{

// MEmilio implements various models based on ordinary differential equations (ODEs). ODE-based models are a

// subclass of compartmental models in which individuals are grouped into subpopulations called compartments.

// In this tutorial we will setup and run MEmilio's ODE-based SECIR-type model. This model is particularly

// suited for pathogens with pre- or asymptomatic infection states and when severe or critical symptoms are possible.

// The model assumes perfect immunity after recovery. The used infection states or compartments are Susceptible (S),

// Exposed(E), Non-symptomatically Infected (Ins), Symptomatically Infected (Isy), Severely Infected (Isev),

// Critically Infected (Icri), Dead (D) and Recovered (R). The transitions are depicted in the following figure.

// *** Set up model. ***

// We need to specify basic parameters. In this tutorial, we use a simple model without spatial resolution and

// with only one age group.

size_t num_agegroups = 1;

// We first define the `total_population` size and the simulation horizong through the start day `t0`, and the

// simulation's end point `tmax`. By default, the ODE is solved with adaptive time stepping and the initial time step is `dt`.

ScalarType total_population = 100000;

ScalarType t0 = 0;

ScalarType tmax = 100;

ScalarType dt = 0.1;

// Create model

mio::osecir::Model<ScalarType> model(num_agegroups);

// Next, we have to set the epidemiological model parameters which include the average stay times per infection

// state, the state transition probabilities, and the contact frequency. A list of all parameters can be found

// at https://memilio.readthedocs.io/en/latest/cpp/models/osecir.html. The parameters can be set as follows:

// Set infection state stay times (in days)

model.parameters.get<mio::osecir::TimeExposed<ScalarType>>() = 3.2;

model.parameters.get<mio::osecir::TimeInfectedNoSymptoms<ScalarType>>() = 2.;

model.parameters.get<mio::osecir::TimeInfectedSymptoms<ScalarType>>() = 6.;

model.parameters.get<mio::osecir::TimeInfectedSevere<ScalarType>>() = 12.;

model.parameters.get<mio::osecir::TimeInfectedCritical<ScalarType>>() = 8.;

// Set infection state transition probabilities

model.parameters.get<mio::osecir::RelativeTransmissionNoSymptoms<ScalarType>>() = 0.67;

model.parameters.get<mio::osecir::TransmissionProbabilityOnContact<ScalarType>>() = 0.1;

model.parameters.get<mio::osecir::RecoveredPerInfectedNoSymptoms<ScalarType>>() = 0.2;

model.parameters.get<mio::osecir::RiskOfInfectionFromSymptomatic<ScalarType>>() = 0.25;

model.parameters.get<mio::osecir::SeverePerInfectedSymptoms<ScalarType>>() = 0.2;

model.parameters.get<mio::osecir::CriticalPerSevere<ScalarType>>() = 0.25;

model.parameters.get<mio::osecir::DeathsPerCritical<ScalarType>>() = 0.3;

//Set contact frequency

ScalarType contact_frequency = 10;

mio::ContactMatrixGroup<ScalarType>& contact_matrix =

model.parameters.get<mio::osecir::ContactPatterns<ScalarType>>();

contact_matrix[0] = mio::ContactMatrix<ScalarType>(Eigen::MatrixX<ScalarType>::Constant(1, 1, contact_frequency));

// In addition to the parameters, the initial number of individuals in each compartment has to be set. If a

// compartment is not set, its initial value is zero by default. In this example, we start our simulation with 1 %

// of the population initially infected, distributing them equally to the `Exposed` and the `InfectedNoSymptoms`

// state, where the latter contains pre- and asymptomatic infectious individuals. With the last line,

// we set the remaining part of the population (99%) to be susceptible.

model.populations[{mio::AgeGroup(0), mio::osecir::InfectionState::Exposed}] = 0.005 * total_population;

model.populations[{mio::AgeGroup(0), mio::osecir::InfectionState::InfectedNoSymptoms}] = 0.005 * total_population;

model.populations.set_difference_from_total({mio::AgeGroup(0), mio::osecir::InfectionState::Susceptible},

total_population);

// To check that all initial parameter and compartmental values are in a meaningful range, MEmilio provides the

// `check_constraints` function. If a value exceeds its meaningful range, a warning is printed and the function

// returns `True`, otherwise it returns `False`.

model.check_constraints();

// *** Simulate model. ***

mio::TimeSeries<ScalarType> result = mio::osecir::simulate<ScalarType>(t0, tmax, dt, model);

// Interpolate time series to full days.

auto interpolated_result = mio::interpolate_simulation_result(result);

// *** Print results. ***

interpolated_result.print_table({"S", "E", "C", "C_confirmed", "I", "I_confirmed", "H", "U", "R", "D"}, 12, 4);

// We export the results as csv which is saved in the current folder. Then we can plot the results using

// plot_secir_results.py.

auto export_status = result.export_csv("../../cpp-tutorials/results_ode.csv");