Figure 2.

Infectious curves for different values of k and fixed β for the negative binomial distribution (NBD) model (Equation (4)). The values of k are shown in the legend. The other parameters are as follows: $\beta =0.5$, $\frac{1}{\alpha }=7$ days, $\frac{1}{\gamma }=5$ days and $\frac{1}{\mu }=70$ years. The initial conditions are $S(0)=99,999,E(0)=0,I(0)=1$ and $R(0)=0$. The top curve in (A) is the infectious curve of the homogeneous-mixing model with a frequency-dependent transmission term [4]; it is compared to the infectious curves of the NBD model; (B) The long trend of the infectious curves of the NBD model with $k=0.0001$ and $k=0.001$.