The Model

Model Overview

This model is fairly big and has many parts that can be turned on or off depending on parameter settings. The model allows for 3 types of transmission: direct, through an environmental stage, and through a vector stage. The (human) host is modeled in some detail, the environment and vectors are modeled with 1 and 2 compartments. The following compartments are included:

The included processes/mechanisms are the following:

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.)

Also note that we made several simplifcations to keep the model from getting too complex. For instance presymptomatic individuals do not shed into the environment and only symptomatic hosts are assumed to be able to infect vectors. Further details relaxing these assumptions could of course be included, at the expense of a larger and more complex model.

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.

\[\dot S = e_h - S (b_P P + b_A A + b_I I + b_E E + b_v I_v) + wR - n_h S \] \[\dot P = S (b_P P + b_A A + b_I I + b_E E + b_v I_v) - g_P P - n_h P\] \[\dot A = f g_P P - g_A A - n_h A\] \[\dot I = (1-f) g_P P - g_I I - n_h I \] \[\dot R = g_A A + (1-d) g_I I - wR - n_h R\] \[\dot D = d g_I I \] \[\dot E = p_I I + p_A A - c E \] \[\dot S_v = e_v - b_h I S_v - n_v S_v \] \[\dot I_v = b_h I S_v - n_v I_v \]

To keep the diagram from getting too cluttered, births and natural deaths are not drawn.