si_partnerships_sti model

inst/starter_models/si_partnerships_sti/README.Rmd

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+---
+title: "STI Partnership Model"
+output:
+  html_document:
+    df_print: paged
+---
+
+```{r setup}
+library(macpan2)
+library(ggplot2)
+```
+
+## Introduction
+
+This document describes a **Sexually Transmitted Infection (STI) Partnership Model** implemented in `macpan2`. The model simulates how STIs spread within a population where individuals form and dissolve partnerships, incorporating both **within-partner transmission** and **external transmission**.
+
+## Model Description
+
+The compartments in the model are:
+
+- **S**: Susceptible individuals
+- **I**: Infected individuals
+- **SS**: Susceptible-Susceptible partnerships
+- **SI**: Susceptible-Infected partnerships
+- **II**: Infected-Infected partnerships
+
+### Dynamics:
+
+1. **Partnership Formation**: Susceptible individuals form partnerships, transitioning into the **SS** or **SI** compartments.
+2. **Partnership Dissolution**: Partnerships dissolve, moving individuals back to the **S** or **I** compartments.
+3. **Within-Partner Transmission**: Infected partners in **SI** compartments transmit infection to their susceptible partners, transitioning them to **II**.
+4. **External Transmission**: Susceptible individuals can be infected through external sources, moving from **S** to **I**.
+
+## Model Simulation
+
+We use the pre-defined model from the library.
+
+```{r load_model}
+# Load the pre-specified STI model
+model <- mp_tmb_library("starter_models", "si_partnerships_sti", package = "macpan2")
+```
+
+## Running the Simulation
+
+The simulation is run for 100 time steps, and results are captured for analysis.
+
+```{r run_simulation}
+simulated_results <- model |> 
+  mp_simulator(time_steps = 100, outputs = c("S", "I", "SS", "SI", "II")) |> 
+  mp_trajectory()
+```
+
+## Results
+
+The plot below shows the changes in population across the compartments over time.
+
+```{r plot_results}
+ggplot(simulated_results, aes(x = time, y = value, color = matrix)) +
+  geom_line() +
+  facet_wrap(~ matrix, scales = "free_y") +
+  theme_bw() +
+  labs(title = "STI Partnership Model Dynamics", x = "Time", y = "Population")
+```
+
+## Conclusion
+
+This model simulates STI spread through partnerships and external sources, offering insights into the role of relationship dynamics in disease transmission. The model can be expanded to explore additional features such as heterogeneity in the population or multiple infection strains.

inst/starter_models/si_partnerships_sti/tmb.R

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+# Load macpan2 library
+library(macpan2)
+
+# Define the model with two-sided formulas for initial conditions and N
+spec <- mp_tmb_model_spec(
+
+  # Define the initial population sizes using two-sided formulas
+  before = list(
+    S ~ 900,    # 900 susceptible individuals
+    I ~ 100,    # 100 infected individuals
+    SS ~ 200,   # 200 Susceptible-Susceptible partnerships
+    SI ~ 100,   # 100 Susceptible-Infected partnerships
+    II ~ 50,    # 50 Infected-Infected partnerships
+    N ~ S + I + 2*(SS + SI + II)  # Total population size as the sum of individuals
+  ),
+
+  # Define partnership formation and dissolution flows
+  during = list(
+    mp_per_capita_flow("S", "SS", "partner_form_rate * S / N", "form_new_partnership"),
+    mp_per_capita_flow("SS", "S", "partner_dissolve_rate", "partnership_dissolution"),
+
+    # Within-partner transmission (SI -> II)
+    mp_per_capita_flow("SI", "II", "beta_SI * I / N", "within_partner_transmission"),
+
+    # Between-partner transmission (S -> I)
+    mp_per_capita_flow("S", "I", "beta_external * I / N", "external_transmission")
+  ),
+
+  # Define default transmission rates and other parameters
+  default = list(
+    partner_form_rate = 0.05,    # Partnership formation rate
+    partner_dissolve_rate = 0.02, # Partnership dissolution rate
+    beta_SI = 0.1,               # Transmission rate within SI partnerships
+    beta_external = 0.05         # External transmission rate
+  )
+)