Assume that a given population consists of susceptibles (S), exposed (E), infectives (I), and recovered/immune (R) individuals. Suppose that S +E+

I + R = 1 for all time. A seasonally driven epidemic model is given by S˙ = μ(1−S)−βSI, E˙ = βSI −(μ+α)E, I˙ = αE−(μ+γ )I, where β =contact rate, α−1 =mean latency period, γ −1 =mean infectivity period, and μ−1 =mean lifespan. The seasonality is introduced by assuming that β = B(1 + Acos(2πt)), where B ≥ 0 and 0 ≤ A ≤ 1. Plot phase portraits when A = 0.18, α = 35.84, γ = 100, μ = 0.02, and B = 1800 for the initial conditions: (i) S(0) = 0.065,E(0) = 0.00075, I (0) = 0.00025, and (ii) S(0) = 0.038,E(0) = 3.27 × 10−8, I (0) = 1.35 × 10−8. Interpret the results for the populations.