Table 1.

Loop-based ${\mathcal{R}}_0$ calculations for temperate phage models.

Temperate phage dynamics	Lytic loop P1	Lysogenic loop P2	Lyso–lytic loop P3
Resource-explicit model with implicit infections (Stewart and Levin 1984)	$\stackrel{V\to V}{\overbrace{(1-p)\left(\frac{\beta \varphi S^{*}}{\rho }\right)}}$	$\stackrel{L\to L}{\overbrace{\frac{\psi (R^{*})}{\gamma +\rho +\nu }}}$	$\stackrel{L\to V}{\overbrace{\left(\frac{\gamma }{\gamma +\rho +\nu }\right)}}\stackrel{V\to L}{\overbrace{\left(\frac{\beta \varphi S^{*}}{\rho }\right)p}}$
Resource-implicit model with implicit infections (Berngruber et al. 2013)	$\stackrel{V\to V}{\overbrace{(1-p)\left(\frac{b\beta \varphi S^{*}}{\varphi S^{*}+m}\right)}}$	$\stackrel{L\to L}{\overbrace{\frac{r_L\delta \left(1-S^{*}/K\right)}{m+\gamma }}}$	$\stackrel{L\to V}{\overbrace{\left(\frac{\gamma }{\gamma +m}\right)}}\stackrel{V\to L}{\overbrace{\left(\frac{b\beta \varphi S^{*}}{\varphi S^{*}+m}\right)p}}$
Resource-explicit model with explicit infections (Present)	$\stackrel{E\to I}{\overbrace{(1-p)\left(\frac{\lambda }{\lambda +d_E}\right)}}\stackrel{I\to V}{\overbrace{\left(\frac{\beta \hspace{0.17em}\eta }{\eta +d_I}\right)}}\stackrel{V\to E}{\overbrace{\left(\frac{\varphi S^{*}}{\varphi S^{*}+m}\right)}}$	$\stackrel{L\to L}{\overbrace{\frac{r_L(1-S^{*}/K)}{\gamma +d_L}}}$	$\stackrel{E\to L}{\overbrace{p\left(\frac{\lambda }{\lambda +d_E}\right)}}\stackrel{L\to I}{\overbrace{\left(\frac{\gamma }{\gamma +d_L}\right)}}\stackrel{I\to V}{\overbrace{\left(\frac{\beta \hspace{0.17em}\eta }{\eta +d_I}\right)}}\stackrel{V\to E}{\overbrace{\left(\frac{\varphi S^{*}}{\varphi S^{*}+m}\right)}}$
Resource-implicit model with explicit infections (Present)	$\stackrel{E\to I}{\overbrace{(1-p)\left(\frac{\lambda }{\lambda +d_E}\right)}}\stackrel{I\to V}{\overbrace{\left(\frac{\beta \hspace{0.17em}\eta }{\eta +d_I}\right)}}\stackrel{V\to E}{\overbrace{\left(\frac{\varphi S^{*}}{\varphi S^{*}+m}\right)}}$	$\stackrel{L\to L}{\overbrace{\frac{\psi (R^{*})}{\gamma +d_L}}}$	$\stackrel{E\to L}{\overbrace{p\left(\frac{\lambda }{\lambda +d_E}\right)}}\stackrel{L\to I}{\overbrace{\left(\frac{\gamma }{\gamma +d_L}\right)}}\stackrel{I\to V}{\overbrace{\left(\frac{\beta \hspace{0.17em}\eta }{\eta +d_I}\right)}}\stackrel{V\to E}{\overbrace{\left(\frac{\varphi S^{*}}{\varphi S^{*}+m}\right)}}$