DSAIDE - Dynamical Systems Approach to Infectious Disease Epidemiology
A collection of Shiny/R Apps to explore and simulate the population dynamics of infectious diseases.
Written and maintained by Andreas Handel, with contributions from others.
For this module, we will explore an SEIR model. This model is implemented in a stochastic framework. Read about the model in the “Model” tab. Then do the tasks described in the “What to do” tab.
This model tracks susceptibles, exposed/pre-sympomatic, infected/symptomatic and recovered hosts. The following compartments are included:
The included processes/mechanisms are the following:
The flow diagram for the model implemented in this app is:
Flow diagram for this model.
Note that this model is not an ordinary differential equation model. It is instead its stochastic equivalent. We can specify the model by writing down every possible transition/event/reaction that can occur and their propensities (the propensity multiplied with the time step gives the probability that a given event/transition occurs). For our model these are the following:
Event type | Transitions | Propensity |
---|---|---|
Infection | S => S-1, E => E+1 | S(bEE+bII) |
Progression to Symptoms | E => E-1, I => I+1 | gEE |
Recovery | I => I-1, R => R+1 | gII |
Waning of Immunity | R => R-1, S => S+1 | wR |
Births | S => S+1 | eS |
Death of susceptible | S => S-1 | nS |
Death of exposed | E => E-1 | nE |
Death of symptomatic | I => I-1 | nI |
Death of recovered | R => R-1 | nR |
Note: Some of the simulations might take a few seconds to run. While they run, you should see a ‘Simulation running’ message.
simulate_stochastic.R
. You can call this function directly, without going through the shiny app. Check the help file for the function for more information.?DSAIDE
at the R console.Black, F L. 1966. “Measles Endemicity in Insular Populations: Critical Community Size and Its Evolutionary Implication.” Journal of Theoretical Biology 11 (2): 207–11.
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Lloyd-Smith, James O, Paul C Cross, Cheryl J Briggs, Matt Daugherty, Wayne M Getz, John Latto, Maria S Sanchez, Adam B Smith, and Andrea Swei. 2005. “Should We Expect Population Thresholds for Wildlife Disease?” Trends in Ecology & Evolution 20 (9): 511–19. doi:10.1016/j.tree.2005.07.004.