diff --git a/cpp/models/ide_secir/README.md b/cpp/models/ide_secir/README.md index 78362fbf73..9e9a142f12 100644 --- a/cpp/models/ide_secir/README.md +++ b/cpp/models/ide_secir/README.md @@ -1,22 +1,52 @@ # IDE SECIR model -This model is based on Integro-differential equations. The eight compartments -- Susceptible, may become exposed at any time -- Exposed, becomes infected after some time -- InfectedNoSymptoms, becomes InfectedSymptoms or Recovered after some time -- InfectedSymptoms, becomes InfectedSevere or Recovered after some time -- InfectedSevere, becomes InfectedCritical or Recovered after some time -- InfectedCritical, becomes Recovered or Dead after some time -- Recovered -- Dead +This model is based on integro-differential equations. +The eight compartments +- `Susceptible` ($S$), may become Exposed at any time +- `Exposed` ($E$), becomes InfectedNoSymptoms after some time +- `InfectedNoSymptoms` ($I_{NS}$), becomes InfectedSymptoms or Recovered after some time +- `InfectedSymptoms` ($I_{Sy}$), becomes InfectedSevere or Recovered after some time +- `InfectedSevere` ($I_{Sev}$), becomes InfectedCritical or Recovered after some time +- `InfectedCritical` ($I_{Cr}$), becomes Recovered or Dead after some time +- `Recovered` ($R$) +- `Dead` ($D$) are used to simulate the spread of the disease. +Below is an overview of the model architecture and its compartments. +The variables $\sigma_{z_1}^{z_2}$ refer to a transition from a compartment $z_1$ to a compartment $z_2$. -The simulation runs in discrete time steps using a non-standard numerical scheme. This approach is based on the paper "A non-standard numerical scheme for an age-of infection epidemic model" by Messina et al., Journal of Computational Dynamics, 2022. +![tikzIDESECIR](https://github.com/SciCompMod/memilio/assets/70579874/3500421a-035c-4ce1-ae95-a54d8097be82) + +The model parameters used are the following: + +| Mathematical variable | C++ variable name | Description | +|---------------------------- | --------------- | -------------------------------------------------------------------------------------------------- | +| $\phi$ | `ContactPatterns` | Average number of contacts of a person per day. | +| $k$ | `Seasonality` | The influence of the seasons is taken into account with the seasonality parameter. | +| $\rho$ | `TransmissionProbabilityOnContact` | Transmission risk for people located in the Susceptible compartment. | +| $\xi_{I_{NS}}$ | `RelativeTransmissionNoSymptoms` | Proportion infected people with no symptoms who are not isolated. | +| $\xi_{I_{Sy}}$ | `RiskOfInfectionFromSymptomatic` | Proportion of infected persons with symptoms who are not isolated. | +| $N$ | `m_N` | Total population. | +| $D$ | Entry of `m_populations` | Number of dead people. | +| $\mu_{z_1}^{z_2}$ | `TransitionProbabilities` | Probability of transitioning from compartment $z_1$ to compartment $z_2$. | +| $\gamma_{z_1}^{z_2}(\tau)$ | `TransitionDistributions` | Expected proportion of people who are still in compartment $z_1$ $\tau$ days after entering this compartment and who will move to compartment $z_2$ later in the course of the disease. | + +The simulation runs in discrete time steps using a non-standard numerical scheme. This approach is based on the paper ["A non-standard numerical scheme for an age-of infection epidemic model" by Messina et al., Journal of Computational Dynamics, 2022](https://doi.org/10.3934/jcd.2021029). ## Examples An example can be found at: -- examples/ide_secir.cpp \ No newline at end of file +- [IDE minimal example](../../examples/ide_secir.cpp) + +## Initialization + +- The file [parameters_io](parameters_io.h) provides functionality to compute initial data for the IDE-SECIR model based on real data. An example for this initialization method can be found at [IDE initialization example](../../examples/ide_initialization.cpp). + +- There are various options for initializing a fictional scenario. Regardless of the approach, you must provide a history of values for the transitions and additional information to compute the initial distribution of the population in the compartments. This information must be of the following type: + + - You can state the number of total confirmed cases `total_confirmed_cases` at time $t_0$. The number of recovered people is set accordingly and the remaining values are derived in the model before starting the simulation. + - You can set the number of people in the `Susceptible` compartment at time $t_0$ via `m_populations`. Initial values of the other compartments are derived in the model before starting the simulation. + - You can set the number of people in the `Recovered` compartment at time $t_0$ via `m_populations`. Initial values of the other compartments are derived in the model before starting the simulation. + - If none of the above is used, the force of infection formula and the values for the initial transitions are used consistently with the numerical scheme proposed in [Messina et al (2022)](https://doi.org/10.3934/jcd.2021029) to set the `Susceptible`s. diff --git a/cpp/models/ode_secir/README.md b/cpp/models/ode_secir/README.md index aecbe10ac5..ed971c9739 100644 --- a/cpp/models/ode_secir/README.md +++ b/cpp/models/ode_secir/README.md @@ -20,7 +20,7 @@ Below is an overview of the model architecture and its compartments. | $\phi$ | `ContactPatterns` | Matrix of daily contact rates / number of daily contacts between different age groups. | | $\rho$ | `TransmissionProbabilityOnContact` | Transmission risk for people located in one of the susceptible compartments. | | $\xi_{I_{NS}}$ | `RelativeTransmissionNoSymptoms` | Proportion of nonsymptomatically infected people who are not isolated. | -| $\xi_{I_{Sy}}$ | `riskFromInfectedSymptomatic` | Proportion of infected people with symptomps who are not isolated (time-dependent if `TestAndTraceCapacity` used). | +| $\xi_{I_{Sy}}$ | `riskFromInfectedSymptomatic` | Proportion of infected people with symptoms who are not isolated (time-dependent if `TestAndTraceCapacity` used). | | $N_j$ | `Nj` | Total population of age group $j$. | | $D_i$ | `Di` | Number of death people of age group $i$. | | $T_{E}$ | `TimeExposed` | Time in days an individual stays in the Exposed compartment. |