Host Heterogeneity - Practice

Overview

For this module, we will explore a simple SIR model with 2 types of hosts. 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 susceptibles, infected and recovered of 2 different types. Think of those types as e.g. males/females, children/adults, etc.

The following compartments are included, twice for each type (i=1,2):

The included processes/mechanisms are the following:

Model Implementation

The flow diagram and equations describe the model implemented in this app:

Flow diagram for this model. Natural births and deaths are not drawn.

Flow diagram for this model. Natural births and deaths are not drawn.

\[\dot S_1 = - S_1 (b_{11} I_1 + b_{21} I_2) + w_1 R_1 \] \[\dot I_1 = S_1 (b_{11} I_1 + b_{21} I_2) - g_1 I_1 \] \[\dot R_1 = g_1 I_1 - w_1 R_1 \] \[\dot S_2 = - S_2 (b_{22} I_2 + b_{12} I_1) + w_2 R_2 \] \[\dot I_2 = S_2 (b_{22} I_2 + b_{12} I_1) - g_2 I_2 \] \[\dot R_2 = g_2 I_2 - w_2 R_2 \]

What to do

The tasks below are described in a way that assumes everything is in units of MONTHS (rate parameters, therefore, have units of inverse months). If any quantity is not given in those units, you need to convert it first (e.g. if it says a year, you need to convert it to 12 months).

Task 1:

Set the model parameters such that it corresponds to the following setting:

Task 2:

Task 3:

Task 4:

Task 5:

Task 6:

Transmission only between hosts of different type could for instance represent a sexually transmitted disease in a heterosexual population, with the 2 types of hosts being females and males.

Task 7:

Task 8:

Task 9:

Task 10:

Task 11:

Task 12:

Task 13:

Task 14:

Task 15:

Further Information

References

Beldomenico, Pablo M, and Michael Begon. 2010. “Disease Spread, Susceptibility and Infection Intensity: Vicious Circles?” Trends in Ecology & Evolution 25 (1): 21–27. https://doi.org/10.1016/j.tree.2009.06.015.

Lloyd-Smith, J. O., S. J. Schreiber, P. E. Kopp, and W. M. Getz. 2005. “Superspreading and the Effect of Individual Variation on Disease Emergence.” Nature 438 (7066): 355–59. https://doi.org/10.1038/nature04153.

Yorke, J. A., H. W. Hethcote, and A. Nold. 1978. “Dynamics and Control of the Transmission of Gonorrhea.” Sex Transm Dis 5 (2): 51–56.