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.

Stochastic Dynamics and Extinctions - Practice

Overview

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.

The Model

Model Overview

This model tracks susceptibles, exposed/pre-sympomatic, infected/symptomatic and recovered hosts. The following compartments are included:

The included processes/mechanisms are the following:

Model Implementation

The flow diagram for the model implemented in this app is:

Flow diagram for this model.

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

What to do

Note: Some of the simulations might take a few seconds to run. While they run, you should see a ‘Simulation running’ message.

Task 1:

Task 2:

Task 3:

Task 4:

Task 5:

Task 6:

Task 7:

Answers

Answer 1:

Answer 2:

Answer 3:

Further Information

References

Black, F L. 1966. “Measles Endemicity in Insular Populations: Critical Community Size and Its Evolutionary Implication.” Journal of Theoretical Biology 11 (2): 207–11.

Keeling, M J. 1997. “Modelling the Persistence of Measles.” Trends in Microbiology 5 (12): 513–18. doi:10.1016/S0966-842X(97)01147-5.

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.


This package is built and maintained by Andreas Handel, with contributions from others.
All text and figures are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Software/Code is licensed under GPL-3.