docs(model): add sir tutorials

#100

docs/tutorials/sir.py

@@ -0,0 +1,55 @@
+# ---
+# jupyter:
+#   jupytext:
+#     text_representation:
+#       extension: .py
+#       format_name: percent
+#       format_version: '1.3'
+#       jupytext_version: 1.16.4
+#   kernelspec:
+#     display_name: .venv
+#     language: python
+#     name: python3
+# ---
+
+# %% [markdown]
+# # SIR Model
+#
+# In this tutorial, we will learn how to use the SIR model.
+
+# %%
+import plotly.express as px
+
+from hamilflow.models.sir import SIR
+
+# %% [markdown]
+# ## Model
+
+# %%
+sir_1 = SIR(
+    system={
+        "beta": 0.03,
+        "alpha": 0.1,
+        "delta_t": 0.1,
+    },
+    initial_condition={
+        "susceptible_0": 999,
+        "infected_0": 1,
+        "recovered_0": 0,
+    },
+)
+
+# %%
+n_steps = 100
+
+sir_1_results = sir_1.generate_from(n_steps=n_steps)
+sir_1_results.head()
+
+# %%
+px.line(
+    sir_1_results,
+    x="t",
+    y=["S", "I", "R"],
+)
+
+# %%

hamilflow/models/sir.py

@@ -111,7 +111,7 @@ def generate_from(self, n_steps: int) -> pd.DataFrame:
         :param n_steps: Number of steps to simulate
         :return: DataFrame with time, S, I, R columns
         """
-        time_steps = np.arange(0, n_steps) * self.system.delta_t
+        time_steps = np.arange(1, n_steps) * self.system.delta_t
 
         return self(time_steps)
 
@@ -155,8 +155,8 @@ def __call__(self, t: TypeTime) -> pd.DataFrame:
 
             delta_s, delta_i, delta_r = self._step(susceptible, infected)
 
-            susceptible += delta_s
-            infected += delta_i
-            recovered += delta_r
+            susceptible = max(susceptible + delta_s, 0)
+            infected = max(infected + delta_i, 0)
+            recovered = max(recovered + delta_r, 0)
 
         return pd.DataFrame(results)