From 4722a5511c139599265a7fcc7a59a7bba1614f56 Mon Sep 17 00:00:00 2001
From: Phil Elson <philip.elson@cern.ch>
Date: Mon, 26 Oct 2020 20:12:54 +0100
Subject: [PATCH 1/2] Simplify the concentration calculation.

---
 cara/models.py | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/cara/models.py b/cara/models.py
index 1e2ca4bc..dd8262bb 100644
--- a/cara/models.py
+++ b/cara/models.py
@@ -266,6 +266,13 @@ class Model:
 
         return k + self.virus.decay_constant + self.ventilation.air_exchange(self.room, time)
 
+    def collect_time_state_changes(self):
+        """
+        All time dependent entities on this model must provide information about
+        the times at which their state changes.
+
+        """
+
     @functools.lru_cache()
     def concentration(self, time: float) -> float:
         t = time
@@ -286,4 +293,5 @@ class Model:
         else:
             # Concentration while infected not present.
             end_concentration = self.concentration(t1)
-            return (end_concentration + ((np.exp(IVRR * t1) - 1) * end_concentration)) * np.exp(-IVRR * t)
+            fac = np.exp(IVRR * (t1 - t))
+            return end_concentration * fac

From 9e9f1a28bc8eef815520bde63ef5eb58086a68b9 Mon Sep 17 00:00:00 2001
From: Phil Elson <philip.elson@cern.ch>
Date: Mon, 26 Oct 2020 20:21:15 +0100
Subject: [PATCH 2/2] Fix a bug in the calculation of the concentration.

---
 cara/models.py                      | 5 ++---
 cara/tests/test_known_quantities.py | 2 +-
 2 files changed, 3 insertions(+), 4 deletions(-)

diff --git a/cara/models.py b/cara/models.py
index dd8262bb..69f642a6 100644
--- a/cara/models.py
+++ b/cara/models.py
@@ -287,9 +287,8 @@ class Model:
         elif t0 < t <= t1:
             # Concentration while infected present.
             init_concentration = self.concentration(t0)
-            time_present = t - t0
-            fac = np.exp(-IVRR * time_present)
-            return ((ER + Ni) / (IVRR * V)) * (1 - fac) + init_concentration * fac
+            fac = np.exp(IVRR * (t0 - t))
+            return ((ER * Ni) / (IVRR * V)) * (1 - fac) + init_concentration * fac
         else:
             # Concentration while infected not present.
             end_concentration = self.concentration(t1)
diff --git a/cara/tests/test_known_quantities.py b/cara/tests/test_known_quantities.py
index 8976a558..b87a318b 100644
--- a/cara/tests/test_known_quantities.py
+++ b/cara/tests/test_known_quantities.py
@@ -64,7 +64,7 @@ def test_r0(baseline_model):
     concentrations = [baseline_model.concentration(t) for t in ts]
     npt.assert_allclose(
         concentrations,
-        [0.000000e+00, 2.909211e-01, 1.273836e-04, 2.909210e-01, 5.577662e-08],
+        [0.000000e+00, 2.891970e-01, 1.266287e-04, 2.891969e-01, 5.544607e-08],
         rtol=1e-5
     )