Exercise 7 #2
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| Original file line number | Diff line number | Diff line change |
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| @@ -1,6 +1,6 @@ | ||
| import marimo | ||
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| __generated_with = "0.24.0" | ||
| app = marimo.App(width="medium") | ||
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@@ -49,7 +49,7 @@ def _(): | |
| @app.cell | ||
| def _(mo): | ||
| mo.md(r""" | ||
| We set the simulation start time `t0` and the end time `tmax`.: | ||
| """) | ||
| return | ||
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@@ -58,7 +58,6 @@ def _(mo): | |
| def _(): | ||
| t0 = 0 | ||
| tmax = 100 | ||
| return t0, tmax | ||
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@@ -104,20 +103,20 @@ def _(mo): | |
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| @app.cell | ||
| def _(AgeGroup, model, np, num_age_groups): | ||
| for i in range(num_age_groups): | ||
| # Set infection state stay times (in days) | ||
| model.parameters.TimeExposed[AgeGroup(i)] = 3.2 | ||
| model.parameters.TimeInfectedNoSymptoms[AgeGroup(i)] = 2. | ||
| model.parameters.TimeInfectedSymptoms[AgeGroup(i)] = 6. | ||
| model.parameters.TimeInfectedSevere[AgeGroup(i)] = 12. | ||
| model.parameters.TimeInfectedCritical[AgeGroup(i)] = 8. | ||
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| # Set infection state transition probabilities | ||
| model.parameters.RelativeTransmissionNoSymptoms[AgeGroup(i)] = 0.67 | ||
| model.parameters.TransmissionProbabilityOnContact[AgeGroup(i)] = 0.1 | ||
| model.parameters.RecoveredPerInfectedNoSymptoms[AgeGroup(i)] = 0.2 | ||
| model.parameters.RiskOfInfectionFromSymptomatic[AgeGroup(i)] = 0.25 | ||
| model.parameters.DeathsPerCritical[AgeGroup(i)] = 0.3 | ||
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| # The groups have an increasing risk of severe and critical infections | ||
| model.parameters.SeverePerInfectedSymptoms[AgeGroup(0)] = 0.2 | ||
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@@ -128,7 +127,8 @@ def _(AgeGroup, model, np, num_age_groups): | |
| model.parameters.CriticalPerSevere[AgeGroup(2)] = 0.25 * 2 | ||
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| # Set contact frequency | ||
| model.parameters.ContactPatterns.cont_freq_mat[0].baseline = np.ones( | ||
| (num_age_groups, num_age_groups)) * 10 | ||
| return | ||
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@@ -159,13 +159,15 @@ def _(mo): | |
| @app.cell | ||
| def _(AgeGroup, model, num_age_groups, osecir, total_population_per_region): | ||
| # The population is equally distributed among the age groups | ||
| for j in range(num_age_groups): | ||
| # 1% of the population is initially infected, 0.5% Exposed and 0.5% in the pre- or asymptomatic state | ||
| model.populations[AgeGroup(j), osecir.InfectionState.Exposed] = 0.005 * \ | ||
| total_population_per_region / num_age_groups | ||
| model.populations[AgeGroup(j), osecir.InfectionState.InfectedNoSymptoms] = 0.005 * \ | ||
| total_population_per_region / num_age_groups | ||
| # The rest of the population is Susceptible | ||
| model.populations.set_difference_from_group_total_AgeGroup( | ||
| (AgeGroup(j), osecir.InfectionState.Susceptible), total_population_per_region / num_age_groups) | ||
| return | ||
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@@ -180,7 +182,7 @@ def _(mo): | |
| @app.cell | ||
| def _(graph, model, t0): | ||
| # Add node with id 0 and copy beforehand initialized model to it | ||
| graph.add_node(id=0, model=model, t0=t0) | ||
| return | ||
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@@ -195,13 +197,14 @@ def _(mo): | |
| @app.cell | ||
| def _(AgeGroup, model, num_age_groups, osecir, total_population_per_region): | ||
| # The population is equally distributed among the age groups | ||
| for k in range(num_age_groups): | ||
| # No infected individuals | ||
| model.populations[AgeGroup(k), osecir.InfectionState.Exposed] = 0 | ||
| model.populations[AgeGroup( | ||
| k), osecir.InfectionState.InfectedNoSymptoms] = 0 | ||
| # The total population is Susceptible | ||
| model.populations.set_difference_from_group_total_AgeGroup( | ||
| (AgeGroup(k), osecir.InfectionState.Susceptible), total_population_per_region / num_age_groups) | ||
| return | ||
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@@ -216,7 +219,7 @@ def _(mo): | |
| @app.cell | ||
| def _(graph, model, t0): | ||
| # Add node with id 0 and copy beforehand initialized model to it | ||
| graph.add_node(id=1, model=model, t0=t0) | ||
| return | ||
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@@ -231,35 +234,50 @@ def _(mo): | |
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| @app.cell | ||
| def _(graph, mio, model, np, num_age_groups, osecir): | ||
| # One coefficient per (age group x compartment) | ||
| mobility_coefficients = 0.1 * np.ones(model.populations.numel()) | ||
| # Dead individuals do not commute | ||
| for l in range(num_age_groups): | ||
| mobility_coefficients[l * (int(osecir.InfectionState.Dead)+1) + | ||
| int(osecir.InfectionState.Dead)] = 0 | ||
| mobility_params = mio.MobilityParameters(mobility_coefficients) | ||
| # Add two edges to graph | ||
| graph.add_edge(0, 1, mobility_params) | ||
| graph.add_edge(1, 0, mobility_params) | ||
| # Individuals are exchanged every half day | ||
| dt_exchange = 0.5 | ||
| return (dt_exchange,) | ||
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| @app.cell | ||
| def _(mo): | ||
| mo.md(r""" | ||
| ## Model simulation | ||
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| We now have finished initializing the metapopulation model. The graph-based simulation is created and advanced until `tmax` via: | ||
| """) | ||
| return | ||
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| @app.cell | ||
| def _(dt_exchange, graph, osecir, t0, tmax): | ||
| import os | ||
| # Silence C++ log output; it can deadlock marimo's output pipe on Windows | ||
| devnull = os.open(os.devnull, os.O_WRONLY) | ||
| saved_stdout, saved_stderr = os.dup(1), os.dup(2) | ||
| os.dup2(devnull, 1) | ||
| os.dup2(devnull, 2) | ||
| try: | ||
| # Create graph simulation and advance until tmax | ||
| sim = osecir.MobilitySimulation(graph, t0, dt=dt_exchange) | ||
| sim.advance(tmax) | ||
| finally: | ||
| os.dup2(saved_stdout, 1) | ||
| os.dup2(saved_stderr, 2) | ||
| os.close(devnull) | ||
| os.close(saved_stdout) | ||
| os.close(saved_stderr) | ||
| return (sim,) | ||
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@@ -288,16 +306,18 @@ def _(mo): | |
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| @app.cell | ||
| def _(osecir, result_region0, result_region1): | ||
| result_region0_interpolated = osecir.interpolate_simulation_result( | ||
| result_region0) | ||
| result_region1_interpolated = osecir.interpolate_simulation_result( | ||
| result_region1) | ||
| return result_region0_interpolated, result_region1_interpolated | ||
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| @app.cell | ||
| def _(mo): | ||
| mo.md(r""" | ||
| ## Visualization of model output | ||
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| Finally, we can compare the trajectories of all infection states for both regions. In the following, we plot the number of `InfectedNoSymptoms` aggregated over all age groups for both regions: | ||
| """) | ||
| return | ||
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@@ -312,8 +332,10 @@ def _(osecir, plt, result_region0_interpolated, result_region1_interpolated): | |
| # Plot the number of non-symptomatically infected for both regions | ||
| fig, ax = plt.subplots() | ||
| time = result_array_0[0, :] | ||
| InfectedNoSymptoms_0 = result_array_0[1 + int(osecir.InfectionState.InfectedNoSymptoms), :] + result_array_0[1 + int(osecir.InfectionState.InfectedNoSymptoms) + int( | ||
| osecir.InfectionState.Dead) + 1, :] + result_array_0[1 + int(osecir.InfectionState.InfectedNoSymptoms) + 2 * (int(osecir.InfectionState.Dead) + 1), :] | ||
| InfectedNoSymptoms_1 = result_array_1[1 + int(osecir.InfectionState.InfectedNoSymptoms), :] + result_array_1[1 + int(osecir.InfectionState.InfectedNoSymptoms) + int( | ||
| osecir.InfectionState.Dead) + 1, :] + result_array_1[1 + int(osecir.InfectionState.InfectedNoSymptoms) + 2 * (int(osecir.InfectionState.Dead) + 1), :] | ||
| ax.plot(time, InfectedNoSymptoms_0, label='Infected No Symptoms Region 1') | ||
| ax.plot(time, InfectedNoSymptoms_1, label='Infected No Symptoms Region 2') | ||
| ax.set_xlabel('Time [days]') | ||
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