# Wolbachia

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## WHAT IS IT?

This model simulates the dynamics of a population of mosquitoes, in which a subset has the bacterial symbiont *Wolbachia*. The model shows how the population that has Wolbachia increases (or not) over time.

## HOW IT WORKS

Female mosquitoes from species such as *Aedes aegypti* when carrying *Wolbachia* generally
generate offspring that also have *Wolbachia* (vertical transmission).

Eggs from female mosquitoes that do not have *Wolbachia* fail to produce offspring when fertilized by male mosquitoes that do have *Wolbachia* due to cytoplasmic incompatibility.

It has been shown that a mosquito such as *Aedes aegypti*, when carrying *Wolbachia*, do not transmit, either partially or totally, pathogens of diseases such as dengue, chikungunya etc.
*Wolbachia* may also decrease mosquito fitness, by reducing its breeding rate or its survival rate.
For these reasons, efforts to generate *Wolbachia*-carrying mosquitoes are an important path for control of such diseases.

The model will show how the two subpopulations progress over time and, eventually, one population is supressed, depending on mosquito fitness and the initial frequency of population that carries *Wolbachia*.

The vertical transmission is assumed to be perfect, and cytoplasmic incompatibility is also assumed to happen in the case of crossings between males with *Wolbachia* and *Wolbachia*-free females.

## HOW TO USE IT

Each "tick" represents a day in the time scale of this model.

The model starts with a population of nMosquitoes, each of which may have *Wolbachia*. The number of mosquitoes that have *Wolbachia* will depend on the frequency chosen by setting the freqInitWolbachia slider.
The carrying capacity is set at maximum 4000.

Mosquitoes move randomly in the world. Red mosquitoes (shown as red dots) have *Wolbachia* and blue ones (blue dots) do not.

The average lifetime for *Wolbachia*-free mosquitoes is determined by normal-lifespan.
A female mosquito that does not carry Wolbachia produces offspring at rate rateOffspring.

Conversely, the average lifetime for *Wolbachia*-carrying mosquitoes is determined by a fraction of normal-lifespan given by fracLifespanWolbachia.
A female mosquito that carries *Wolbachia* produces offspring at rate given by a fraction of rateOffspring given by fracRateOffspWolbachia.

After setting parameters, press SETUP, then GO.

## RELATED MODELS

This model has a setup and structure adapted from the Virus model (Uri Wilensky).

## HOW TO CITE

If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:

Villela, D. (2013). NetLogo Wolbachia model. NetLogo Modeling Commons. Program for Scientific Computing, Oswaldo Cruz Foundation, Rio de Janeiro, Brazil.

Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

## COPYRIGHT AND LICENSE

Copyright 2013 Daniel Villela.

## Comments and Questions

;; Model for simulate mosquitoes infected with bacterial symbiont Wolbachia turtles-own [ wolb? ;; if true, the turtle has Wolbachia wolb-carrying-count ;; how long the turtle has Wolbachia age ;; how many weeks old the turtle is recover-prob ;; not really used (set to zero) x-pos y-pos ] globals [ %infected ;; percentage of the population has Wolbachia carrying-capacity ;; the number of turtles that can be in the world at one time initialInfected avgWolb avgNorm lifespan-with-Wolbachia ;; ndays-week ] to setup clear-all setup-constants setup-turtles update-global-variables reset-ticks end ;; Create a variable number of mosquitoes (nMosquitoes) of which initialWolbachia is ;; the number of mosquitoes that start with Wolbachia to setup-turtles set-default-shape turtles "dot" crt nMosquitoes [ set x-pos random-xcor set y-pos random-xcor setxy x-pos y-pos set age random normal-lifespan set wolb-carrying-count 0 set recover-prob 0 set size 0.5 ;; easier to see get-free ] ask n-of initialInfected turtles [ set age random lifespan-with-Wolbachia ;; setxy ((random world-height/4)- world-height/8) ((random world-width/4)- world-width/8) setxy (x-pos / 4.0) (y-pos / 4.0) get-wolb ] end to get-wolb ;; turtle procedure set wolb? true set color red end to get-free ;; turtle procedure set wolb? false set wolb-carrying-count 0 set color blue end to setup-constants set carrying-capacity 4000 set initialInfected freqInitWolbachia * nMosquitoes ;; set ndays-week 7 set avgNorm rateOffspring * normal-lifespan set lifespan-with-Wolbachia fracLifespanWolbachia * normal-lifespan set avgWolb (fracRateOffspWolbachia * rateOffspring) * lifespan-with-Wolbachia end to go get-older move reproduce-wolbachia update-global-variables tick end to update-global-variables if count turtles > 0 [ set %infected (count turtles with [wolb?]) / (count turtles) * 100 ] end ;;Turtle counting variables are advanced. to get-older ask turtles [ set age age + 1 if wolb? [ set wolb-carrying-count (wolb-carrying-count + 1) ] ;; Turtles die of old age once their age equals the ;; lifespan (set at 1500 in this model). ifelse wolb? [ if age > lifespan-with-Wolbachia [ die ] ] [ if age > normal-lifespan [ die ] ] ] end ;;Turtles move about at random. to move ask turtles [ rt random 100 lt random 100 fd 1 ] end to reproduce-wolbachia ;; ask turtles with [not sick?] ask turtles [ if (count turtles) < carrying-capacity [ ifelse wolb? ;; for sick the average offspring is set for a normal lifespan ;; change to hatch a vqariable number b [ if (random lifespan-with-Wolbachia) < avgWolb [ hatch 1 [ set age 1 lt 45 fd 1 get-wolb ] ] ] [ if (random normal-lifespan) < avgNorm and (random 100) > %infected [ hatch 1 [set age 1 lt 45 fd 1 get-free] ] ] ] ] end ; Copyright 2013 Daniel Villela. ; See Info tab for full copyright and license.

There are 2 versions of this model.

## Attached files

File | Type | Description | Last updated | |
---|---|---|---|---|

Wolbachia.png | preview | Preview for 'Wolbachia' | over 6 years ago, by Daniel Villela | Download |

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