We now use "s" for spleen compartments and flows

vignettes/articles/diagram.tex

@@ -46,8 +46,8 @@
     \node[comp,right=1cm of bone] (ucirc) {\(U_c\)\,: uRBCs in circulation};
     \node[comp,right=1cm of ucirc] (icirc) {\(I_c\)\,: iRBCs in circulation};
     \node[comp,right=1cm of icirc] (iseq) {\(I_q\)\,: Sequestered iRBCs};
-    \node[comp,below=1cm of ucirc] (uspl) {\(U_r\)\,: uRBCs in spleen};
-    \node[comp,below=1cm of icirc] (ispl) {\(I_r\)\,: iRBCs in spleen};
+    \node[comp,below=1cm of ucirc] (uspl) {\(U_s\)\,: uRBCs in spleen};
+    \node[comp,below=1cm of icirc] (ispl) {\(I_s\)\,: iRBCs in spleen};
     \node[below=1cm of uspl] (uexit) {};
     \node[below=1cm of ispl] (iexit) {};
 
@@ -61,7 +61,7 @@
     \draw[flow] (uspl.105) -- (ucirc.255) node[midway,left] {\(\delta'_u\)};
     \draw[flow] (icirc.285) -- (ispl.75) node[midway,right] {\(\delta_i\)};
     \draw[flow] (ispl.105) -- (icirc.255) node[midway,left] {\(\delta'_i\)};
-    \draw[flow] (uspl) -- (ispl) node[midway,above] {\(\alpha_r\)};
+    \draw[flow] (uspl) -- (ispl) node[midway,above] {\(\alpha_s\)};
     \draw[flow] (uspl) -- (uexit) node[midway,right] {\(\lambda_u\)};
     \draw[flow] (ispl) -- (iexit) node[midway,right] {\(\lambda_i\)};
   \end{tikzpicture}

vignettes/articles/model-description.Rmd

@@ -40,29 +40,29 @@ pkgdown:
 \newcommand{\nc}[1][]{n(a#1, t#1)}
 \newcommand{\rc}[1][]{r(a#1, t#1)}
 \newcommand{\Rc}[1][]{R_c(a#1, t#1)}
-\newcommand{\Rr}[1][]{R_r(a#1, t#1)}
+\newcommand{\Rr}[1][]{R_s(a#1, t#1)}
 \newcommand{\Nc}[1][]{N_c(a#1, t#1)}
-\newcommand{\Nr}[1][]{N_r(a#1, t#1)}
+\newcommand{\Nr}[1][]{N_s(a#1, t#1)}
 \newcommand{\Uc}[1][]{U_c(a#1, t#1)}
-\newcommand{\Ur}[1][]{U_r(a#1, t#1)}
+\newcommand{\Ur}[1][]{U_s(a#1, t#1)}
 \newcommand{\Ic}[1][]{I_c(a#1, t#1)}
-\newcommand{\Ir}[1][]{I_r(a#1, t#1)}
+\newcommand{\Ir}[1][]{I_s(a#1, t#1)}
 \newcommand{\Iq}[1][]{I_q(a#1, t#1)}
 \newcommand{\Icat}[2]{I_c(#1, #2)}
-\newcommand{\Irat}[2]{I_r(#1, #2)}
+\newcommand{\Irat}[2]{I_s(#1, #2)}
 \newcommand{\Iqat}[2]{I_q(a1, #2)}
 \newcommand{\Mac}[1][]{M(t#1)}
 \newcommand{\Macu}[1][]{M_u(t#1)}
 \newcommand{\Maci}[1][]{M_i(t#1)}
 \newcommand{\Ucnet}[1][]{\mathbf{U_c}(t#1)}
-\newcommand{\Urnet}[1][]{\mathbf{U_r}(t#1)}
+\newcommand{\Urnet}[1][]{\mathbf{U_s}(t#1)}
 \newcommand{\Icnet}[1][]{\mathbf{I_c}(t#1)}
-\newcommand{\Irnet}[1][]{\mathbf{I_r}(t#1)}
+\newcommand{\Irnet}[1][]{\mathbf{I_s}(t#1)}
 \newcommand{\Uss}{U_{ss}}
 \newcommand{\rss}{r_{ss}}
 \newcommand{\Rss}{R_{ss}}
 \newcommand{\Nss}{N_{ss}}
-\newcommand{\Urss}{U_{r,ss}}
+\newcommand{\Urss}{U_{s,ss}}
 
 \newcommand{\Turbc}{T_{\mathrm{urbc}}}
 \newcommand{\Tirbc}{T_{\mathrm{irbc}}}
@@ -233,7 +233,7 @@ These steady-state parameters define the initial (uninfected) cell populations:
   \\
   N_c(a, t=0) &= \Nss(a)
   \\
-  U_r(a, t=0) &= \Urss(a)
+  U_s(a, t=0) &= \Urss(a)
   \\
   M(t=0) &= M_0
 \end{align}
@@ -245,7 +245,7 @@ We start with a small number \(I_0\) of infected RBCs in the circulation, with a
   \\
   I_q(a, t=0) &= I_c(a, t=0) \cdot (1 - \exp[-\zeta])
   \\
-  I_r(a, t=0) &= I_c(a, t=0) \cdot (1 - \exp[-\delta_i]) \cdot \exp(- \lambda_i)
+  I_s(a, t=0) &= I_c(a, t=0) \cdot (1 - \exp[-\delta_i]) \cdot \exp(- \lambda_i)
 \end{align}
 
 The initial cell populations for the baseline parameter values are shown in Figures \@ref(fig:nr0), \@ref(fig:U0), and \@ref(fig:I0).
@@ -475,10 +475,10 @@ The removal rate \(\delta_u\) of uninfected RBCs from the circulation into the s
 | \(g_d^U\)           | Slope parameter   | \(`r p$gdUloss`\)       |
 | \(\delta_{50}^U\)   | Scaling parameter | \(`r p$UIdelta50uRBC`\) |
 
-We denote the number of uRBCs removed in a time-step as \(U_{c \to r}\):
+We denote the number of uRBCs removed in a time-step as \(U_{c \to s}\):
 
 \begin{align}
-  U_{c \to r}(a, t) &= \Uc[-1] \cdot (1 - \exp[-\delta_u(a, t)])
+  U_{c \to s}(a, t) &= \Uc[-1] \cdot (1 - \exp[-\delta_u(a, t)])
 \end{align}
 
 ```{r deltauinner, class.source = 'fold-hide', echo = ! knitr::is_latex_output(), fig.cap = 'The uRBC removal rate \\(\\delta_u(a, t)\\) from the circulation into the spleen when the scaling factor \\(F_U = 1\\).'}
@@ -524,10 +524,10 @@ Uninfected RBCs in the spleen return to the circulation at rate \(\delta'_u\), w
 | \(\mathrm{\mu_U}\)    | Scaling parameter | \(`r p$mu_deltaUr`\)    |
 | \(\mathrm{\sigma_U}\) | Scaling parameter | \(`r p$sigma_deltaUr`\) |
 
-We denote the number of uRBCs released in a time-step as \(U_{r \to c}\):
+We denote the number of uRBCs released in a time-step as \(U_{s \to c}\):
 
 \begin{align}
-  U_{r \to c}(a, t) &= \Ur[-1] \cdot \exp[- \lambda_u(a, t)]
+  U_{s \to c}(a, t) &= \Ur[-1] \cdot \exp[- \lambda_u(a, t)]
     \cdot (1 - \exp[-\delta'_u(a)])
 \end{align}
 
@@ -545,16 +545,16 @@ ggplot(df_duprime, aes(age / 24, value)) +
 \clearpage
 # RBC infection
 
-Uninfected RBCs are infected at rates \(\alpha_c\) and \(\alpha_r\) in the circulation and spleen, respectively, which depend on the age-specific merozoite preference \(\beta\):
+Uninfected RBCs are infected at rates \(\alpha_c\) and \(\alpha_s\) in the circulation and spleen, respectively, which depend on the age-specific merozoite preference \(\beta\):
 
 \begin{align}
   \alpha_c(a, t) &= \mathrm{PMF} \cdot
     \frac{\beta(a) \cdot U_c(a, t - 1)}{
       \sum_{a'} \left[\beta(a') \cdot U_c(a', t - 1)\right]}
   \\
-  \alpha_r(a, t) &= \mathrm{PMF} \cdot
-    \frac{\beta(a) \cdot U_r(a, t - 1)}{
-      \sum_{a'} \left[\beta(a') \cdot U_r(a', t - 1)\right]}
+  \alpha_s(a, t) &= \mathrm{PMF} \cdot
+    \frac{\beta(a) \cdot U_s(a, t - 1)}{
+      \sum_{a'} \left[\beta(a') \cdot U_s(a', t - 1)\right]}
 \end{align}
 
 Merozoites are released when infected RBCs rupture at age \(\Tirbc\).
@@ -565,9 +565,9 @@ Here we use the notation \(\nabla_{x \to y}\) to define the number of uRBCs infe
     I_c^\nabla + I_q(\Tirbc, t-1)
   ]
   \\
-  \nabla_{r \to c}(a, t) &= \alpha_c(a, t) \cdot \omega \cdot I_r^\nabla
+  \nabla_{s \to c}(a, t) &= \alpha_c(a, t) \cdot \omega \cdot I_s^\nabla
   \\
-  \nabla_{r \to r}(a, t) &= \alpha_r(a, t) \cdot (1 - \omega) \cdot I_r^\nabla
+  \nabla_{s \to s}(a, t) &= \alpha_s(a, t) \cdot (1 - \omega) \cdot I_s^\nabla
 \end{align}
 
 These in turn are defined in terms of the iRBCs that remain in the circulation and spleen, respectively:
@@ -575,15 +575,15 @@ These in turn are defined in terms of the iRBCs that remain in the circulation a
 \begin{align}
   I_c^\nabla &= I_c(\Tirbc, t-1) \cdot \exp[-\delta_i] \cdot \exp[-\zeta]
   \\
-  I_r^\nabla &= I_r(\Tirbc, t-1) \cdot \exp[-\delta'_i] \cdot \exp[-\lambda_i]
+  I_s^\nabla &= I_s(\Tirbc, t-1) \cdot \exp[-\delta'_i] \cdot \exp[-\lambda_i]
 \end{align}
 
 We can then define the total number of infected RBCs in the circulation and in the spleen:
 
 \begin{align}
-  \nabla_c(t) &= \sum_a \nabla_{c \to c}(a, t) + \sum_a \nabla_{r \to c}(a, t)
+  \nabla_c(t) &= \sum_a \nabla_{c \to c}(a, t) + \sum_a \nabla_{s \to c}(a, t)
   \\
-  \nabla_r(t) &= \sum_a \nabla_{r \to r}(a, t)
+  \nabla_s(t) &= \sum_a \nabla_{s \to s}(a, t)
 \end{align}
 
 | Symbol           | Description                                                                   | Baseline value |
@@ -643,10 +643,10 @@ The removal rate \(\delta_i\) of infected RBCs from the circulation into the spl
 @Safeuk08 conducted in vitro experiments that showed 11% and 20% of Pf rings and schizonts, respectively, are retained in the spleen in every passage of the iRBCs through the spleen.
 Accordingly, we assume here that \(\delta_{iS} \approx 2 \cdot \delta_{iR}\).
 
-We denote the number of iRBCs removed in a time-step as \(I_{c \to r}\):
+We denote the number of iRBCs removed in a time-step as \(I_{c \to s}\):
 
 \begin{align}
-  I_{c \to r}(a, t) &= \Ic[-1] \cdot (1 - \exp[-\delta_i(a, t)])
+  I_{c \to s}(a, t) &= \Ic[-1] \cdot (1 - \exp[-\delta_i(a, t)])
 \end{align}
 
 ```{r deltaiinner, class.source = 'fold-hide', echo = ! knitr::is_latex_output(), fig.cap = 'The iRBC removal rate \\(\\delta_i(a, t)\\) from the circulation into the spleen when the scaling factor \\(F_I = 1\\).'}
@@ -705,10 +705,10 @@ We assume that ring-stage RBCs are more likely to return to the circulation than
 | \(\delta_I^{sl}\)  | Slope parameter           | \(`r p$deltaIa_slope`\)  |
 | \(\delta_I^{c50}\) | Half-maximal age          | \(`r p$deltaIa_c50`\)    |
 
-We denote the number of iRBCs released in a time-step as \(I_{r \to c}\):
+We denote the number of iRBCs released in a time-step as \(I_{s \to c}\):
 
 \begin{align}
-  I_{r \to c}(a, t) &= \Ir[-1] \cdot \exp[- \lambda_i(a, t)]
+  I_{s \to c}(a, t) &= \Ir[-1] \cdot \exp[- \lambda_i(a, t)]
     \cdot (1 - \exp[-\delta'_i(a)])
 \end{align}
 
@@ -815,7 +815,7 @@ The macrophage population is defined with respect to the steady-state ratio of m
 | \(\lambda_u^{\mathrm{sel}}\) | Rate parameter for uRBCs               | \(`r p$lambdaU.sel`\) |
 | \(\lambda_i^{\mathrm{sel}}\) | Rate parameter for iRBCs               | \(`r p$lambdaI.sel`\) |
 | \(k_M\)                      | Scaling factor                         | \(`r p$kM`\)          |
-| \(b_M\)                      | Steady-state ratio of \(M\) to \(U_r\) | \(`r p$bM`\)          |
+| \(b_M\)                      | Steady-state ratio of \(M\) to \(U_s\) | \(`r p$bM`\)          |
 | \(\gamma_M\)                 | Scaling factor                         | \(`r p$gamma_M`\)     |
 | \(T_M\)                      | Age at which reticulocytes mature      | \(`r p$T_M`\) hours   |
 
@@ -837,21 +837,21 @@ We can now define the update rules for the RBC populations in the circulation an
   \Rc &= \begin{cases}
     0
     & \text{for } a = 1 \\
-    R_{c \to c}(a, t) + U_{r \to c}(a, t)
+    R_{c \to c}(a, t) + U_{s \to c}(a, t)
       + r_{\to c}(a, t)
       - \nabla_{c \to c}(a, t)
-      - \nabla_{r \to c}(a, t)
+      - \nabla_{s \to c}(a, t)
     & \text{for } 1 < a \le T_M
   \end{cases}
   \\
   \Nc &= \begin{cases}
-    R_{c \to c}(a, t) + U_{r \to c}(a, t)
+    R_{c \to c}(a, t) + U_{s \to c}(a, t)
       - \nabla_{c \to c}(a, t)
-      - \nabla_{r \to c}(a, t)
+      - \nabla_{s \to c}(a, t)
     & \text{for } a = T_M + 1 \\
-    N_{c \to c}(a, t) + U_{r \to c}(a, t)
+    N_{c \to c}(a, t) + U_{s \to c}(a, t)
       - \nabla_{c \to c}(a, t)
-      - \nabla_{r \to c}(a, t)
+      - \nabla_{s \to c}(a, t)
     & \text{for } T_M + 1 < a \le T_U
   \end{cases}
   \\
@@ -860,19 +860,19 @@ We can now define the update rules for the RBC populations in the circulation an
     N_c(a, t)  & \text{for } T_R < a \le T_U
   \end{cases}
   \\
-  \Ur &= U_{r \to r}(a, t) + U_{c \to r}(a, t) - \nabla_{r \to r}(a, t)
+  \Ur &= U_{s \to s}(a, t) + U_{c \to s}(a, t) - \nabla_{s \to s}(a, t)
   \\
   \Ic &=\begin{cases}
     \nabla_c(t)
     & \text{for } a = 1 \\
-    I_{c \to c}(a, t) + I_{r \to c}(a, t)
+    I_{c \to c}(a, t) + I_{s \to c}(a, t)
     & \text{for } 1 < a \le T_I
   \end{cases}
   \\
   \Ir &= \begin{cases}
-    \nabla_r(t)
+    \nabla_s(t)
     & \text{for } a = 1 \\
-    I_{r \to r}(a, t) + I_{c \to r}(a, t)
+    I_{s \to s}(a, t) + I_{c \to s}(a, t)
     & \text{for } 1 < a \le T_I
   \end{cases}
 \end{align}
@@ -884,11 +884,11 @@ where:
   \\
   N_{c \to c}(a, t) &= \Nc[-1] \cdot \exp[-\delta_u]
   \\
-  U_{r \to r}(a, t) &= \Ur[-1] \cdot \exp[-\delta'_u - \lambda_u]
+  U_{s \to s}(a, t) &= \Ur[-1] \cdot \exp[-\delta'_u - \lambda_u]
   \\
   I_{c \to c}(a, t) &= \Ic[-1] \cdot \exp[-\delta_i - \zeta]
   \\
-  I_{r \to r}(a, t) &= \Ic[-1] \cdot \exp[-\delta'_i - \lambda_i]
+  I_{s \to s}(a, t) &= \Ic[-1] \cdot \exp[-\delta'_i - \lambda_i]
 \end{align}
 
 \clearpage