This proyect is an interactive web application, developed with Shiny to explore and visualize various mathematical and stochastic models related to the spread of infectious diseases, specifically Covid-19.
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Deterministic Models: The included deterministic models are based on systems of ODE's that describe how different population groups (Succeptible, Infected, Recovered) evolve over time. They assume a closed and homogeneous population, where every individual interacts the same way.
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SIR Model:
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The population is divided into three groups:
- S: Susceptible individuals who can catch the disease.
- I: Infected individuals who can spread the disease.
- R: Recovered individuals who are no longer susceptible or infectious
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The model uses parameters like transmission rate and recovery rate to simulate disease dynamics. Also R_0, the basic reproduction number, is a metric to understand if a pandemic will spread or decline.
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Extended SIR model with vaccination: This model incorporates a V (Vaccinated) group to simulate the effects of vaccination campaigns, through a parameter u, representing the number of people vaccinated per day.
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Stochastic Models: They introduce randomness into the model dynamics, making them more realistic for capturing uncertainties and variations. These model use random variables to model different processes in each part of the model.
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Basic Stochastic Model: This model uses random variables (Bernoulli and Binomial distribution) to determine wether a succeptible individual becomes infected or an infected individual recovers.
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Simulations generate different outcomes even with the same initial conditions, helping explore best and worst case scenarios.
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Extended Stochastic Model: This model builds from the previous, but adds more detailed groups, such as:
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$\mathbf{E}$ : Exposed individuals in the incubation period. -
$\mathbf{I_s}$ : Symptomatic infected individuals. -
$\mathbf{I_a}$ : Asymptomatic infected individuals. -
$\mathbf{Q}$ : Quarantined individuals. -
$\mathbf{D}$ : Deceased individuals. -
$\mathbf{R}$ . Recovered individuals with temporary inmunity.
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Parameters like quarantine probability, mask usage, or vaccination timing allow for simulating the impact of interventions on the epidemic's progression.
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Visual comparisons 📋
- Through the use of ggplot and different R libraries, the application provides visual toosl to compare:
- The effects of vaccination and no vaccination within deterministic models.
- Variability in epidemic outcomes due to randomness in stochastic models
- How interventions (e.g., masks, quarantine) influence outcomes over time.
- How to run the application:
- Clone the repository or download the app.R file.
- Install the required packages:
install.packages(c("shiny", "shinydashboard", "shinyjs", "ggplot2", "deSolve", "ggiraph", "data.table"))- Open the app.R file in RStudio.
- Run the app using:
shiny::runApp()- The app will start to run in your web browser.
- Juan Pablo Guerrero Escudero (A01706810, Campus Querétaro)
- Romina Nájera Fuentes (A01424411, Campus Querétaro)
- Juan Braulio Olivares Rodríguez (A01706880, Campus Querétaro)