Multi Pathogen Dynamics - Documentation

Overview

This app allows you to explore a model with 2 pathogens. Read about the model in the “Model” tab. Then do the tasks described in the “What to do” tab.

The Model

Model Overview

This model tracks susceptible hosts, hosts infected with either pathogen 1, pathogen 2 or both, and individuals recovered from infection with pathogen 1, pathogen 2 or both. As usual, infected hosts are assumed to be infectious.

The following compartments are included:

The included processes/mechanisms are the following:

Model Implementation

The flow diagram and the set of differential equations for the mathematical model implemented in this app are as follows:

Flow diagram for this model.

Flow diagram for this model.

\[\dot S = - (b_{1} (I_1+I_{1X}) + b_{2} (I_2+I_{2X}) + b_{12}I_{12}) S \] \[\dot I_1 = (b_{1} (I_1+I_{1X}) + ab_{12} I_{12})S - (g_1 + b_{2} (I_2+I_{2X}) + b_{12} I_{12}) I_1\] \[\dot I_2 = (b_{2} (I_2+I_{2X}) + (1-a) b_{12} I_{12})S - (g_2 + b_{1}(I_1 + I_{1X}) + b_{12} I_{12}) I_2\] \[\dot I_{12} = (b_{2} (I_2+I_{2X}) + b_{12} I_{12}) I_1 + (b_{1}(I_1 + I_{1X}) + b_{12} I_{12}) I_2 - g_{12} I_{12}\] \[\dot R_1 = g_1 I_1 - (b_2 (I_2 + I_{2X}) + b_{12} I_{12}) R_1\] \[\dot R_2 = g_2 I_2 - (b_1 (I_1 + I_{1X}) + b_{12} I_{12}) R_2\] \[\dot I_{1X} = (b_1 (I_1 + I_{1X}) + b_{12} I_{12}) R_2 - g_{1} I_{1X}\] \[\dot I_{2X} = (b_2 (I_2 + I_{2X}) + b_{12} I_{12}) R_1 - g_{2} I_{2X}\] \[\dot R_{12} = g_{1} I_{1X} + g_{2} I_{2X} + g_{12} I_{12} \]

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:

Task 7:

Further Information

References