Fig. 2.

Simulation of transmission model of SARS-CoV-2 presented in Eqs. (2.1)–(2.6) for (left) ${\mathcal{R}}_0=2$ and (right) ${\mathcal{R}}_0=3$. We achieved this change in ${\mathcal{R}}_0$ by altering the parameter $\lambda$, which is the per day detection rate of symptomatic cases, thus illustrating the potential value of rapid case detection. Note that a larger ${\mathcal{R}}_0$ leads to a faster epidemic and a greater fraction of the population becoming infected. The horizontal, dotted gray line in each panel indicates the herd immunity threshold (i.e. the value of $S$ that corresponds to $\mathcal{R}=1$). Note that infection declines, but does not immediately disappear, after crossing the herd immunity threshold. Parameter values: ${\beta }_A=0.12,{\beta }_P=0.4,{\beta }_C=0.4,\phi =0.50,\nu =0.25,{\gamma }_{\mathrm{A}}=0.1,{\gamma }_{\mathrm{C}}=0.1,{\gamma }_{\mathrm{Q}}=0.1,{\alpha }_{\mathrm{C}}=0.001,{\alpha }_Q=0.001$,(left) $\lambda =0.2323$, (right) $\lambda =0.024$. Initial conditions: $S\left(0\right)=1,I_A\left(0\right)=0.0001,I_P\left(0\right)=0.0001,I_C\left(0\right)=0,Q\left(0\right)=0,R\left(0\right)=0$.