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