The Differential Equations That Model Diseases
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
In this brief tutorial, I will describe the simplest way of modeling a deadly infectious disease, such as COVID-19. I will show that at early times, the disease grows exponentially, but at late times, falls off like a Bell curve. I will solve the equations numerically with Python. A common mathematical model is the so-called compartmental model, where diseases can move people between "categories" such as healthy, infectious, or truly sick. This is a large, well established field and there are many good resources on this topic. I started with the SIAM review article The mathematics of infectious diseases. However, there are many excellent textbooks and more modern reviews as well.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- DOE Contract Number:
- 89233218CNA000001
- OSTI ID:
- 1606334
- Report Number(s):
- LA-UR--20-22439
- Country of Publication:
- United States
- Language:
- English
Similar Records
Differential contagiousness of respiratory disease across the United States
Distributed Delay Differential Equation Representations of Cyclic Differential Equations
Ethical considerations in infectious disease modelling for public health policy: the case of school closures
Journal Article
·
Thu Sep 21 20:00:00 EDT 2023
· Epidemics
·
OSTI ID:2008284
Distributed Delay Differential Equation Representations of Cyclic Differential Equations
Journal Article
·
Mon Aug 23 20:00:00 EDT 2021
· SIAM Journal of Applied Mathematics
·
OSTI ID:1836986
Ethical considerations in infectious disease modelling for public health policy: the case of school closures
Journal Article
·
Thu Sep 25 20:00:00 EDT 2025
· Interface Focus (Online)
·
OSTI ID:3001289