The Model

Model Overview

This model tracks susceptibles, wild-type infected untreated, wild-type infected treated, drug-resistant infected and recovered hosts. The following compartments are included:

The included processes/mechanisms are the following:

Model Implementation

The flow diagram for the model implemented in this app is:

Flow diagram for this model.

Flow diagram for this model.

Note that this model is not an ordinary differential equation model. It is instead its stochastic equivalent. We can specify the model by writing down every possible transition/event/reaction that can occur and their propensities (the propensity multiplied with the time step gives the probability that a given event/transition occurs). For our model these are the following:

Event type Transitions Propensity
S turn into Iu S => S-1, Iu => Iu+1 (1-f) * (bu * (1-cu) * Iu + bt * (1-ct) * It) * S
S turn into It S => S-1, It => It+1 f * (bu * (1-cu) * Iu + bt * (1-ct) * It) * S
S turn into Ir S => S-1, Ir => Ir+1 (bu * cu * Iu + bt * ct * It + br * Ir) * S
Recovery of Iu Iu => Iu-1, R => R+1 gu * Iu
Recovery of It It => It-1, R => R+1 gt * It
Recovery of Ir Ir => Ir-1, R => R+1 gr * Ir