Fig. 2

Natural history of infective people and the variation of infectivity. In an actual situation, a person may be infected at some unknown point in time (Infection) and the infectivity to other people gradually increases up to its maximum around the time when the illness is well developed and recognized (Illness onset). It then is drained as the process of recovery from infection proceeds, which may be clinically observed by antipyresis (Antipyresis), though weak infectivity may remain. For simplicity, such time variation of infectivity is modeled using a piecewise constant function that takes a non-zero constant value λ₀ only from one point in time (labeled as Infectious) to another point near Antipyresis. The modeled infectivity function is temporally controlled by four period parameters: a (pre-symptomatic and non-infectious), b (pre-symptomatic and infectious), d (symptomatic and infectious) and e (extended infective after recovery)