Skip to content
Menu
中文Sign in
← All questions

What are the differential equations of the basic SIR model shown here?

The basic SIR model is written as a system of ordinary differential equations describing transfers between compartments: susceptibles decrease by infection, infecteds gain infections and lose cases by recovery or removal, and recovereds increase by removal from the infected class. The equations are dSdt=−βSI\frac{dS}{dt}=-\beta SI, dIdt=βSI−γI\frac{dI}{dt}=\beta SI-\gamma I, and dRdt=γI\frac{dR}{dt}=\gamma I.

Conditions

  • The population is modeled as well mixed.
  • The dynamics are represented by global rate equations rather than spatially resolved equations.

Reasoning, step by step

  1. Identify the three compartments: S(t)S(t) for susceptible, I(t)I(t) for infected, and R(t)R(t) for recovered or removed.
  2. Write the rate of change for S as the negative infection term: dSdt=−βSI\frac{dS}{dt}=-\beta SI.
  3. Write the rate of change for I as new infections minus removals: dIdt=βSI−γI\frac{dI}{dt}=\beta SI-\gamma I.
  4. Write the rate of change for R as the removal flow from infected individuals: dRdt=γI\frac{dR}{dt}=\gamma I.

Example

The board displays the system dSdt=−βSI\frac{dS}{dt}=-\beta SI, dIdt=βSI−γI\frac{dI}{dt}=\beta SI-\gamma I, dRdt=γI\frac{dR}{dt}=\gamma I, and the lecturer calls them simple rate equations similar to chemical kinetics.

Common misconceptions

  • Assuming the model includes spatial resolution or contact networks.
  • Confusing the removal rate with the transmission rate.

Watch the explanation

0:10 – 2:30Watch this moment ↗

Explore next

Answers are generated from source material and independently checked. Consult the original video or creator if something is unclear.