Characterizing Infection States - Documentation

Overview

This app allows you to explore a model that has several more compartments than the basic SIR model discussed in the Introduction to ID app. Read about the model in the “Model” tab. Then do the tasks described in the “What to do” tab.

The Model

Model Overview

In the Introduction to ID app, you explored a simple 3-compartment model, the basic SIR model. The model for this app has a few additional compartments, which allows us to include more details/realism into our model. We again focus on tracking individuals with regard to their infection/disease status. For this model, we track the following compartments/stages:

Of course, as with the basic SIR model, we could include further details by extending the number of compartments. In general, for each additional feature you want to track, the existing number of compartments needs to be replicated by the discrete categories you have. For gender, one would need to have 2x the compartments. Similarly if one wanted to stratify according to young/medium/old age, 3x the compartments are required, etc.

In addition to specifying the compartments of a model, we need to specify the dynamics determining the changes for each compartment. In general, more compartments leads to more processes and more parameters governing these processes.

For this model, we include the following processes:

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.

\[\dot S = -S (b_P P + b_A A + b_I I)\] \[\dot P = S (b_P P + b_A A + b_I I) - g_P P\] \[\dot A = f g_P P - g_A A\] \[\dot I = (1-f) g_P P - g_I I\] \[\dot R = g_A A + (1-d) g_I I\] \[\dot D = d g_I I\]

What to do

The tasks below are described in a way that assumes everything is in units of days (rate parameters, therefore, have units of inverse days). If any quantity is not given in those units, you need to convert it first (e.g. if it says a week, you need to convert it to 7 days).

Task 1:

Task 2:

Task 3:

Task 4:

Task 5:

Task 6:

Further Information

References

Kajita, Emily, Justin T Okano, Erin N Bodine, Scott P Layne, and Sally Blower. 2007. “Modelling an Outbreak of an Emerging Pathogen.” Nature Reviews. Microbiology 5 (9): 700–709. doi:10.1038/nrmicro1660.

Keeling, Matt J, and Pejman Rohani. 2008. Modeling Infectious Diseases in Humans and Animals. Princeton University Press.

Milwid, Rachael, Andreea Steriu, Julien Arino, Jane Heffernan, Ayaz Hyder, Dena Schanzer, Emma Gardner, et al. 2016. “Toward Standardizing a Lexicon of Infectious Disease Modeling Terms.” Frontiers in Public Health 4: 213. doi:10.3389/fpubh.2016.00213.

Vynnycky, Emilia, and Richard White. 2010. An Introduction to Infectious Disease Modelling. Oxford University Press.