Table 1 Notation in the age-structured compartment model and corresponding PDEs

S(t,τ)

Susceptible

f

Fraction of asymptomatic infections

E(t,τ)

Exposed

1/γ

Incubation time

I _a (t,τ)

Asymptomatically infected

1/r _a

Duration of the asymptomatic period

I _s (t,τ)

Symptomatically infected

1/r _s

Duration of the symptomatic period

R(t,τ)

Recovered

1/μ

Duration of the temporary immunity

β(τ)

Age-dependent infection rate

after natural clearance of asymptomatic infection

λ(τ)

Age-dependent screening rate

1/r _PID

Duration of acute PID onset