Figure 6.

(a) Point prevalence, I(t)/N, from the system in Eq. (1) with respect to time. (b) Distance D(t) kept by individuals through the epidemic. (c) Zoomed version of (b). (d) Transmission rate ${\beta }_3(t)$ $={\beta }_3(D(t))$ from Eq. (8). All plots in the figure consider ${\beta }_3(D)$ as the transmission rate. Black, red and blue curves correspond to $D_{\ast }=0.75(\mathrm{m})$, $D_{\ast }=1.05(\mathrm{m})$, and $D_{\ast }=1.35(\mathrm{m})$ respectively. These correspond to societies of small ([0, 100)), medium ([100, 120]) and large ($[120,\infty )$) natural-distance types respectively (see Table 1). The other parameter values were taken to be ${\beta }_{\ast }=0.5$; $\gamma =0.2$, $\nu =1$, ${\lambda }_1=0.03$, ${\lambda }_2=0.3$. The ${\mathcal{R}}_0$ value for each society type is: ${\mathcal{R}}_0=3.5$ (black), ${\mathcal{R}}_0=2.5$ (red), ${\mathcal{R}}_0=1.9$ (blue). The initial condition $D(0)=D_{\ast }$ was used for each type of society.