Recently, my colleague, Professor Liang Kong, gave a very interesting talk at the Conference on Security and Information Technologies with AI, Internet Computing and Big-data Applications (SITAIBA 2023(link is external)). His talk, Prediction of the Prevalence of COVID-19 Using Epidemic Differential Equations and Deep Learning Network, was based on his joint work with UIS CSC faculty, Yanhui Guo and Chung-wei Lee (“Enhancing COVID-19 Prevalence Forecasting: A Hybrid Approach Integrating 2 Epidemic Differential Equations and Recurrent Neural Networks,” this paper will be abbreviated as KGL thereafter in this blog post).

This work has been reported in a press release "Faculty Revolutionizing Science: CHST's Breakthroughs in AI and Computational Research" (This work was funded by SHIELD Illinois, an U of Illinois System’s initiative to make the innovative saliva-based COVID-19 widely available in the state of Illinois–see our reporting here, "Leavaging mathematical modeling and deep learning to predict the spread of COVID-19").

The purpose of this post is to provide additional details on KGL and to help beginning students gain a deeper appreciation of the fascinating concepts underlying this interesting research.

1. The Big Picture: Studying the Prevalence of Infectious Diseases

Prevalence, in the present context, refers to the proportion of a population that is affected by a specific disease at a given point in time. In the context of COVID-19, it is like taking the pademic’s temperature. By studying prevalence, we can see whether things are heating up or cooling down, predict future outbreaks, and even identify areas needing extra help. This knowledge helps guide important disease mitigation strategies. It helps us to understand how different groups are affected and ensure everyone has access to the care they need.

2. KGL's Approach and Its Novelties

In their paper, Kong, Guo and Lee use a hybrid model, combining differential equations and neural networks to study the spread of COVID-19.

Specifically, KGL’s model is based on the SIRD model. Here, SIRD stands for Susceptible, Infected, and Recovered, and Deceased. The SIRD is an extension of the SIR model, a classic and fundamental model used in epidemiology and proposed by W.O. Kermack and A.G. McKendrick in 1927 ("A contribution to the mathematical theory of epidemics"); it has been cited 14,000+ times according to Google Scholar. The difference in the two models is in “D” (SIRD includes the deceased population). Both the SIR and the SIRD models are a set of differential equations, and they have been used to study the spread of various infectious diseases, contributing a significant theoretical foundation for public health interventions.

The SIRD model, while effective, lacks consideration for human mobility effects and contact structures. These factors are intricate and complex, and their inclusion would render the model mathematically challenging to handle, according to the traditional approach of mathematical modeling. Rather than directly modeling these intricate factors, KGL utilizes data-informed learning (using neural networks) to estimate their impacts and integrate them into a modified version of the SIRD model.

KGL shows that their model surpasses standard temporal models in three-day ahead predictions, underscoring its efficacy and potential impact in the ongoing battle against the pandemic, a very promising result!

3. Conclusion

KGL is an example of AI-informed mathematical modeling, the intersection of math and AI that witnesses innovation and holds great promise. 

Dr. Kong is also interested in physics-informed machine learning. He is currently working with Chris Denq, one of our math majors. Chris was recently accepted into the UIS MAT Directed Research/Reading (DRR) Program.

Interested readers would also be interested in a recent paper by Dr. Kong: “Epidemic modeling using differential equations with implementation in R,” published in International Journal of Mathematical Education in Science and Technology. For details, please visit Dr. Kong's website. 

Dr. Kong is also interested in exploring how AI-generated content (AIGC) can improve mathematics and data science education. He was selected as one of the 2023-2025 Online, Professional, and Engaged Learning (OPEL) Faculty Fellows. He can be reached at lkong9@uis.edu. 

If you are interested in the intersection of math and AI, contact us! You may want to check out my recent talk on the mathematics and concepts behind large language models (aiming at beginners at undergraduate level).

(Dr. Hei-Chi Chan, MAT/PHI, hchan1@uis.edu, February 30, 2024)

Keywords: UIS Mathematical Sciences Department, UIS MAT Directed Research/Reading (DRR) Program, UIS College of Health, Science and Technology (CHST), Mathematical Modeling, artificial intelligence (AI), and COVID-19

Postscript. We have gathered some resources for readers who want to learn more about the topic.

• The SIR model: 
  • The MATH of Pandemics | Intro to the SIR Model (Dr. Trefor Bazett)
  • Oxford Mathematician explains SIR Disease Model for COVID (Tom Rocks Maths)
• Neural networks are a type of artificial intelligence that mimics the human brain's interconnected network of neurons. They process data using interconnected nodes in a layered structure, enabling computers to learn from data, make “intelligent” decisions or predictions, and solve complex problems.
  • But what is a neural network? (3Blue1Brown) 
• Physics-Informed Neural Networks
  • How Do Physics-Informed Neural Networks Work? (Jordan Harrod)

Physics-informed neural networks for fluid mechanics (Ricardo Vinuesa)