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.

ID Patterns - Practice

Overview

This app allows you to explore a model that tracks the same compartments as the Characteristics of ID model. If you haven’t yet explored the Characteristics of ID model, I suggest you try out that one first. The model for this app adds a few more processes. It includes natural births and deaths of hosts, seasonal variation in transmission, and waning immunity.

Also note that for this model, the time units are in months, not days. 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 has the same compartments as the one we saw previously. They are listed and described again:

We include the following processes in this model:

Note that we only track people that die due to the disease in our \(D\) compartment. All hosts dying due to other causes just “exit the system” and we don’t further keep track of them (though we could add another compartment to “collect” and track all individuals who died from non disease related causes.)

Model Implementation

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

Flow diagram for this model.

Flow diagram for this model.

\[b_P^s = b_P(1+\sigma \sin(2\pi t /12))\] \[b_A^s = b_A(1+\sigma \sin(2\pi t /12))\] \[b_I^s = b_I(1+\sigma \sin(2\pi t /12))\] \[\dot S = \lambda - S (b_P^s P + b_A^s A + b_I^s I) + wR - n S \] \[\dot P = S (b_P^s P + b_A^s A + b_I^s I) - g_P P - n P\] \[\dot A = f g_P P - g_A A - n A\] \[\dot I = (1-f) g_P P - g_I I - n I \] \[\dot R = g_A A + (1-d) g_I I - wR - n R\] \[\dot D = d g_I I \]

Since we do not track people dying due to non-disease causes, all the “n - arrows” are not pointing to another compartment, instead those individuals just “leave the system”. Similarly new susceptibles enter the system (are born) from “outside the system”.

Also note that the transmission rates, bi, can be time varying as described above.

What to do

Note: Some of the simulations might take a few seconds to run. Be patient.

Task 1:

Task 2:

Task 3:

Task 4:

Task 5:

Task 6:

Task 7:

Task 8:

Task 9:

Task 10:

Further Information

References

Altizer, Sonia, Andrew Dobson, Parviez Hosseini, Peter Hudson, Mercedes Pascual, and Pejman Rohani. 2006. “Seasonality and the Dynamics of Infectious Diseases.” Ecology Letters 9 (4): 467–84. doi:10.1111/j.1461-0248.2005.00879.x.

Dowell, S F. 2001. “Seasonal Variation in Host Susceptibility and Cycles of Certain Infectious Diseases.” Emerging Infectious Diseases 7 (3): 369–74. doi:10.3201/eid0703.010301.


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.