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.

Evolutionary Dynamics - Practice

Overview

For this module, we will explore a stochastic SIR-type model with 2 different pathogen strains, wild-type and a drug resistant mutant in the presence of drug treatment. 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, wild-type infected untreated, wild-type infected treated, drug resistant infected 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
S turn into Iu S => S-1, Iu => Iu+1 (1-f) * (bu * (1-cu) * Iu + bt * (1-ct) * It) * S
S turn into It S => S-1, It => It+1 f * (bu * (1-cu) * Iu + bt * (1-ct) * It) * S
S turn into Ir S => S-1, Ir => Ir+1 (bu * cu * Iu + bt * ct * It + br * Ir) * S
Recovery of Iu Iu => Iu-1, R => R+1 gu * Iu
Recovery of It It => It-1, R => R+1 gt * It
Recovery of Ir Ir => Ir-1, R => R+1 gr * Ir

What to do

All parameters described below and in the model are assumed to be in units of (inverse) days

Task 1:

Task 2:

Task 3:

Task 4:

Task 5:

Task 6:

Further Information

References

Handel, Andreas, Ira M Longini Jr, and Rustom Antia. 2009. “Antiviral Resistance and the Control of Pandemic Influenza: The Roles of Stochasticity, Evolution and Model Details.” J Theor Biol 256 (1). Department of Biology, Emory University, Atlanta, GA 30322, USA. andreas.handel@gmail.com: 117–25. doi:10.1016/j.jtbi.2008.09.021.


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.