Fig. 1

The decrease and increase of the infected population depending on the newly infected population I(t,0). Let a _† =1, γ(a)≡1 and X∈(0,1) be a uniform random variable. For I(t,0)=U(t)+0.001X(>U(t)), the infected population I(t,a) increases and will diverge (upper two figures). For I(t,0)= max(U(t)−0.001X,0)(<U(t)), the infected population I(t,a) decreases and will converge to 0 (lower two figures)