Summary
SIR and related compartment models predict epidemic dynamics and the effect of interventions.
In depth
SIR: dS/dt = -βSI, dI/dt = βSI - γI, dR/dt = γI. R0 = β/γ. Extensions add exposed (SEIR), age structure and networks. Models inform vaccination targets and lockdown decisions but depend on assumptions.
Models are only as good as their assumptions. Compartmental models can include vaccination and waning immunity. Agent-based models simulate individuals.
Key idea: models explore scenarios, they are not crystal balls.
In the SIR model, S is susceptible, I infectious and R recovered; beta is the transmission rate and gamma the recovery rate (1 over infectious period). The epidemic peaks when S falls to gamma over beta, which corresponds to 1 over R0, the herd immunity threshold. SEIR adds a latent period, and agent-based models track individuals and networks.
Kermack and McKendrick's 1927 paper started the theory. Models fit to data forecast peaks, test control measures such as vaccination, school closure and testing, and estimate the impact of reducing contacts. Limitations include uncertain parameters, behaviour changes and heterogeneity, so they give scenarios rather than predictions.
Frequently asked questions
What is Mathematical Epidemiology?
SIR and related compartment models predict epidemic dynamics and the effect of interventions.
Which area of biology covers Mathematical Epidemiology, and how advanced is it?
Mathematical Epidemiology is one of the 52 topics in Immunology & Disease. It is rated Advanced, so it suits learners who want specialist depth. Related topics in this area include Basic Reproduction Number, Infectious Disease Transmission, Epidemiology.
Why does Mathematical Epidemiology matter?
Models were important in COVID-19 policy, and they illustrate how simple equations capture epidemic dynamics.
Can you give an example of Mathematical Epidemiology?
The Kermack-McKendrick model dates to 1927.
What should I learn before Mathematical Epidemiology?
Work through the Beginner topics in Immunology & Disease first, such as Immune System, Viruses, Innate Immunity, then return to Mathematical Epidemiology. Advanced topics assume the Intermediate vocabulary.
What topics are related to Mathematical Epidemiology?
The closest topics to Mathematical Epidemiology are Basic Reproduction Number, Infectious Disease Transmission, Epidemiology, Vaccines. Comparing them side by side is a good way to see how the ideas connect.
How can I check that I understand Mathematical Epidemiology?
Read the summary and the in-depth section, then use the quick check on the interactive lesson for Mathematical Epidemiology. To practise the whole of Immunology & Disease, use the Immunology & Disease quiz.
How is Mathematical Epidemiology different from Basic Reproduction Number?
Mathematical Epidemiology: SIR and related compartment models predict epidemic dynamics and the effect of interventions. Basic Reproduction Number: R0 is the average number of new infections one case causes in a fully susceptible population. Read both side by side and note what each one explains.
How should I study Mathematical Epidemiology step by step?
First, read the summary and write the definition in your own words. Second, read the in-depth section and note any example. Third, compare it with Basic Reproduction Number and explain the difference aloud. Finally, take the Immunology & Disease quiz and come back to this page for any question you miss.