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.

Host Heterogeneity - Practice

Overview

For this module, we will explore a simple SIR model with 2 types of hosts. 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, infected and recovered of 2 different types. Think of those types as e.g. males/females, children/adults, etc.

The following compartments are included, twice for each type (i=1,2):

The included processes/mechanisms are the following:

Model Implementation

The flow diagram and the mathematical model which are implemented in this app are as follows:

Flow diagram for this model. Natural births and deaths are not drawn.

Flow diagram for this model. Natural births and deaths are not drawn.

\[\dot S_1 = e_1 - S_1 (b_{11} I_1 + b_{12} I_2) + w_1 R_1 - n_1 S_1 \] \[\dot I_1 = S_1 (b_{11} I_1 + b_{12} I_2) - g_1 I_1 - n_1 I_1 \] \[\dot R_1 = g_1 I_1 - w_1 R_1 - n_1 R_1\] \[\dot S_2 = e_2 - S_2 (b_{22} I_2 + b_{21} I_1) + w_2 R_2 - n_2 S_2 \] \[\dot I_2 = S_2 (b_{22} I_2 + b_{21} I_1) - g_2 I_2 - n_2 I_2 \] \[\dot R_2 = g_2 I_2 - w_2 R_2 - n_2 R_2\]

What to do

Task 1:

Task 2:

Task 3:

Task 4:

Task 5:

Task 6:

Task 7:

Task 8:

Task 9:

Further Information

References

Beldomenico, Pablo M, and Michael Begon. 2010. “Disease Spread, Susceptibility and Infection Intensity: Vicious Circles?” Trends in Ecology & Evolution 25 (1): 21–27. doi:10.1016/j.tree.2009.06.015.

Lloyd-Smith, J. O., S. J. Schreiber, P. E. Kopp, and W. M. Getz. 2005. “Superspreading and the Effect of Individual Variation on Disease Emergence.” Nature 438 (7066). Department of Environmental Science, Policy; Management, 140 Mulford Hall, University of California, Berkeley, California 94720-3114, USA. jls@nature.berkeley.edu: 355–59. doi:10.1038/nature04153.

Yorke, J. A., H. W. Hethcote, and A. Nold. 1978. “Dynamics and Control of the Transmission of Gonorrhea.” Sex Transm Dis 5 (2). Institute for Physical Science; Technology, University of Maryland, College Park, USA.: 51–56.


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.