The Model

Model Overview

For this app, we’ll use the basic compartmental SIR model. We allow for 3 different stages/compartments:

In addition to specifying the compartments of a model, we need to specify the dynamics determining the changes for each compartment. Broadly speaking, there are processes that increase the number of individuals in a given compartment/stage, and processes that lead to a reduction. Those processes are sometimes called in-flows and out-flows.

For our system, we specify the following processes/flows:

Model Implementation

The flow diagram and the set of equations which are used to implement this model are as follows:

Model Figure

Model Figure

\[S_{v} = (1-ef)S_0\] \[R_0 = efS_{v}\] \[\dot S =\lambda -\beta SI - nS + wR\] \[\dot I = \beta S I - \gamma I - nI\] \[\dot R = \gamma I - nR - wR\]

Here, \(S_0\) is the initial population of susceptibles, and \(S_{v}\) is the susceptible population after vaccination. Vaccinated individuals are moved to the \(R\) compartment prior to the start of the outbreak.