Incorporate Michael's suggestions in appendix

docs/tex/tex_descriptions/models/sm_covid/model_description.tex

@@ -5,7 +5,8 @@
 \section{Model description}
 
 \subsection{General approach}
-We use a semi-mechanistic compartmental model of COVID-19 transmission governed by ordinary differential equations (ODEs). 
+We use a semi-mechanistic compartmental model of COVID-19 transmission governed by ordinary differential equations (ODEs) to
+simulate country-specific COVID-19 epidemics during the first three years of the pandemic (2020-2022). 
 Our model captures important factors of COVID-19 transmission and disease such as age-specific characteristics, 
 heterogeneous mixing, vaccination and the emergence of different variants of concern. 
 The ODE-based model is used to capture only states relevant to transmission, whereas hospitalisations and deaths are

docs/tex/tex_descriptions/models/sm_covid/odes.tex

@@ -5,7 +5,7 @@
 the average duration of active disease is denoted $w$. The relative susceptibility to infection with strain $s$ of individuals aged $a$ with 
 vaccination status $v$ is denoted $\rho_{a,v,s}$. The term $b_{a,v,s}(t)$ designates the introduction of individuals of age $a$ and 
 with vaccination status $v$ that are infected with strain $s$ (infection seeding). Vaccination is characterised by the age-specific
-and time-variant per-capita vaccination rate $w_a$. Finally, $\chi_{s,\sigma}$ represents the relative susceptibility to infection
+and time-variant per-capita vaccination rate $\omega_a$. Finally, $\chi_{s,\sigma}$ represents the relative susceptibility to infection
 with strain $\sigma$ for individuals whose most recent infection episode was with strain $s$. Using this new notation combined 
 with those previously introduced, we can describe the model with the following set of ordinary differential equations:
 

docs/tex/tex_descriptions/models/sm_covid/stratifications/immunity.tex

@@ -10,7 +10,7 @@
 are allocated. Note that in the event that the population-level vaccine coverage exceeds 80\%, the saturation coverage was set equal to the population-level coverage. 
 
 Let us consider two successive time points $t_i$ and $t_{i+1}$ for which vaccination data are available. Let us denote $r_{a, i}$ and $r_{a, i+1}$ the associated vaccine 
-coverage for age group $a$. The time-variant and age-specific vaccination rate per capita $w_a(t)$ verifies:
+coverage for age group $a$. The time-variant and age-specific vaccination rate per capita $\omega_a(t)$ verifies:
 
 \begin{equation}
     1 - r_{a, i+1} = (1 - r_{a, i})e^{-w_a(t)(t_{i+1} - t_i)} \quad, \forall t \in [t_i, t_{i+1}) .
@@ -19,7 +19,7 @@
 Then, 
 \begin{equation}
     \label{eq:vacc}
-    w_a(t) = \frac{\ln(1 - r_{a, i}) - \ln(1 - r_{a, i+1})}{t_{i+1} - t_i} \quad, \forall t \in [t_i, t_{i+1}) ,
+    \omega_a(t) = \frac{\ln(1 - r_{a, i}) - \ln(1 - r_{a, i+1})}{t_{i+1} - t_i} \quad, \forall t \in [t_i, t_{i+1}) ,
 \end{equation}
 where $\ln(x)$ represents the natural logarithm of $x$.