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U.S. Department of Energy
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The Differential Equations That Model Diseases

Technical Report ·
DOI:https://doi.org/10.2172/1606334· OSTI ID:1606334
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

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