Tutorial-1.md

@@ -125,5 +125,47 @@ The trajectory can readily be plotted using the `plot()` function:
 plot(traj_dm)
 ```
 
-<img src="vignettes/TiPS_files/figure-markdown_github/unnamed-chunk-13-1.png" width="576" style="display: block; margin: auto;" />
+<img src="uploads/1763f73344d5ce4664ade2aa912215b6/unnamed-chunk-13-1.png"  width="350" height="230">
 
+### *τ*-leap method
+
+The default mode of the simulator is the *τ*-leap method. The `method` argument must be specified and fixed to `àpproximate`. The time-step `tau` is by default set to 0.05. Let's fix its value to 0.009:
+
+``` r
+traj_tl <- safe_sir_simu(
+  paramValues = theta,
+  initialStates = initialStates,
+  times = time,
+  method = "approximate",
+  tau = 0.009)
+```
+
+We obtain the same type of output as with the direct method:
+
+``` r
+head(traj_tl$traj)
+#>    Time          Reaction Nrep    S I R
+#> 1 0.000              init    1 9999 1 0
+#> 2 0.342 S [beta*S*I] -> I    1 9998 2 0
+#> 3 0.648 S [beta*S*I] -> I    1 9997 3 0
+#> 4 0.963 S [beta*S*I] -> I    1 9996 4 0
+#> 5 0.990  I [gamma*I] -> R    1 9996 3 1
+#> 6 1.008 S [beta*S*I] -> I    1 9995 4 1
+```
+
+The trajectory can also be plotted using the `plot` function.
+
+### Mixed method
+
+To run simulations with the `mixed` algorithm (basically switching between the direct method and the *τ*-leap method depending on the number of reactions occurring per unit of time), the `method` argument must be specified and fixed to `mixed`. The time-step `tau` is by default set to 0.05. Let's fix its value to 0.009 :
+
+``` r
+traj_mm <- safe_sir_simu(
+    paramValues = theta,
+    initialStates = initialStates,
+    times = time,
+    method = "mixed",
+    tau = 0.009)
+```
+
+Outputs are similar to the other methods and the trajectory can also be plotted using the `plot` function.