researchers.

Contribution

It introduces an extended SIR model incorporating social measures and offers MATLAB code, enhancing understanding and predictive capabilities of epidemic spread.

Findings

Social measures influence model parameters and disease outcomes.

Mathematical models can simulate effects of lockdowns and quarantine.

Model limitations depend on data accuracy and abstraction level.

Abstract

In this research, we study the propagation patterns of epidemic diseases such as the COVID-19 coronavirus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected-recovered (SIR) family of compartmental models. It is shown how social measures such as distancing, regional lockdowns, quarantine and global public health vigilance, influence the model parameters, which can eventually change the mortality rates and active contaminated cases over time, in the real world. As with all mathematical models, the predictive ability of the model is limited by the accuracy of the available data and to the so-called \textit{level of abstraction} used for modeling the problem. In order to provide the broader audience of researchers a better understanding of spreading patterns of epidemic diseases, a short introduction on biological systems modeling is also presented and the Matlab source codes for the simulations are provided online.