Let L i (t) be a nonnegative continuous random variable that represents the duration of contact exposure, starting at time t, required for susceptible i to become infected. We assume that L i (t) is distributed exponentially with mean 1/λ i (t), where λ i (t) represents the instantaneous force of infection applied to susceptible i at time t [55] [56] [57] . The probability that susceptible i, whose contact exposure has started at time t, will develop infection at time t + Δt is then given as