Table 1.

Summary of experimental conditions, corresponding model, and set of parameters to be estimated

Experimental Model	Mathematical Model	Analytical Solution	Parameters
	$\{\begin{array}{l}\frac{dS}{dt}={\rho }_{S}S\hfill \\ \frac{dR}{dt}=0\hfill \end{array}$	$\begin{array}{c}S(t)=S_0\exp \left({\rho }_{S}t\right);\\ R(t)=R_0.\end{array}$	S0, R0, ρS
	$\{\begin{array}{l}\frac{dS}{dt}=0\hfill \\ \frac{dR}{dt}={\rho }_{R}R\hfill \end{array}$	$\begin{array}{c}S(t)=S_0\\ R(t)=R_0\exp \left({\rho }_{R}t\right).\end{array}$	S0, R0, ρR
	$\{\begin{array}{c}\frac{dS}{dt}={\rho }_{S}S\left(1-\frac{S+R}{K}\right)\\ \frac{dR}{dt}=0\\ \frac{dF}{dt}=0\\ \frac{dA}{dt}=0\end{array}$	$\begin{array}{l}S(t)=\frac{K-R_0}{1+\left(\frac{K-R_0}{S_0}-1\right)\exp \left[\left(\frac{R_0}{K}-1\right){\rho }_{S}t\right]};\hfill \\ \begin{array}{l}R(t)=R_0;\hfill \\ F(t)=F_0;\hfill \end{array}\hfill \\ \begin{array}{l}A(t)=0.\hfill \end{array}\hfill \end{array}$	S0, R0, K
	$\{\begin{array}{c}\frac{dS}{dt}=0\\ \frac{dR}{dt}=\left({\rho }_R+\eta A\right)R\left(1-\frac{S+R}{K}\right)\\ \frac{dF}{dt}=-\theta F\\ \frac{dA}{dt}=\theta F\end{array}$	$\begin{array}{l}S(t)=S_0;\\ \begin{array}{c}R(t)=\frac{K-S_0}{1+\left(\frac{K-S_0}{R_0}-1\right)\exp \left[\left(\frac{S_0}{K}-1\right)\left(\left({\rho }_R+\tilde{\eta }\right)t-\frac{\tilde{\eta }}{\theta }\left(1-e^{-\theta t}\right)\right)\right]};\\ F(t)=F_0\exp (-\theta t);\\ A(t)=F_0(1-\exp (-\theta t));\end{array}\end{array}$	$\begin{array}{l}{S}_0,R_0,\tilde{\eta }\\ (\tilde{\eta }=\eta F_0)\end{array}$
	$\{\begin{array}{c}\frac{dS}{dt}=0\\ \frac{dR}{dt}=\left({\rho }_R+(\eta -\alpha )A\right)R\left(1-\frac{S+R}{K}\right)\\ \frac{dF}{dt}=-\theta F\\ \frac{dA}{dt}=\theta F\end{array}$	$\begin{array}{l}S(t)=S_0;\\ \begin{array}{c}R(t)=\frac{K-S_0}{1+\left(\frac{K-S_0}{R_0}-1\right)\exp \left[\left(\frac{S_0}{K}-1\right)\left(\left({\rho }_R+\tilde{\eta }-\tilde{\alpha }\right)t-\frac{\tilde{\eta }-\tilde{\alpha }}{\theta }\left(1-e^{-\theta t}\right)\right)\right]};\\ F(t)=F_0\exp (-\theta t);\\ A(t)=F_0(1-\exp (-\theta t));\end{array}\end{array}$	$\begin{array}{l}{S}_0,R_0,\tilde{\alpha }\\ (\tilde{\alpha }=\alpha F_0)\end{array}$

Data are fitted to S(t) + R(t).

Initial conditions for cell line model are: S(0) = S₀, R(0) = R₀, for mouse model: S(0) = S₀, R(0) = R₀, F(0) = F₀, A(0) = 0.

Note that S₀ and R₀ represent different quantities depending on the model (cell count for cell line model, and tumor volume for mouse model).