Age-Structured Epidemic: McKendrick–Von Foerster

PDE model: ∂n/∂t + ∂n/∂a = −(μ(a)+λ(a,t))·n — age-dependent infection and mortality
The McKendrick–Von Foerster equation (1926/1959) tracks population density n(a,t) by age a and time t. Extended to epidemics: susceptibles S(a,t), infected I(a,t), recovered R(a,t) with age-dependent rates. The force of infection λ(a,t) = ∫ β(a,a')I(a',t)da' couples age groups through a mixing matrix β. Age structure profoundly affects herd immunity threshold and optimal vaccination strategies.
Age Distribution at t
Epidemic Curves (total S,I,R)
Attack rate: — | Peak I: — | Herd immunity: —%