SciCompMod · HenrZu · Mar 20, 2026 · Mar 20, 2026 · Mar 20, 2026 · Mar 20, 2026
diff --git a/cpp/examples/CMakeLists.txt b/cpp/examples/CMakeLists.txt
@@ -18,17 +18,17 @@ add_executable(adapt_rk_example adapt_rk_test.cpp)
 target_link_libraries(adapt_rk_example PRIVATE memilio)
 target_compile_options(adapt_rk_example PRIVATE ${MEMILIO_CXX_FLAGS_ENABLE_WARNING_ERRORS})
 
-add_executable(ode_seir_example ode_seir.cpp)
-target_link_libraries(ode_seir_example PRIVATE memilio ode_seir)
-target_compile_options(ode_seir_example PRIVATE ${MEMILIO_CXX_FLAGS_ENABLE_WARNING_ERRORS})
-
-add_executable(ode_seirdb_example ode_seirdb.cpp)
-target_link_libraries(ode_seirdb_example PRIVATE memilio ode_seirdb)
-target_compile_options(ode_seirdb_example PRIVATE ${MEMILIO_CXX_FLAGS_ENABLE_WARNING_ERRORS})
-
-add_executable(ode_seir_ageres_example ode_seir_ageres.cpp)
-target_link_libraries(ode_seir_ageres_example PRIVATE memilio ode_seir)
-target_compile_options(ode_seir_ageres_example PRIVATE ${MEMILIO_CXX_FLAGS_ENABLE_WARNING_ERRORS})
+add_executable(ode_seir_example ode_seir.cpp)
+target_link_libraries(ode_seir_example PRIVATE memilio ode_seir)
+target_compile_options(ode_seir_example PRIVATE ${MEMILIO_CXX_FLAGS_ENABLE_WARNING_ERRORS})
+
+add_executable(ode_seirdb_example ode_seirdb.cpp)
+target_link_libraries(ode_seirdb_example PRIVATE memilio ode_seirdb)
+target_compile_options(ode_seirdb_example PRIVATE ${MEMILIO_CXX_FLAGS_ENABLE_WARNING_ERRORS})
+
+add_executable(ode_seir_ageres_example ode_seir_ageres.cpp)
+target_link_libraries(ode_seir_ageres_example PRIVATE memilio ode_seir)
+target_compile_options(ode_seir_ageres_example PRIVATE ${MEMILIO_CXX_FLAGS_ENABLE_WARNING_ERRORS})
 
 add_executable(ode_sir_example ode_sir.cpp)
 target_link_libraries(ode_sir_example PRIVATE memilio ode_sir)
@@ -108,6 +108,10 @@ add_executable(ode_secir_graph_example ode_secir_graph.cpp)
 target_link_libraries(ode_secir_graph_example PRIVATE memilio ode_secir)
 target_compile_options(ode_secir_graph_example PRIVATE ${MEMILIO_CXX_FLAGS_ENABLE_WARNING_ERRORS})
 
+add_executable(ode_secir_traveltime_example ode_secir_traveltime_mobility.cpp)
+target_link_libraries(ode_secir_traveltime_example PRIVATE memilio ode_secir)
+target_compile_options(ode_secir_traveltime_example PRIVATE ${MEMILIO_CXX_FLAGS_ENABLE_WARNING_ERRORS})
+
 add_executable(graph_stochastic_mobility_example graph_stochastic_mobility.cpp)
 target_link_libraries(graph_stochastic_mobility_example PRIVATE memilio ode_secir)
 target_compile_options(graph_stochastic_mobility_example PRIVATE ${MEMILIO_CXX_FLAGS_ENABLE_WARNING_ERRORS})

diff --git a/cpp/examples/ode_secir_traveltime_mobility.cpp b/cpp/examples/ode_secir_traveltime_mobility.cpp
@@ -0,0 +1,172 @@
+/* 
+* Copyright (C) 2020-2026 MEmilio
+*
+* Authors: Henrik Zunker
+*
+* Contact: Martin J. Kuehn <[email protected]>
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+/**
+ * Example for the travel-time-aware metapopulation mobility model with three patches. 
+ *
+ * Only A has initial infections. Individuals from A commute to B via C, spending time in C's mobility node during transit.
+ * Due to the time spent in the mobility node, C residents get infected early on, and B receives infections both from
+ * arriving A commuters and from C residents who commute directly to B.
+ *
+ * This example demonstrates the travel-time-aware Graph-ODE model from:
+ *
+ * H. Zunker et al., "Novel travel time aware metapopulation models ...", (2025), doi.org/10.1371/journal.pcbi.1012630
+ */
+
+#include "memilio/config.h"
+#include "memilio/mobility/metapopulation_mobility_traveltime.h"
+#include "ode_secir/model.h"
+#include "ode_secir/infection_state.h"
+#include "ode_secir/parameters.h"
+#include "memilio/compartments/simulation.h"
+
+#include <iostream>
+#include <iomanip>
+#include <string>
+
+using FP    = double;
+using Model = mio::osecir::Model<FP>;
+using Sim   = mio::osecir::Simulation<FP>;
+
+static Model build_model(double N, double I0)
+{
+    Model model(1 /*age groups*/);
+
+    model.populations[{mio::AgeGroup(0), mio::osecir::InfectionState::Susceptible}]        = N - I0;
+    model.populations[{mio::AgeGroup(0), mio::osecir::InfectionState::InfectedNoSymptoms}] = I0;
+
+    model.parameters.set<mio::osecir::StartDay<FP>>(0);
+    model.parameters.set<mio::osecir::Seasonality<FP>>(0.0);
+
+    model.parameters.get<mio::osecir::TimeExposed<FP>>()[mio::AgeGroup(0)]            = 3.2;
+    model.parameters.get<mio::osecir::TimeInfectedNoSymptoms<FP>>()[mio::AgeGroup(0)] = 2.0;
+    model.parameters.get<mio::osecir::TimeInfectedSymptoms<FP>>()[mio::AgeGroup(0)]   = 5.8;
+    model.parameters.get<mio::osecir::TimeInfectedSevere<FP>>()[mio::AgeGroup(0)]     = 9.5;
+    model.parameters.get<mio::osecir::TimeInfectedCritical<FP>>()[mio::AgeGroup(0)]   = 7.1;
+
+    model.parameters.get<mio::osecir::TransmissionProbabilityOnContact<FP>>()[mio::AgeGroup(0)]  = 0.08;
+    model.parameters.get<mio::osecir::RelativeTransmissionNoSymptoms<FP>>()[mio::AgeGroup(0)]    = 0.7;
+    model.parameters.get<mio::osecir::RecoveredPerInfectedNoSymptoms<FP>>()[mio::AgeGroup(0)]    = 0.09;
+    model.parameters.get<mio::osecir::RiskOfInfectionFromSymptomatic<FP>>()[mio::AgeGroup(0)]    = 0.25;
+    model.parameters.get<mio::osecir::MaxRiskOfInfectionFromSymptomatic<FP>>()[mio::AgeGroup(0)] = 0.45;
+    model.parameters.get<mio::osecir::TestAndTraceCapacity<FP>>()                                = 35;
+    model.parameters.get<mio::osecir::SeverePerInfectedSymptoms<FP>>()[mio::AgeGroup(0)]         = 0.2;
+    model.parameters.get<mio::osecir::CriticalPerSevere<FP>>()[mio::AgeGroup(0)]                 = 0.25;
+    model.parameters.get<mio::osecir::DeathsPerCritical<FP>>()[mio::AgeGroup(0)]                 = 0.3;
+
+    auto& cm                                 = model.parameters.get<mio::osecir::ContactPatterns<FP>>();
+    cm.get_cont_freq_mat()[0].get_baseline() = Eigen::MatrixX<FP>::Constant(1, 1, 10.0);
+
+    return model;
+}
+
+static void print_row(const std::string& label, const auto& node_prop)
+{
+    const auto& last = node_prop.local_sim.get_result().get_last_value();
+    const int iS     = static_cast<int>(mio::osecir::InfectionState::Susceptible);
+    const int iE     = static_cast<int>(mio::osecir::InfectionState::Exposed);
+    const int iINS   = static_cast<int>(mio::osecir::InfectionState::InfectedNoSymptoms);
+    std::cout << std::left << std::setw(8) << label << "  S=" << std::setw(10) << static_cast<long>(last[iS])
+              << "  E=" << std::setw(8) << static_cast<long>(last[iE]) << "  INS=" << std::setw(8)
+              << static_cast<long>(last[iINS]) << "  Total=" << static_cast<long>(last.sum()) << "\n";
+}
+
+int main()
+{
+    mio::set_log_level(mio::LogLevel::warn);
+
+    const FP t0   = 0.0;
+    const FP tmax = 30.0;
+    const FP dt   = 0.5;
+
+    // -- Population sizes -------------------------------------------------
+    const double N_A  = 500'000.0;
+    const double N_B  = 300'000.0;
+    const double N_C  = 80'000.0;
+    const double I0_A = N_A * 0.001; // 0.1 % infected at start
+    const double I0_B = 0.0;
+    const double I0_C = 0.0;
+
+    // -- Mobility parameters -----------------------------------------------
+    // A -> B trip passes through C (path = {A, C, B}, n_patches = 3).
+    // travel_time_AB = 2 * tt_patch_AC_CB; with n_steps=120 this yields tt_per_patch = 3 sub-steps/patch.
+    // step_depart_AB = 62  ->  A's commuters are in C's mobility_sim at outbound sub-steps 65–67
+    //                                                            and at return sub-steps 114–116.
+    //
+    // B <-> C (path = {B,C} or {C,B}, n_patches = 2).
+    // tt_direct_BC = 2/24  ->  tt_per_patch = 5 sub-steps/patch.
+    //   C->B: step_depart = 60  ->  C->B commuters in C's mobility_sim at outbound sub-steps 60–64,
+    //         and return sub-steps 115–119.
+    //   B->C: step_depart = 70  ->  B->C commuters in C's mobility_sim at outbound sub-steps 75–79,
+    //         and return sub-steps 110–114.
+    // During the return phase, all three groups share C's mobility_sim:
+    //   A->B return (114–116), B->C return (110–114) at sub-step 114
+    //   A->B return (114–116), C->B return (115–119) at sub-steps 115–116
+    // All three groups therefore share C's mobility_sim and can infect each other during transit.
+    const FP tt_patch_AC_CB = 1.0 / 24.0; // 1 h per patch (A <-> C)
+    const FP tt_direct_BC   = 2.0 / 24.0; // 2 h one-way B <-> C (5 sub-steps/patch -> schedule overlap in C)
+    const FP stay_dur_AB    = 8.0 / 24.0;
+    const FP stay_dur_C     = 6.0 / 24.0;
+
+    const FP mob_coeff_AB = 0.05; // 5 % of A commute to B
+    const FP mob_coeff_BC = 0.08; // 8 % of B/C commute to each other
+
+    const int nc                       = static_cast<int>(mio::osecir::InfectionState::Count);
+    const Eigen::VectorX<FP> coeffs_AB = Eigen::VectorX<FP>::Constant(nc, mob_coeff_AB);
+    const Eigen::VectorX<FP> coeffs_BC = Eigen::VectorX<FP>::Constant(nc, mob_coeff_BC);
+
+    // Nodes (index 0=A, 1=B, 2=C)
+    mio::Graph<mio::TravelTimeNodeProperty<FP, Sim>, mio::TravelTimeEdge<FP>> graph;
+    graph.add_node(0, build_model(N_A, I0_A), t0, stay_dur_AB);
+    graph.add_node(1, build_model(N_B, I0_B), t0, stay_dur_AB);
+    graph.add_node(2, build_model(N_C, I0_C), t0, stay_dur_C);
+
+    // A -> B via C
+    const FP tt_AB                    = 2.0 * tt_patch_AC_CB;
+    const std::vector<size_t> path_AB = {0, 2, 1}; // A -> C -> B
+    graph.add_edge(0, 1, mio::MobilityParameters<FP>(coeffs_AB), tt_AB, path_AB);
+
+    // B <-> C
+    graph.add_edge(1, 2, mio::MobilityParameters<FP>(coeffs_BC), tt_direct_BC, std::vector<size_t>{1, 2});
+    graph.add_edge(2, 1, mio::MobilityParameters<FP>(coeffs_BC), tt_direct_BC, std::vector<size_t>{2, 1});
+
+    // -- Run simulation ----------------------------------------------------
+    auto sim = mio::make_traveltime_sim<FP>(t0, dt, std::move(graph));
+    sim.advance(tmax);
+
+    // -- Results -----------------------------------------------------------
+    std::cout << "Patch A starts with " << I0_A << " infected. A traveler from A travels to B via C.\n"
+              << "C is transit-only for A->B; C also has its own B<->C travelers.\n"
+              << "B and C start healthy and infections reach them through transit mixing.\n\n";
+
+    std::cout << std::string(62, '-') << "\n";
+    std::cout << "\n Results after " << tmax << " days \n\n";
+    print_row("A", sim.get_graph().nodes()[0].property);
+    print_row("B", sim.get_graph().nodes()[1].property);
+    print_row("C", sim.get_graph().nodes()[2].property);
+    std::cout << std::string(62, '-') << "\n";
+
+    std::cout << "\nDuring the return phase, A-transit commuters and C<->B commuters\n"
+              << "share C's mobility_sim and can infect each other during transit.\n"
+              << "This effect is not captured by standard metapopulation models\n"
+              << "without explicit travel time.\n";
+
+    return 0;
+}
diff --git a/cpp/memilio/CMakeLists.txt b/cpp/memilio/CMakeLists.txt
@@ -77,6 +77,8 @@ add_library(memilio
     mobility/metapopulation_mobility_instant.cpp
     mobility/metapopulation_mobility_stochastic.h
     mobility/metapopulation_mobility_stochastic.cpp
+    mobility/metapopulation_mobility_traveltime.h
+    mobility/metapopulation_mobility_traveltime.cpp
     mobility/graph_simulation.h
     mobility/graph_simulation.cpp
     mobility/graph.h

diff --git a/cpp/memilio/mobility/metapopulation_mobility_traveltime.cpp b/cpp/memilio/mobility/metapopulation_mobility_traveltime.cpp
@@ -0,0 +1,24 @@
+/* 
+* Copyright (C) 2020-2026 MEmilio
+*
+* Authors: Henrik Zunker
+*
+* Contact: Martin J. Kuehn <[email protected]>
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+#include "memilio/mobility/metapopulation_mobility_traveltime.h"
+
+namespace mio
+{
+} // namespace mio