a, The SEIRS model with demography. Rates are β (contact), σ (latency), γ (recovery), ω (loss of immunity), α (infection-induced death) and µ (birth and background death). b, The SEIRS trajectory of S (black), E (green), I (orange) and R (blue) and their endemic equilibrium values for R0 = 3, 1/γ = 14 days, 1/σ = 7 days, 1/ω = 1 year, 1/µ = 76 years, α = 0 and β = 0.21/day. A closer view of the I and E trajectories is shown with log y axis. Calculations over 1,000 time steps with S(0) = 0.999 and E(0) = 0.001, I(0) = R(0) = 0.