diff --git a/game/src/common/overlays.rs b/game/src/common/overlays.rs
index c4bfa54e5d..52d227d6dc 100644
--- a/game/src/common/overlays.rs
+++ b/game/src/common/overlays.rs
@@ -836,6 +836,7 @@ impl Overlays {
 
             Some(PandemicModel::calculate(
                 app.primary.sim.get_analytics(),
+                app.primary.sim.get_all_people(),
                 app.primary.sim.time(),
                 &mut XorShiftRng::from_seed([42; 16]),
             ))
diff --git a/sim/src/pandemic.rs b/sim/src/pandemic.rs
index 01b36f855c..98a6e4ec27 100644
--- a/sim/src/pandemic.rs
+++ b/sim/src/pandemic.rs
@@ -1,17 +1,21 @@
-use crate::{Analytics, PersonID};
+use crate::{Analytics, Person, PersonID};
 use geom::{Duration, Time};
 use map_model::BuildingID;
 use rand::Rng;
 use rand_xorshift::XorShiftRng;
-use std::collections::{BTreeMap, BTreeSet};
+use std::cmp::Ordering;
+use std::collections::{BTreeMap, BTreeSet, BinaryHeap};
 
 pub struct PandemicModel {
     pub infected: BTreeSet<PersonID>,
+    hospitalized: BTreeSet<PersonID>,
     // Since when has a person been inside a building?
     // TODO This is an awkward data structure; abstutil::MultiMap is also bad, because key removal
     // would require knowing the time. Want something closer to
     // https://guava.dev/releases/19.0/api/docs/com/google/common/collect/Table.html.
     bldg_occupants: BTreeMap<BuildingID, Vec<(PersonID, Time)>>,
+
+    events: BinaryHeap<Item>,
 }
 
 impl PandemicModel {
@@ -23,66 +27,121 @@ impl PandemicModel {
     // This recomputes everything every time the UI asks for it. That's fine for the scale of
     // simulations now; everything else in Analytics works the same way. The faster streaming
     // version is very straightforward -- cache this output and only process new events.
-    pub fn calculate(analytics: &Analytics, now: Time, rng: &mut XorShiftRng) -> PandemicModel {
+    pub fn calculate(
+        analytics: &Analytics,
+        population: &Vec<Person>,
+        now: Time,
+        rng: &mut XorShiftRng,
+    ) -> PandemicModel {
         let mut state = PandemicModel {
             infected: BTreeSet::new(),
+            hospitalized: BTreeSet::new(),
             bldg_occupants: BTreeMap::new(),
+            events: BinaryHeap::new(),
         };
 
-        // Track people's movements through buildings
+        // Seed initially infected people.
+        for p in population {
+            if rng.gen_bool(0.1) {
+                state.infected.insert(p.id);
+
+                if rng.gen_bool(0.1) {
+                    state.events.push(Item {
+                        time: Time::START_OF_DAY
+                            + rand_duration(rng, Duration::hours(1), Duration::hours(3)),
+                        event: Event::Hospitalized(p.id),
+                    });
+                }
+            }
+        }
+
+        // Seed events in the pandemic model from the traffic simulaton.
         for (time, person, bldg, left) in &analytics.building_transitions {
             if *time > now {
                 break;
             }
-            if *left {
-                // TODO Messy to mutate state inside a retain closure
-                let mut inside_since: Option<Time> = None;
-                state
-                    .bldg_occupants
-                    .entry(*bldg)
-                    .or_insert_with(Vec::new)
-                    .retain(|(p, t)| {
-                        if *p == *person {
-                            inside_since = Some(*t);
-                            false
-                        } else {
-                            true
-                        }
-                    });
-                // TODO A person left a building, but they weren't inside of it? Bug -- few
-                // possible causes...
-                if inside_since.is_none() {
-                    continue;
-                }
-                let inside_since = inside_since.unwrap();
+            state.events.push(Item {
+                time: *time,
+                event: if *left {
+                    Event::LeaveBldg(*person, *bldg)
+                } else {
+                    Event::EnterBldg(*person, *bldg)
+                },
+            });
+        }
 
-                // Was this person leaving infected while they were inside?
-                if !state.infected.contains(person) {
-                    let mut longest_overlap_with_infected = Duration::ZERO;
-                    for (p, t) in &state.bldg_occupants[bldg] {
-                        if !state.infected.contains(p) {
-                            continue;
-                        }
-                        // How much time was p inside the building with person?
-                        let dt = *time - (*t).max(inside_since);
-                        longest_overlap_with_infected = longest_overlap_with_infected.max(dt);
+        // TODO Seed Event::EnterBus(person, car ID) and Seed::LeaveBus(person, car ID). Have to
+        // remember some more info in Analytics first. The TripPhaseStarting event almost has
+        // everything needed to build this. But the point is, the building and bus events can be
+        // interleaved properly using the queue.
+
+        // Process events in time-order
+        while let Some(item) = state.events.pop() {
+            let time = item.time;
+            if time > now {
+                break;
+            }
+            match item.event {
+                Event::LeaveBldg(person, bldg) => {
+                    // TODO Messy to mutate state inside a retain closure
+                    let mut inside_since: Option<Time> = None;
+                    state
+                        .bldg_occupants
+                        .entry(bldg)
+                        .or_insert_with(Vec::new)
+                        .retain(|(p, t)| {
+                            if *p == person {
+                                inside_since = Some(*t);
+                                false
+                            } else {
+                                true
+                            }
+                        });
+                    // TODO A person left a building, but they weren't inside of it? Bug -- few
+                    // possible causes...
+                    if inside_since.is_none() {
+                        continue;
                     }
-                    if longest_overlap_with_infected > Duration::hours(1) && rng.gen_bool(0.1) {
-                        state.infected.insert(*person);
+                    let inside_since = inside_since.unwrap();
+
+                    // Was this person leaving infected while they were inside?
+                    if !state.infected.contains(&person) {
+                        let mut longest_overlap_with_infected = Duration::ZERO;
+                        for (p, t) in &state.bldg_occupants[&bldg] {
+                            if !state.infected.contains(p) {
+                                continue;
+                            }
+                            // How much time was p inside the building with person?
+                            let dt = time - (*t).max(inside_since);
+                            longest_overlap_with_infected = longest_overlap_with_infected.max(dt);
+                        }
+                        if longest_overlap_with_infected > Duration::hours(1) && rng.gen_bool(0.1) {
+                            state.infected.insert(person);
+                            if rng.gen_bool(0.1) {
+                                state.events.push(Item {
+                                    time: time
+                                        + rand_duration(
+                                            rng,
+                                            Duration::hours(1),
+                                            Duration::hours(3),
+                                        ),
+                                    event: Event::Hospitalized(person),
+                                });
+                            }
+                        }
                     }
                 }
-            } else {
-                state
-                    .bldg_occupants
-                    .entry(*bldg)
-                    .or_insert_with(Vec::new)
-                    .push((*person, *time));
-
-                // Bit of a hack to seed initial state per person here, but eh
-                if *time == Time::START_OF_DAY {
-                    if rng.gen_bool(0.1) {
-                        state.infected.insert(*person);
-                    }
+                Event::EnterBldg(person, bldg) => {
+                    state
+                        .bldg_occupants
+                        .entry(bldg)
+                        .or_insert_with(Vec::new)
+                        .push((person, time));
+                }
+                Event::Hospitalized(person) => {
+                    state.hospitalized.insert(person);
+                    // TODO We need a way to tell the Sim to cancel any future trips. So there is a
+                    // feedback loop... not sure the best way to structure this yet.
                 }
             }
         }
@@ -90,3 +149,39 @@ impl PandemicModel {
         state
     }
 }
+
+#[derive(PartialEq, Eq)]
+struct Item {
+    time: Time,
+    event: Event,
+}
+
+impl PartialOrd for Item {
+    fn partial_cmp(&self, other: &Item) -> Option<Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+impl Ord for Item {
+    fn cmp(&self, other: &Item) -> Ordering {
+        // BinaryHeap is a max-heap, so reverse the comparison to get smallest times first.
+        let ord = other.time.cmp(&self.time);
+        if ord != Ordering::Equal {
+            return ord;
+        }
+        // The tie-breaker if time is the same is arbitrary, but deterministic
+        self.event.cmp(&other.event)
+    }
+}
+
+#[derive(PartialEq, Eq, PartialOrd, Ord)]
+enum Event {
+    EnterBldg(PersonID, BuildingID),
+    LeaveBldg(PersonID, BuildingID),
+    Hospitalized(PersonID),
+}
+
+fn rand_duration(rng: &mut XorShiftRng, low: Duration, high: Duration) -> Duration {
+    assert!(high > low);
+    Duration::seconds(rng.gen_range(low.inner_seconds(), high.inner_seconds()))
+}