Spatially-implicit modelling of disease-behaviour interactions in the context of non-pharmaceutical interventions

Figure 1.  Typical network distributions of susceptible contacts, $S$, neighbors who practice social distancing techniques, $S_p$ (as well as the respective calculations of the basic reproduction number) around the initial infection source, where all other members of the host population are fully susceptible (i.e. state $S$). The population size is $N=40000$, each individual has $n=4$ neighbors and model parameters are $\tau=0.75$ $day^{-1}$, $\tau_p=0.1$ $day^{-1}$, $\sigma=0.25$ $day^{-1}$, $\xi=\rho=0.5$ $day^{-1}$ and $\kappa=0.01$ $day^{-1}$

Figure 2.  The basic reproduction number as a function of social learning from protective contacts at a rate $\xi$, and from infectious contacts at a rate $\rho$, where the transmission rate to protective individuals is $\tau_p=0.1$ $day^{-1}$ (a) and $\tau_p=0.5$ $day^{-1}$ (b). In all these plots $N = 40000,n=4$, $\tau=0.75$ $day^{-1}$, $\sigma=0.25$ $day^{-1}$, $C_{S_pS_p}=0,C_{S_pS}=3/4$, $\kappa= 0$ $day^{-1}$ and $s_p=1/N$

Figure 3.  Infection peak versus initial distribution of single infected individuals with 4 state $S_p$ neighbors (a, d, g, j), time series for susceptible individuals who protect (b, e, h, k) and time series for infectious individuals (c, f, i, l), varying the number of 1 infected node plus 4 $S_p$ neighbors at the beginning of the outbreak (the rest of the population is fully susceptible). In (a to f) $\xi=0.25$ $day^{-1}$, $\rho=0$ $day^{-1}$; in (g to l) $\xi=0$ $day^{-1}$, $\rho=0.25$ $day^{-1}$; in (a, b, c and g, h, i) $\tau_p=0.6$ $day^{-1}$; in (d, e, f and j, k, l) $\tau_p=0.1$ $day^{-1}$. Model parameters common to all graphs are $\tau=0.8$ $day^{-1}$, $\sigma=0.25$ $day^{-1}$ and $\kappa=0$ $day^{-1}$

Figure 4.  Infection peak versus rate of disease transmission to protective individuals, $\tau_p$, and the initial distribution of single infected individuals with 4 state $S_p$ neighbors (and all other members of the host population are fully susceptible, $S$), where $\xi=0.25$ $day^{-1}$, $\rho=0$ $day^{-1}$ (a) and $\xi=0$ $day^{-1}$, $\rho=0.25$ $day^{-1}$ (b). Other model parameters are $\tau=0.8$ $day^{-1}$, $\sigma=0.25$ $day^{-1}$ and $\kappa=0$ $day^{-1}$

Figure 5.  Cumulative infections as a function of social learning from both infectious and state $S_p$ neighbors at rates $\rho$ and $\xi$, respectively, where the initial conditions are 1 infected node and 1 state $S_p$ neighbor while the rest of the population is fully susceptible (i.e. state $S$), and $\tau_p=0.1$ $day^{-1}$ (a), $\tau_p=0.2$ $day^{-1}$ (b), $\tau_p=0.3$ $day^{-1}$ (c). Other model parameters are $\tau=0.8$ $day^{-1}$, $\sigma=0.25$ $day^{-1}$ and $\kappa=0$ $day^{-1}$.

Figure 6.  Cumulative infections as a function of social learning from both infectious and state $S_p$ neighbors at rates $\rho$ and $\xi$, respectively, where the initial conditions are 1 infected node and 1 state $S_p$ neighbor while the rest of the population is fully susceptible (i.e. state $S$). Model parameters are $\tau=0.8$ $day^{-1}$, $\sigma=0.25$ $day^{-1}$ and $\kappa=0$ $day^{-1}$

Figure 7.  Infection peak versus the rate at which protective susceptible individuals forget, $\kappa$, varying regimes for social contagion parameters $\xi$ and $\rho$. Initial conditions are 1 infected node and 2 state $S_p$ neighbors while the rest of the population is fully susceptible (i.e state $S$). Other model parameters are $\tau=0.8$ $day^{-1}$, $\tau_p=0.3$ $day^{-1}$ and $\sigma=0.25$ $day^{-1}$

Figure 8.  Cumulative infections as a function of the initial number of state $S_p$ individuals and the time at which the infection is introduced, varying $\xi$ and $\rho$, for the scenario of exposure learning only (dark grey surface) and social learning only (light grey surface). Other model parameters are $\tau=0.8$ $day^{-1}$, $\tau_p=0.001$ $day^{-1}$, $\sigma=0.25$ $day^{-1}$ and $\kappa=0$ $day^{-1}$