Vector Borne Transmission

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. mosquitoes. 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 only a 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 this model.

Flow diagram for this model.

Model equations:

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

What to do

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

Task 2

Task 3

Task 4

Task 5

Task 6

Task 7

Task 8

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. https://doi.org/10.1016/S0140-6736(12)61151-9.