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.

Direct Transmission Modes - Practice

Overview

This app allows you to explore a model with 2 different modes of direct transmission. Read about the model in the “Model” tab. Then do the tasks described in the “What to do” tab.

The Model

Model Overview

This is a simple SIR model with births and deaths and 2 types of direct transmission, density-dependent and frequency-dependent (based on the terminology in (Begon et al. 2002) - see Further Information tab for references).

This model has the following compartments:

The processes being modeled are:

The force of infection, \(\lambda\), depends on the transmission model. For density-dependent transmission, it is given by \(\lambda = b_d I / A\), where A is the area of the scenario under consideration (e.g. a city). For frequency-dependent transmission, we have \(\lambda = b_f I / N\), where N is the size of the population, N=S+I+R.

Model Implementation

The flow diagram and the set of ordinary differential equations (ODE) which are used to implement this model are as follows:

Flow diagram for this model.

Flow diagram for this model.

\[\dot S =b - \lambda S + wR - nS\] \[\dot I = \lambda S - g I -nI\] \[\dot R = g I - wR - nR\]

with \(\lambda = b_d I / A\) for density-dependent transmission and \(\lambda = b_f I / N\) for frequency-dependent transmission.

Model Comments

Note that quite often, we assume that the area is constant and do not include it in the model or even talk about it. Often, the population size is also assumed to be constant. In that case, the 2 types of transmission models behave the same. But as soon as area or population size change, the model results differ. Which is what you can explore with this simulation.

What to do

A general note: Some of the tasks below are fairly open ended. You shouldn’t go through the tasks like a check-list. Instead, explore these simulations, play with them, query them. As you do, loop through iterations of formulating your expectations for a specific scenario/task, running the model and observing results, and if results don’t agree with your expectations, figure out why. Essentially, “do science/research”.

Task 1:

Task 2:

Task 3:

Task 4:

Task 5:

Answers

This section does not have the shinytab label and is therefore ignored and not included in the app. One could provide the answers here. Note that if this file is supplied with the package, the answers are in principle available, so most users might not know where/how to look.

Answer 1:

Answer to task 1.

Further Information

References

Begon, M., M. Bennett, R. G. Bowers, N. P. French, S. M. Hazel, and J. Turner. 2002. “A Clarification of Transmission Terms in Host-Microparasite Models: Numbers, Densities and Areas.” Epidemiol Infect 129 (1). ences, The University of Liverpool, UK.: 147–53.


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.