928 add a flow chart for the lct model

cpp/models/lct_secir/README.md

@@ -1,23 +1,59 @@
 # LCT SECIR model
 
 This model is based on the Linear Chain Trick. 
+
+The Linear Chain Trick provides the option to use Erlang-distributed sojourn times in the compartments through the use of subcompartments. 
+The normal ODE models have (possibly unrealistic) exponentially distributed sojourn times.
+The LCT model can still be described by an ordinary differential equation system.
+
 For the concept see 
 - Lena Plötzke, "Der Linear Chain Trick in der epidemiologischen Modellierung als Kompromiss zwischen gewöhnlichen und Integro-Differentialgleichungen", 2023. (https://elib.dlr.de/200381/, German only)
 - P. J. Hurtado und A. S. Kirosingh, "Generalizations of the ‘Linear Chain Trick’: incorporating more flexible dwell time distributions into mean field ODE models“, 2019. (https://doi.org/10.1007/s00285-019-01412-w)
 
 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
+- `Susceptible` ($S$), may become exposed at any time
+- `Exposed` ($E$), becomes infected 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. 
 It is possible to include subcompartments for the five compartments Exposed, InfectedNoSymptoms, InfectedSymptoms, InfectedSevere and InfectedCritical.
 
-A simple example can be found at: examples/lct_secir.cpp. 
+Below is an overview of the model architecture and its compartments.
+
+![tikzLCTSECIR](https://github.com/SciCompMod/memilio/assets/70579874/6a5d5a95-20f9-4176-8894-c091bd48bfb7)
+
+| Mathematical variable                   | C++ variable name | Description |
+|---------------------------- | --------------- | -------------------------------------------------------------------------------------------------- |
+| $\phi$                      |  `ContactPatterns`               | Average number of contacts of a person per day. |
+| $\rho$                      |  `TransmissionProbabilityOnContact`               | Transmission risk for people located in the susceptible compartments. |
+| $\xi_{I_{NS}}$               |  `RelativeTransmissionNoSymptoms`               | Proportion of nonsymptomatically infected people who are not isolated. |
+| $\xi_{I_{Sy}}$               | `RiskOfInfectionFromSymptomatic`                | Proportion of infected people with symptomps who are not isolated. |
+| $N$                         | `m_N0`   | Total population. |
+| $D$                         |  `D`  | Number of death people. |
+| $n_E$                         |  Defined via `InfectionState`  | Number of subcompartments of the Exposed compartment. |
+| $n_{NS}$                         |  Defined via `InfectionState`  | Number of subcompartments of the InfectedNoSymptoms compartment. |
+| $n_{Sy}$                         |  Defined via `InfectionState`  | Number of subcompartments of the InfectedSymptoms compartment. |
+| $n_{Sev}$                         | Defined via `InfectionState`  | Number of subcompartments of the InfectedSevere compartment.|
+| $n_{Cr}$                         |  Defined via `InfectionState`  | Number of subcompartments of the InfectedCritical compartment. |
+| $T_E$                    |  `TimeExposed`               | Average time in days an individual stays in the Exposed compartment. |
+| $T_{I_{NS}}$                    |  `TimeInfectedNoSymptoms`               | Average time in days an individual stays in the InfectedNoSymptoms compartment. |
+| $T_{I_{Sy}}$                    |  `TimeInfectedSymptoms`               | Average time  in days an individual stays in the InfectedSymptoms compartment. |
+| $T_{I_{Sev}}$                       |  `TimeInfectedSevere`               | Average time in days an individual stays in the InfectedSevere compartment. |
+| $T_{I_{Cr}}$                       |  `TimeInfectedCritical`               | Average time in days an individual stays in the InfectedCritical compartment. |
+| $\mu_{I_{NS}}^{R}$              |   `RecoveredPerInfectedNoSymptoms`              | Probability of transition from compartment InfectedNoSymptoms to Recovered. |  
+| $\mu_{I_{Sy}}^{I_{Sev}}$              |   `SeverePerInfectedSymptoms`              | Probability of transition from compartment InfectedSymptoms to InfectedSevere. |
+| $\mu_{I_{Sev}}^{I_{Cr}}$              |   `CriticalPerSevere`              | Probability of transition from compartment InfectedSevere to InfectedCritical. |  
+| $\mu_{I_{Cr}}^{D}$              |   `DeathsPerCritical`              | Probability of dying when in compartment InfectedCritical. |   
+
+The notation of the compartments with indices here stands for subcompartments and not for age groups or similar, as in some ODE models. Accordingly, $I_{NS,n_{NS}}$, for example, stands for the number of people in the $n_{NS}$-th subcompartment of the InfectedNoSymptoms compartment.
+
+
+## Examples
 
+A simple example can be found at [LCT minimal example](../../examples/lct_secir.cpp).
 

cpp/models/ode_secir/README.md

@@ -14,7 +14,7 @@ The model consists of the following major classes:
 
 Below is an overview of the model architecture and its compartments.
 
-![secir_model](https://github.com/SciCompMod/memilio/assets/69154294/d99b257b-1cc2-447d-8e32-ba3aa8329c0c)
+![secir_model](https://github.com/SciCompMod/memilio/assets/70579874/46b09e8a-d083-4ef9-8328-21975890b60f)
 | Mathematical variable                   | C++ variable name | Description |
 |---------------------------- | --------------- | -------------------------------------------------------------------------------------------------- |
 | $\phi$                      |  `ContactPatterns`               | Matrix of daily contact rates / number of daily contacts between different age groups. |
@@ -23,8 +23,8 @@ Below is an overview of the model architecture and its compartments.
 | $\xi_{I_{Sy}}$               | `riskFromInfectedSymptomatic`                | Proportion of infected people with symptomps 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 $i$. |
-| $\frac{1}{T_{E}}$                    |  `rateE`               | Time in days an individual stays in the Exposed compartment  (Computed from `SerialInterval` and `IncubationPeriod`). |
-| $\frac{1}{T_{I_{NS}}}$                    |  `rateINS`               | Time in days an individual stays in the InfectedNoSymptoms compartment (Computed from `SerialInterval` and `IncubationPeriod`). |
+| $\frac{1}{T_{E}}$                    |  `rateE`               | Reciprocal of the time in days an individual stays in the Exposed compartment  (Computed from `SerialInterval` and `IncubationPeriod`). |
+| $\frac{1}{T_{I_{NS}}}$                    |  `rateINS`               | Reciprocal of the time in days an individual stays in the InfectedNoSymptoms compartment (Computed from `SerialInterval` and `IncubationPeriod`). |
 | $T_{I_{Sy}}$                    |  `TimeInfectedSymptoms`               | Time in days an individual stays in the InfectedSymptoms compartment. |
 | $T_{I_{Sev}}$                       |  `TimeInfectedSevere`               | Time in days an individual stays in the InfectedSevere compartment. |
 | $T_{I_{Cr}}$                       |  `TimeInfectedCritical`               | Time in days an individual stays in the InfectedCritical compartment. |