DSAIDE - Dynamical Systems Approach to Infectious Disease Epidemiology

A collection of Shiny/R Apps to explore and simulate the population dynamics of infectious diseases.
Written and maintained by Andreas Handel, with contributions from others.

Vector Borne Transmission - Practice

Overview

This app allows you to explore a simple model for vector-borne transmission. Read about the model in the “Model” tab. Then do the tasks described in the “What to do” tab.

The Model

Model Overview

This is a simple 2 species (hosts and vectors) model, using the basic SIR framework as follows.

The model has the following compartments:

We assume that once a vector is infected, it stays infected until it dies. Therefore, recovered vectors are not included in the model.

The processes being modeled are:

We envision hosts to be humans and vectors to be e.g. mosquitos. We further assume the time scale for the model is short enough that we can ignore births and deaths for human hosts but not vectors. This is likely a decent approximation as long as our simulation time is not more than few years.

Model Implementation

The flow diagram and the set of ordinary differential equations (ODE) which are used to implement this model are as follows:

Flow diagram for the model with environmental transmission.

Flow diagram for the model with environmental transmission.

\[\dot S_h = - b_1 S_h I_v + w R_h\] \[\dot I_h = b_1 S_h I_v - g I_h\] \[\dot R_h = g I_h - w R_h\] \[\dot S_v =b - b_2 S_v I_h - n S_v\] \[\dot I_v = b_2 S_v I_h - n I_v\]

What to do

A general note: Some of the tasks below are fairly open ended. You shouldn’t go through the tasks like a check-list. Instead, explore these simulations, play with them, query them. As you do, loop through iterations of formulating your expectations for a specific scenario/task, running the model and observing results, and if results don’t agree with your expectations, figure out why. Essentially, “do science/research”.

The simulation is assumed to run in units of months, i.e. all rate parameters are assumed to be in inverse months.

Task 1:

Task 2:

Task 3:

Task 4:

Task 5:

Task 6:

Answers

This section does not have the shinytab label and is therefore ignored and not included in the app. One could provide the answers here. Note that if this file is supplied with the package, the answers are in principle available.

Answer 1:

Answer to task 1.

Further Information

References

Kilpatrick, A Marm, and Sarah E Randolph. 2012. “Drivers, Dynamics, and Control of Emerging Vector-Borne Zoonotic Diseases.” Lancet (London, England) 380 (9857): 1946–55. doi:10.1016/S0140-6736(12)61151-9.

Luz, Paula M, Claudio J Struchiner, and Alison P Galvani. 2010. “Modeling Transmission Dynamics and Control of Vector-Borne Neglected Tropical Diseases.” PLoS Neglected Tropical Diseases 4 (10): e761. doi:10.1371/journal.pntd.0000761.


This package is built and maintained by Andreas Handel, with contributions from others.
All text and figures are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Software/Code is licensed under GPL-3.