# Schistosomiasis

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## WHAT IS IT?

Shistosomiasis is a disease caused by parasitic worms *Schistosoma mansoni* and others.

## HOW IT WORKS

The disease is caused by parasitic worms that go through life stages.
When worm eggs are hatched in water (rivers etc.) they release miracidium which will find snails (*Biomphalaria glabrata*, and others) as intermediary hosts. Once the intermediary hosts are infected, miracidium will form sporocysts. After a few generations of sporocysts, snails produce cercariae, which are released into water and might contaminate human beings when in contact by penetrating humans' skin. The life stages will follow to develop into an adult worm that reside most commonly in human intestines.
For our purposes here, we consider the lifestages: eggs, miracidium, cercariae, and worm.

Number of Humans is N1 (fixed at N1=50). Number of snails is set fixed at N2=50.

Worm -- The worm survive at each time interval with probability pWorm. They are created when a human gets in touch with cercariae and cercariae penetrate human skin with rate Beta_{1} (assumed almost perfect).

Miracidium -- Miracidium are created at rate lambda1Eggs and survice with probability pMiracidium.

Cercariae -- They are created at rate lambda1LibCercariae and survive with probability pCercariae.

Snail -- Snails are assumed at a fixed level. A fraction of them is infected initially which starts the process. It is assumed that the mortality rate is equal to the birth rate. For simplicity, then, whenever a snail dies another one is given birth. In practical terms, the result is the replacement of a possibly infected one by an uninfected snail. The probability of turning a snail into an uninfected state is pSnail.

lambda1Eggs -- rate of eggs produced per female worm lambda1LibCercariae -- rate of cercariae releasing per infected snail

f -- fraction of snails that survive to produce cercariae.

The model in Anderson and May also includes parameters (Beta_{1} and Beta_{2}) which are considered almost perfect here (their values set fixed at 0.99).

## HOW TO USE IT

To use the model, set the variables described above, press SETUP, and then GO.

The plot shows the number of infected humans, total number of miracidiums, total number of cercariae, and the number of infected snails.

## THINGS TO NOTICE

The green part of the world represents non-aquatic areas, whereas the blue part of the world represents aquatic area (rivers, for instance).

An infection to a human can happen only in water.

## THINGS TO TRY

By changing values for the parameters, it is possible to create scenarios in which schistosomiasis disappears, whereas it is also possible to see situations in which humans (and also snails) keep infected for long periods of time. The result indeed depends on the basic reprodution number R_{0} as described in Anderson and May (1992).

## RELATED MODELS

This model uses the same setup of the El Farol model by Uri Wilensky. There are patches for the bar. In this model, these patches represent the river. The rest of the area is area where humans circulate and eventually go to the river.

## CREDITS AND REFERENCES

Model created by:

Daniel A.M. Villela PROCC - FIOCRUZ Av. Brasil, 4365 Rio de Janeiro, RJ, Brazil

E-mail: dvillela AT fiocruz . br

This model is inspired by the modeling of schistosomiasis described in the book by Roy Anderson and Robert May.

Anderson, Roy M., Robert M. May, and B. Anderson. Infectious diseases of humans: dynamics and control. Vol. 28. Oxford: Oxford university press, 1992.

## 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, Daniel (2013). NetLogo Schistosomiasis 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 Institute on Complex Systems, Northwestern University, Evanston, IL.

## COPYRIGHT AND LICENSE

Copyright 2013 Daniel Villela.

## Comments and Questions

breed [ miracidiums miracidium ] breed [ humans human ] breed [ cercariaes cercariae ] breed [ snails snail ] breed [ schistosomas schistosoma ] globals [ home-patches water-patches N1 N2 N2inf ;; probability of moving into snails area pmove lambda1 lambda2 beta1 beta2 ] turtles-own [ mu ;; mortality rate infected? ] to setup clear-all set-default-shape humans "person" set-default-shape snails "dot" set-default-shape cercariaes "triangle" set-default-shape miracidiums "triangle" set beta1 0.99 set beta2 0.99 set pmove 0.5 set home-patches patches with [pycor < 0 or (pxcor < 0 and pycor >= 0)] ask home-patches [ set pcolor green ] set water-patches patches with [pxcor > 0 and pycor > 0] ask water-patches [ set pcolor blue ] set N1 50 ;; create humans create-humans N1 [ set color white set infected? false move-to-empty-one-of home-patches ] ;; create snails set N2 50 set N2inf 20 ;; infected ones create-snails N2inf [ set color white set infected? true move-to-empty-one-of water-patches ] create-snails N2 - N2inf [ set color white set infected? false move-to-empty-one-of water-patches ] ;; start the clock reset-ticks end to go ask humans [ ;; movement of humans ifelse random-float 1 < pmove [ move-to-empty-one-of home-patches ] [ move-to one-of water-patches if any? cercariaes-here with [ infected? = true ] and random-float 1 < beta1 [ set infected? true ] if infected? [ mymake-miracidiums ] ] if infected? and random-float 1 < ( 1 - pworm ) [ set infected? false ] ] ask snails [ ;; model assumes that as some of them die new snails appear ;; so the number stays at a constant level ifelse random-float 1 < (1 - pSnail) [ set infected? false ] [ move-to one-of water-patches if any? miracidiums-here with [ infected? = true ] and random-float 1 < beta2 [ set infected? true ] ;; model has f as fraction of snails that survive to release cercariae if infected? and random-float 1 < f [ mymake-cercariae ] ] ] ask miracidiums [ ifelse random-float 1 < ( 1 - pMiracidium ) [ die ] [ move-to one-of water-patches ] ] ask cercariaes [ ifelse random-float 1 < ( 1 - pCercariae ) [ die ] [ move-to one-of water-patches ] ] tick end to mymake-cercariae hatch-cercariaes random ( 2 * lambda2LibCercariae) [ set infected? true set color red move-to one-of water-patches ] end to mymake-miracidiums hatch-miracidiums random ( 2 * lambda1Eggs) [ set infected? true ;; set color red move-to one-of water-patches ] end ;; same procedure in the El Farol model by Uri Wilenski to move-to-empty-one-of [locations] ;; turtle procedure move-to one-of locations while [any? other turtles-here] [ move-to one-of locations ] 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 | |
---|---|---|---|---|

Schistosomiasis.png | preview | Preview for 'Schistosomiasis' | about 10 years ago, by Daniel Villela | Download |

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