A spatial epidemic model with contact and mobility restrictions

Figures & data

Figure 1. Endemic case in the long run (with $\mathit{\mu }=0$). Left to right $\mathit{S}$, $\mathit{I}$, $\mathit{R}$.

Figure 2. Evolution of $\mathit{I}$ (with $\mathit{\mu }=0$) for values of $\mathit{\alpha }=0.5,0.4,0.3,0.2$ (left to right).

Figure 3. Optimization with respect to both $\mathit{u}$ and $\mathit{v}$ in the benchmark case. The first two plots present the optimal controls $\mathit{u}$ and $\mathit{v}$, the second three plots give the corresponding $\mathit{S}$, $\mathit{I}$, and $\mathit{R}$.

Figure 4. Optimal control $\mathit{u}$ for time horizon $\mathit{T}=500,1000,2000$, cut at $\mathit{t}=450$.

Figure 5. Infected population in the optimal solution for values of $\mathit{\alpha }=0.2,0.3,0.4,0.5$ (first line), total number of deaths (second line left), and total “control energy” $\mathit{E}$ (second line right)—called “discomfort” on the plot—on $[0,\mathit{T}]$ as functions of $\mathit{\alpha }$.

Figure 6. Total number of deaths (left plot) and total social disutility (right plot) in the optimal solution for multiplier $\hat{c}$ of the contact rates varying between 0.2 and 0.8.

Figure 7. Optimal controls $\mathit{u}(\cdot ,\mathit{x})$ for values of discount $\mathit{r}=0,0.00075,0.0015,0.0030$.

Data availability statement

All data supporting the findings of this study are available within the paper.