The Model

Model Overview

Note: I’ll be using the term individual(s) and host(s) interchangably in the future. This is common usage and I want you to get used to this terminology, therefore I’m switching around on purpose. They mean the same thing in this context.

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, this model could be made to include further details by extendind the compartments. E.g. doubling the compartments would allow us to stratify according to gender. In general, for each additional distinct feature you want to track, the existing number of compartments needs to be replicated by the discrete categories you have. So replicated by 2 for gender, replicated by 3 if we wanted to stratify by young/medium/old age, 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.

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